🔢 Mathematics & Computation

Pure mathematics, computational theory, cryptography, algorithms, formal methods

Quantum mechanics once baffled scientists. Now it's changing the world

Quantum mechanics has journeyed from a strange and controversial idea to the foundation of some of humanity’s most advanced technologies. Now researchers are pushing its boundaries even further, with potential breakthroughs in energy, medicine, computing, and our understanding of the universe.

More: Quantum mechanics once baffled scientists. Now it's changing the world. Now researchers are pushing its boundaries even further, with potential breakthroughs in energy, medicine, computing, and our understanding of the universe.
TL;DR: Quantum mechanics has journeyed from a strange and controversial idea to the foundation of some of humanity’s most advanced technologies.
Read original at Sciencedaily
Further reading: MathSciNetQuanta MagazineAMS Math NewsWikipedia

Free-text answers and LLMs reveal hidden reasons behind human choices

Why do people make the choices they do? Researchers from the Center Synergy of Systems (SynoSys) at TUD Dresden University of Technology, the Max Planck Institute for Human Development, and the University of Basel present their new approach to finding answers to that question. The approach combines observed choices with participants' own descriptions of their decision processes, allowing researchers to study human behavior in greater detail than is possible with behavioral data alone.

More: Free-text answers and LLMs reveal hidden reasons behind human choices. Researchers from the Center Synergy of Systems (SynoSys) at TUD Dresden University of Technology, the Max Planck Institute for Human Development, and the University of Basel present their new approach to finding answers to that question.
TL;DR: Why do people make the choices they do?
Read original at Phys
Further reading: arXiv MathMathSciNetAMS Math NewsWikipedia

Physicists and AI model Claude 'collaborate' to prove a 10-year-old jamming conjecture

A mathematical problem that had remained unsolved for more than 10 years in the physics of complex systems has finally been resolved through an unusual collaboration: one involving two theoretical physicists and an artificial intelligence system. In a study published in the Journal of Statistical Mechanics: Theory and Experiment, Giorgio Parisi, Nobel Prize winner in physics, and Francesco Zamponi, physicist at LaSapienza University of Rome, show how the AI model Claude contributed to finding the proof of a mathematical relation that had resisted researchers' efforts for years.

More: A mathematical problem that had remained unsolved for more than 10 years in the physics of complex systems has finally been resolved through an unusual collaboration: one involving two theoretical physicists and an artificial intelligence system.
TL;DR: A mathematical problem that had remained unsolved for more than 10 years in the physics of complex systems has finally been resolved through an unusual collaboration: one involving two theoretical physicists and an artificial intelligence system.
Read original at Phys
Further reading: arXiv MathStack Exchange MathQuanta MagazineWikipedia

Algorithm for NP-Complete Sudoku

This document proposes a conceptual and constructive solution to the millennium problem $P$ vs $NP$. It is demonstrated that the asymmetrical complexity barrier between verification (P) and resolutio…

More: Algorithm for NP-Complete Sudoku. It is demonstrated that the asymmetrical complexity barrier between verification (P) and resolution (NP) is a direct consequence of using a deficient algebraic coordinate system (sequential brute force).
TL;DR: This document proposes a conceptual and constructive solution to the millennium problem $P$ vs $NP$.
Read original at Zenodo
Further reading: Stack Exchange MathQuanta MagazineAMS Math NewsWikipedia

Statistical method broadens forecasts by modeling uncertainty beyond average outcomes

When it comes to statistics, we usually expect to be informed about what happens "on average." But sometimes the key information lies in deviations from that mean: how likely is heavy rain, and how likely is it to remain dry? So-called distributional regression describes not only the mean but also the distribution of possible values.

More: When it comes to statistics, we usually expect to be informed about what happens "on average." But sometimes the key information lies in deviations from that mean: how likely is heavy rain, and how likely is it to remain dry? So-called distributional regression describes not only the mean but also the distribution of possible values.
TL;DR: When it comes to statistics, we usually expect to be informed about what happens "on average." But sometimes the key information lies in deviations from that mean: how likely is heavy rain, and how likely is it to remain dry?
Read original at Phys
Further reading: Stack Exchange MathQuanta MagazineAMS Math NewsWikipedia

World Cup research reveals strategy to give teams a penalty-shootout edge

One of football's most iconic moments—the penalty shootout—may be far more strategic than previously thought, with new research challenging the notion that the team kicking first holds a major advantage.

More: This article has been reviewed according to Science X's editorial process and policies . Professor Robbie Wilson, from UQ's School of the Environment, said the study showed the psychological situations players faced during the shootout had the greatest impact on the result.
TL;DR: One of football's most iconic moments—the penalty shootout—may be far more strategic than previously thought, with new research challenging the notion that the team kicking first holds a major advantage.
Read original at Phys
Further reading: Quanta MagazineStack Exchange MathAMS Math NewsWikipedia

Thermodynamic Computers Go With the (Energy) Flow

Today’s computers need safeguards against random energy fluctuations. Thermodynamic computers would put those fluctuations to use. The post Thermodynamic Computers Go With the (Energy) Flow first appeared on Quanta Magazine

More: Thermodynamic Computers Go With the (Energy) Flow. Thermodynamic computers would put those fluctuations to use. The post Thermodynamic Computers Go With the (Energy) Flow first appeared on Quanta Magazine
TL;DR: Today’s computers need safeguards against random energy fluctuations.
Read original at Quantamagazine
Further reading: MathSciNetStack Exchange MathQuanta MagazineWikipedia

Statistical test helps judge the value of personalization

From precision medicine to personalized job training, customizing interventions for individuals is often assumed to produce better outcomes than a one-size-fits-all approach. But personalization also comes with costs: it can be more expensive, harder to implement reliably and may require more resources to design.

More: Statistical test helps judge the value of personalization. From precision medicine to personalized job training, customizing interventions for individuals is often assumed to produce better outcomes than a one-size-fits-all approach. But personalization also comes with costs: it can be more expensive, harder to implement reliably and may require more resources to design.
TL;DR: From precision medicine to personalized job training, customizing interventions for individuals is often assumed to produce better outcomes than a one-size-fits-all approach.
Read original at Phys
Further reading: MathSciNetarXiv MathAMS Math NewsWikipedia

Proof of Care in the Age of A.I

I wrote this piece by hand and photographed the pages. After that, I wanted to make the text copy-pasteable.

More: Proof of Care in the Age of A.I. For spacing, the idea was that I’d add spacing characters that’ll be removed in Javascript during the copy-paste event that fires on the webpage. I used ` (backtick) characters for narrow spaces that’ll be fully removed, and multiple spaces between words where I planned to collapse them into just 1 space.
TL;DR: After exporting the SVG file, it required some post-processing: Finally, the SVG is fully added as an <svg> element into the HTML file.
Read original at Jacobfilipp
Further reading: MathSciNetQuanta MagazineAMS Math NewsWikipedia

Revisiting Yliluoma's ordered dither algorithm

Summary: This article discusses Joel Yliluoma’s 2011 ordered dither algorithm (left), explains its internals in greater detail than other treatments, presents new simplified variants (middle), and co…

More: Revisiting Yliluoma's ordered dither algorithm. If the input pixel’s gray value is higher than the threshold, you output a white pixel. The code could look like this: bayer_4x4 = np.array([ [ 0 , 8 , 2 , 10 ], [ 12 , 4 , 14 , 6 ], [ 3 , 11 , 1 , 9 ], [ 15 , 7 , 13 , 5 ]]) def dither_bayer4x4_1bit(img: np.ndarray): img_float = img / 255 # process in [0,1] range H, W, _ = img.
TL;DR: First you acquire a threshold matrix from somewhere.
Read original at 30fps
Further reading: MathSciNetarXiv MathQuanta MagazineWikipedia

Since Chronium 148, Math.tanh is now fingerprintable to link underlying OS

Add as a preferred source Share Fingerprinting is usually about canvas, WebGL, fonts, audio. There is a quieter signal, and it lives in the last bits of a number. Math . tanh ( 0.8 ) // 0.

More: Since Chronium 148, Math.tanh is now fingerprintable to link underlying OS. tanh(0.8) is one that separates all three at once. Claim macOS, return Linux math bits, and you have contradicted your own User-Agent.
TL;DR: A genuine Mac runs Math.tanh through Apple’s math library.
Read original at Scrapfly
Further reading: arXiv MathStack Exchange MathAMS Math NewsWikipedia

How a Richard Feynman formula could explain your dining habits in a new city

One of the dilemmas facing anyone in a new and unfamiliar city is where to dine out. You might consult guides, speak to locals, check reviews, and ultimately, try your luck. But if you're there for a while, at some point you're going to be asking yourself whether to visit new eateries or stick to the ones you've already tried and liked.

More: How a Richard Feynman formula could explain your dining habits in a new city. One of the dilemmas facing anyone in a new and unfamiliar city is where to dine out. You might consult guides, speak to locals, check reviews, and ultimately, try your luck.
TL;DR: But if you're there for a while, at some point you're going to be asking yourself whether to visit new eateries or stick to the ones you've already tried and liked.
Read original at Phys
Further reading: arXiv MathMathSciNetQuanta MagazineWikipedia

Researchers develop AI tool that finds the equations behind complex systems

Clarkson University researchers have developed an artificial intelligence tool that can uncover the mathematical equations governing complex and chaotic systems directly from data. The technology, called KANDy—short for Kolmogorov-Arnold Networks for Dynamics—is designed to help scientists understand systems that are difficult to describe using traditional methods because they are noisy, nonlinear or highly unpredictable.

More: Clarkson University researchers have developed an artificial intelligence tool that can uncover the mathematical equations governing complex and chaotic systems directly from data. The technology, called KANDy—short for Kolmogorov-Arnold Networks for Dynamics—is designed to help scientists understand systems that are difficult to describe using traditional methods because they…
TL;DR: Clarkson University researchers have developed an artificial intelligence tool that can uncover the mathematical equations governing complex and chaotic systems directly from data.
Read original at Phys
Further reading: arXiv MathStack Exchange MathQuanta MagazineWikipedia

Researchers found a Wordle strategy that wins 99% of the time

Researchers developed a Wordle-solving strategy that succeeds 99% of the time by focusing on information gain rather than likely answers. The method uses Shannon entropy to identify guesses that reveal the most about the hidden word. Each guess is designed to slash uncertainty and narrow the possibilities faster. The result significantly outperformed more traditional Wordle tactics.

More: Researchers found a Wordle strategy that wins 99% of the time. The method uses Shannon entropy to identify guesses that reveal the most about the hidden word. The result significantly outperformed more traditional Wordle tactics.
TL;DR: Researchers developed a Wordle-solving strategy that succeeds 99% of the time by focusing on information gain rather than likely answers.
Read original at Sciencedaily
Further reading: MathSciNetarXiv MathQuanta MagazineWikipedia

Connections in Math: the two kinds of random

Disclaimer: no AI was used to write this. Any errors, awkward sentences, and weird tangents are 100% organic, free-range, and human-made.

More: Connections in Math: the two kinds of random. By every statistical measure, these two files are the same : both look like pure, incompressible randomness. The other file I cannot shrink at all, and to send it to you I have to send the whole thing, digit by digit, because there is no shorter description of it than itself.
TL;DR: Imagine two files, and each one holds a million digits.
Read original at Stillthinking
Further reading: Stack Exchange MatharXiv MathQuanta MagazineWikipedia

Visual map of 20,000 words reveals why lip-readers confuse common look-alikes

New research from the University of Kansas uses network science to determine why people make mistakes when lip-reading. Michael Vitevitch, professor of speech-language-hearing at KU, and his co-authors created a visual map of about 20,000 words in English, hoping to better grasp why some words are more difficult to lip-read than others.

More: Visual map of 20,000 words reveals why lip-readers confuse common look-alikes. New research from the University of Kansas uses network science to determine why people make mistakes when lip-reading.
TL;DR: New research from the University of Kansas uses network science to determine why people make mistakes when lip-reading.
Read original at Phys
Further reading: Quanta MagazineStack Exchange MathAMS Math NewsWikipedia

Leanstral 1.5: Proof Abundance for All

Leanstral 1.5, a free Apache-2.0 licensed model with 6B active parameters, delivers a major performance upgrade in formal verification, saturating miniF2F, solving 587/672 PutnamBench problems, and a…

More: Leanstral 1.5: Proof Abundance for All. Fully open-sourced and available via Hugging Face and a free API, Leanstral 1.5 is now accessible for practical proof engineering in Lean 4. Since its launch, Leanstral has offered an open, practical approach to proof engineering in Lean 4 .
TL;DR: Leanstral 1.5, a free Apache-2.0 licensed model with 6B active parameters, delivers a major performance upgrade in formal verification, saturating miniF2F, solving 587/672 PutnamBench problems, and achieving state-of-the-art results on FATE-H (87%) and FATE-X (34%).
Read original at Mistral
Further reading: Stack Exchange MathQuanta MagazineAMS Math NewsWikipedia

Why shorter lists win: Researchers study how people misread rankings

Math is great when it's simple, but then our brain gets involved and complicates everything. Imagine you are on the leadership team for a Big 4 and choosing between two employees for a director-level promotion. One is ranked third out of 12 on her team. The other is ranked sixth out of 24. On paper, both candidates sit at the same relative spot in their groups. Both are in the top quarter. Both have outperformed three-fourths of their peers.

More: Why shorter lists win: Researchers study how people misread rankings. Imagine you are on the leadership team for a Big 4 and choosing between two employees for a director-level promotion. One is ranked third out of 12 on her team.
TL;DR: Math is great when it's simple, but then our brain gets involved and complicates everything.
Read original at Phys
Further reading: Stack Exchange MatharXiv MathQuanta MagazineWikipedia

Opening up 'Zero-Knowledge Proof' technology to promote privacy in age assurance

Today, we open sourced our Zero-Knowledge Proof (ZKP) libraries , fulfilling a promise and building on our partnership with Sparkasse to support EU age assurance .

More: Opening up 'Zero-Knowledge Proof' technology to promote privacy in age assurance. In layperson’s terms, ZKP makes it possible for people to prove that something about them is true without exchanging any other data. With our commitment to making these ZKP tools openly available, Member States can integrate this into their future EUDI Wallets, accelerating their development.
TL;DR: Today, we open sourced our Zero-Knowledge Proof (ZKP) libraries , fulfilling a promise and building on our partnership with Sparkasse to support EU age assurance .
Read original at Blog
Further reading: Quanta MagazineStack Exchange MathAMS Math NewsWikipedia

Mathematics: Its Content, Methods and Meaning

The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries. Mathematics: Its Content, Methods, and Meaning (Three Volumes Bound as One [!

More: Mathematics: Its Content, Methods and Meaning. The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries. Mathematics: Its Content, Methods, and Meaning (Three Volumes Bound as One [!]), by (Can you believe it?) Aleksandrov, Kolmogorov, and Lavrent’ev, is a titanic work, weighing in at 356 + 374 + 351 = 1081 pages.
TL;DR: In Part I (in two parts) a it follows a trajectory from general themes in analysis to analytic geometry, the theory of algebraic equations, and ODE.
Read original at Old
Further reading: Stack Exchange MatharXiv MathQuanta MagazineWikipedia

A physicist's fresh look at the 'prisoner's dilemma' reveals hope for cooperation

The "prisoner's dilemma" is one of the most famous ideas in game theory. For decades, this game has been used to explain why selfishness often beats cooperation. In the prisoner's dilemma, two players can either cooperate or cheat. Cheating always seems to pay off more, so both players end up cheating and losing out even though working together would have given them the biggest reward.

More: A physicist's fresh look at the 'prisoner's dilemma' reveals hope for cooperation. For decades, this game has been used to explain why selfishness often beats cooperation. Cheating always seems to pay off more, so both players end up cheating and losing out even though working together would have given them the biggest reward.
TL;DR: The "prisoner's dilemma" is one of the most famous ideas in game theory.
Read original at Phys
Further reading: MathSciNetarXiv MathQuanta MagazineWikipedia

Mathematicians unleash multifold speed boost for supercomputer simulations of molecules

More than 20% of the workload on the world's 500 fastest supercomputers is spent simulating how atoms and molecules move—with applications ranging from material design to identifying drug interactions to understanding protein folding.

More: This article has been reviewed according to Science X's editorial process and policies . The new method can be rapidly and easily integrated into existing software workflows, meaning the field could soon see drastically reduced time and energy demands for the simulations.
TL;DR: More than 20% of the workload on the world's 500 fastest supercomputers is spent simulating how atoms and molecules move—with applications ranging from material design to identifying drug interactions to understanding protein folding.
Read original at Phys
Further reading: arXiv MathStack Exchange MathAMS Math NewsWikipedia

Scientists finally complete Schrödinger’s 100-year-old color theory

Researchers have finally resolved a key problem in a 100-year-old theory of color, showing that the qualities we perceive in colors are intrinsic to the mathematics of color space itself. The discovery sharpens our understanding of human vision and could lead to more precise color technologies and visualizations.

More: Researchers have finally resolved a key problem in a 100-year-old theory of color, showing that the qualities we perceive in colors are intrinsic to the mathematics of color space itself. The discovery sharpens our understanding of human vision and could lead to more precise color technologies and visualizations.
TL;DR: Researchers have finally resolved a key problem in a 100-year-old theory of color, showing that the qualities we perceive in colors are intrinsic to the mathematics of color space itself.
Read original at Sciencedaily
Further reading: Stack Exchange MatharXiv MathAMS Math NewsWikipedia

Die analysis of the 8087 math coprocessor's fast bit shifter

Floating-point numbers are very useful for scientific programming, but early microprocessors only supported integers directly.

More: Die analysis of the 8087 math coprocessor's fast bit shifter. 1 Although floating-point was common in mainframes back in the 1950s and 1960s, it wasn't until 1980 that Intel introduced the 8087 floating-point coprocessor for microcomputers.
TL;DR: 5 The result was the floating-point architecture of the 8087.
Read original at Righto
Further reading: Stack Exchange MatharXiv MathAMS Math NewsWikipedia

Researchers used math to crack Wordle

Every day, millions of people play Wordle, the popular New York Times game that challenges users to guess a secret five-letter word.

More: Researchers used math to crack Wordle. Using information theory, a team of researchers at Binghamton University, State University of New York, has developed a method to solve the game with a 99% success rate. Watson College of Engineering and Applied Science’s School of Systems Science and Industrial Engineering.
TL;DR: Every day, millions of people play Wordle, the popular New York Times game that challenges users to guess a secret five-letter word.
Read original at Binghamton
Further reading: Stack Exchange MatharXiv MathQuanta MagazineWikipedia

New Zealand scientists working on 'R' win major global award

Scientists working on the revolutionary 'R' programming language invented at the University of Auckland have won a top award intended to be a Nobel Prize for statisticians.

More: This article has been reviewed according to Science X's editorial process and policies . "R is one of the great achievements to come out of this University," says interim Dean of Science Professor Michael Kingsley. "We are delighted and proud of the recognition for an innovation that changed data science and the hard work that everyone has put in."
TL;DR: Scientists working on the revolutionary 'R' programming language invented at the University of Auckland have won a top award intended to be a Nobel Prize for statisticians.
Read original at Phys
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Two Qwen3 models on one DGX Spark: the residency math

Since I started managing the agent fleet through Clawrium , the Hermes count has climbed. More agents on more hosts, more concurrent traffic, all hitting the same Spark.

More: Two Qwen3 models on one DGX Spark: the residency math. The Spark served models through ollama for months. There’s no per-process memory budget, no gpu_memory_utilization knob, no straightforward way to coresident a heavy model for reasoning and a fast model for quick turns.
TL;DR: One model up, single config, easy to bring down.
Read original at Devashish
Further reading: Stack Exchange MathQuanta MagazineAMS Math NewsWikipedia

S-M-A-R-T! These researchers used math to crack Wordle

Every day, millions of people play Wordle, the popular New York Times game that challenges users to guess a secret five-letter word. Using information theory, a team of researchers at Binghamton University, State University of New York, has developed a method to solve the game with a 99% success rate.

More: These researchers used math to crack Wordle. Every day, millions of people play Wordle, the popular New York Times game that challenges users to guess a secret five-letter word. Using information theory, a team of researchers at Binghamton University, State University of New York, has developed a method to solve the game with a 99% success rate.
TL;DR: Using information theory, a team of researchers at Binghamton University, State University of New York, has developed a method to solve the game with a 99% success rate.
Read original at Phys
Further reading: Stack Exchange MatharXiv MathQuanta MagazineWikipedia

Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?

A decades-old proof showed that seven shuffles are enough to mix up a deck of cards. But it requires you to cut the deck with the precision of a professional magician. A new proof gets around that obstacle. The post Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones? first appeared on Quanta Magazine

More: But it requires you to cut the deck with the precision of a professional magician. A new proof gets around that obstacle. But How Many Sloppy Ones?
TL;DR: A decades-old proof showed that seven shuffles are enough to mix up a deck of cards.
Read original at Quantamagazine
Further reading: Stack Exchange MathQuanta MagazineAMS Math NewsWikipedia

Occupancy Math on the AMD MI355X: A From-First-Principles Guide

Ask a GPU kernel engineer how their kernel is doing and occupancy comes up within a sentence or two. It’s the number everyone quotes and the dial everyone reaches for — and, in my experience, the met…

More: Occupancy Math on the AMD MI355X: A From-First-Principles Guide. It’s the number everyone quotes and the dial everyone reaches for — and, in my experience, the metric people understand least. Each is just a fixed hardware budget divided by what your kernel spends, so you can compute the ceiling by hand from the binary: occupancy = min(those four limiters) .
TL;DR: Ask a GPU kernel engineer how their kernel is doing and occupancy comes up within a sentence or two.
Read original at Indianspeedster
Further reading: Stack Exchange MatharXiv MathAMS Math NewsWikipedia

Inference cost at scale with napkin math

If you serve AI models as a part of your product stack, you've likely wondered what kind of scale your GPU cluster tops out at.

More: Inference cost at scale with napkin math. If you bothered to click on this article you know that AI models do many matrix multiplications on massive matrices. So, the cost of a (N,d)*(d,M) matrix product is \( 2NMd \) memory accesses and \(2NMd\) floating-point operations.
TL;DR: Let their product be the matrix \( O_{N \times M} \).
Read original at Injuly
Further reading: Stack Exchange MatharXiv MathQuanta MagazineWikipedia

Redefined conformity model beats averaging in five real-world tests of opinion dynamics

Imagine you poll your friends on how many minutes per pound to roast a turkey. Five respond with 15 minutes; one answers 33 minutes. The most popular model of conformity, the French-Harary-DeGroot model (or more commonly, DeGroot model), assumes that you would carefully weigh all six recommendations, calculating a cooking time of 18 minutes per pound. But under a model of conformity previously published by SFI Complexity Postdoctoral Fellow Kaleda Denton and colleagues, you would disregard the outlier and move ahead with 15.

More: Redefined conformity model beats averaging in five real-world tests of opinion dynamics. The most popular model of conformity, the French-Harary-DeGroot model (or more commonly, DeGroot model), assumes that you would carefully weigh all six recommendations, calculating a cooking time of 18 minutes per pound.
TL;DR: Imagine you poll your friends on how many minutes per pound to roast a turkey.
Read original at Phys
Further reading: Stack Exchange MathQuanta MagazineAMS Math NewsWikipedia

'Basketball Mathematics' help children boost math skills without extra class time

A dribble and a jump shot, followed by a fractions task. That is what physical education classes looked like for a group of pupils, and the pupils not only found the lessons more engaging than usual—they also became better at mathematics with a basketball in their hands, according to a new study from the University of Copenhagen.

More: This article has been reviewed according to Science X's editorial process and policies . Here, fractions were directly linked to basketball activities during physical education classes. The results pleased Jacob Wienecke, associate professor at the Department of Nutrition, Exercise and Sports at the University of Copenhagen and lead researcher on the study now published in the…
TL;DR: That is what physical education classes looked like for a group of pupils, and the pupils not only found the lessons more engaging than usual—they also became better at mathematics with a basketball in their hands, according to a new study from the University of Copenhagen.
Read original at Phys
Further reading: Stack Exchange MatharXiv MathAMS Math NewsWikipedia

Parents helping kids enjoy math may boost achievement as much as content support

How do children learn math? It's shaped by what they know as well as their motivation and engagement. Historically, research on children's math learning has been focused on parents' cognitive practices (such as math talk—informal conversations that involve math), however emerging evidence shows how parents' motivational practices (encouraging independence and helping children enjoy math) may also play a critical role in their math abilities.

More: Parents helping kids enjoy math may boost achievement as much as content support. How do children learn math? Historically, research on children's math learning has been focused on parents' cognitive practices (such as math talk—informal conversations that involve math), however emerging evidence shows how parents' motivational practices (encouraging independence and helping c…
TL;DR: How do children learn math?
Read original at Phys
Further reading: Stack Exchange MathMathSciNetQuanta MagazineWikipedia

Hidden geometry explains why kernel methods separate complex data so well

Are two sets of data genuinely different, or is it because of randomness? This question, known as the two-sample testing problem, becomes notoriously difficult in modern datasets, because they are often high-dimensional, complex, and differences between them can take countless subtle forms.

More: Hidden geometry explains why kernel methods separate complex data so well. Are two sets of data genuinely different, or is it because of randomness? This question, known as the two-sample testing problem, becomes notoriously difficult in modern datasets, because they are often high-dimensional, complex, and differences between them can take countless subtle forms.
TL;DR: Are two sets of data genuinely different, or is it because of randomness?
Read original at Phys
Further reading: Stack Exchange MathQuanta MagazineAMS Math NewsWikipedia

Football tracking data uncovers rival tactics beyond TV formations before 2026 World Cup

From June 11, countless millions of people will be following the football World Cup in Canada, Mexico and the U.S. They will discuss their team's performance, talk like experts about tactics and formations, and cower behind the sofa during penalty shootouts. But a lot of what comes across as gut instinct and long-established football wisdom can now be verified with the help of data.

More: Football tracking data uncovers rival tactics beyond TV formations before 2026 World Cup. They will discuss their team's performance, talk like experts about tactics and formations, and cower behind the sofa during penalty shootouts. But a lot of what comes across as gut instinct and long-established football wisdom can now be verified with the help of data.
TL;DR: From June 11, countless millions of people will be following the football World Cup in Canada, Mexico and the U.S.
Read original at Phys
Further reading: MathSciNetQuanta MagazineAMS Math NewsWikipedia

Crowd flow measurements reveal hidden slowdowns and standstills in dense public spaces

How can public spaces remain safe when large crowds move through them? Engineers and researchers who study these environments often rely on physical models borrowed from fluid dynamics—a branch of physics that describes the collective motion of fluids, whose behavior emerges from the interactions of many particles. But a new study published in the Journal of Statistical Physics: Theory and Experiment highlights a crucial issue: The way data are collected and measured within these models lacks standardization and may overlook important features of human collective behavior. Unlike particles, people are living agents with individual decisions and complex interactions, making their movement harder to capture with traditional approaches.

More: Crowd flow measurements reveal hidden slowdowns and standstills in dense public spaces. How can public spaces remain safe when large crowds move through them? Unlike particles, people are living agents with individual decisions and complex interactions, making their movement harder to capture with traditional approaches.
TL;DR: Engineers and researchers who study these environments often rely on physical models borrowed from fluid dynamics—a branch of physics that describes the collective motion of fluids, whose behavior emerges from the interactions of many particles.
Read original at Phys
Further reading: arXiv MathMathSciNetQuanta MagazineWikipedia

Mental math's shortcut—pupil dilation suggests people start solving before all numbers are in

People often solve simple arithmetic problems, such as basic addition, subtraction, multiplication or division, in their minds. The precise mental processes they rely on to solve these problems, however, are not entirely clear. Researchers at Université de Bordeaux and UCLouvain recently tried to better understand how humans tackle simple math mentally by tracking the size of their pupils.

More: Mental math's shortcut—pupil dilation suggests people start solving before all numbers are in. The precise mental processes they rely on to solve these problems, however, are not entirely clear. Researchers at Université de Bordeaux and UCLouvain recently tried to better understand how humans tackle simple math mentally by tracking the size of their pupils.
TL;DR: People often solve simple arithmetic problems, such as basic addition, subtraction, multiplication or division, in their minds.
Read original at Phys
Further reading: arXiv MathStack Exchange MathAMS Math NewsWikipedia

Universal patterns emerge across 22 languages, mapping how vocabularies evolve

Human languages are known to have grown and changed considerably over the course of history, often reflecting technological, cultural, and societal shifts. Studying the evolution of languages can thus offer valuable insight into how human societies and cultures have transformed over time.

More: Universal patterns emerge across 22 languages, mapping how vocabularies evolve. Human languages are known to have grown and changed considerably over the course of history, often reflecting technological, cultural, and societal shifts. Studying the evolution of languages can thus offer valuable insight into how human societies and cultures have transformed over time.
TL;DR: Human languages are known to have grown and changed considerably over the course of history, often reflecting technological, cultural, and societal shifts.
Read original at Phys
Further reading: Quanta MagazineStack Exchange MathAMS Math NewsWikipedia

A physics explanation shows why US elections keep ending 50:50—and why more spending won't change that

A physics-inspired model calibrated on 40 years of US congressional data pinpoints a spending threshold of roughly 1.8 million USD at which campaigns stop influencing who wins and start fueling polarization instead.

More: This article has been reviewed according to Science X's editorial process and policies . But a new study from the Complexity Science Hub (CSH) suggests a more structural explanation for these near-dead-heat outcomes—one rooted in the physics of phase transitions.
TL;DR: A physics-inspired model calibrated on 40 years of US congressional data pinpoints a spending threshold of roughly 1.8 million USD at which campaigns stop influencing who wins and start fueling polarization instead.
Read original at Phys
Further reading: MathSciNetQuanta MagazineAMS Math NewsWikipedia

World's largest collection of Olympiad-level math problems now available to everyone

Every year, the countries competing in the International Mathematical Olympiad arrive with a booklet of their best, most original problems. Those booklets get shared among delegations, then quietly disappear. No one had ever collected them systematically, cleaned them, and made them available—not for AI researchers testing the limits of mathematical reasoning, and not for the students around the world training for these competitions largely on their own.

More: World's largest collection of Olympiad-level math problems now available to everyone. Those booklets get shared among delegations, then quietly disappear. No one had ever collected them systematically, cleaned them, and made them available—not for AI researchers testing the limits of mathematical reasoning, and not for the students around the world training for these competiti…
TL;DR: Every year, the countries competing in the International Mathematical Olympiad arrive with a booklet of their best, most original problems.
Read original at Phys
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We think norms spread by imitation, but one deceptively simple rule tells a more human story

A paper appearing in Proceedings of the National Academy of Sciences offers a strikingly simple answer to a longstanding question: How do people learn and settle on shared social conventions, from everyday habits to workplace norms? Researchers from the CUNY Graduate Center, the University of Pennsylvania, and Stanford University have found that people do not primarily learn by copying others or by calculating the most likely choice. Instead, they follow a two-stage process—sampling behaviors at first, then committing once enough evidence accumulates.

More: We think norms spread by imitation, but one deceptively simple rule tells a more human story. Researchers from the CUNY Graduate Center, the University of Pennsylvania, and Stanford University have found that people do not primarily learn by copying others or by calculating the most likely choice.
TL;DR: A paper appearing in Proceedings of the National Academy of Sciences offers a strikingly simple answer to a longstanding question: How do people learn and settle on shared social conventions, from everyday habits to workplace norms?
Read original at Phys
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How can opinions be maximally influenced? New research offers insights

Who should you target, and when, to maximize the impact of your message? New research uses mathematical models to show that targeted influence is significantly more effective than random persuasion. In social networks, certain individuals play a key role at specific moments in how ideas spread and how polarization arises.

More: How can opinions be maximally influenced? New research offers insights. In social networks, certain individuals play a key role at specific moments in how ideas spread and how polarization arises.
TL;DR: New research uses mathematical models to show that targeted influence is significantly more effective than random persuasion.
Read original at Phys
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Western music is getting simpler and more repetitive by the day and data prove it

Ever had that moment when a song comes on and it feels strangely familiar, like it reminds you of another song that came out just a few months ago? If you feel this phenomenon has become more frequent, then you are not imagining it. Science agrees with you. A recent study found that Western music is not only starting to sound more alike but is also becoming less structurally complex than in the past.

More: Western music is getting simpler and more repetitive by the day and data prove it. If you feel this phenomenon has become more frequent, then you are not imagining it. A recent study found that Western music is not only starting to sound more alike but is also becoming less structurally complex than in the past.
TL;DR: Ever had that moment when a song comes on and it feels strangely familiar, like it reminds you of another song that came out just a few months ago?
Read original at Phys
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AI tackles one of math's most brutal problems: Inverse PDEs

Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly challenging class of mathematical problems with broad implications for understanding the natural world.

More: This article has been reviewed according to Science X's editorial process and policies . The advance, which the researchers call "Mollifier Layers," could benefit fields as varied as genetics and weather forecasting, because inverse PDEs help scientists work backward from observable patterns to infer the hidden dynamics that produced them.
TL;DR: Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly challenging class of mathematical problems with broad implications for understanding the natural world.
Read original at Phys
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Study warns cost-cutting use of generative AI could increase cyber-attack risks

Newly published research from a leading computer scientist warns that the use of generative AI to design, train, or perform steps within a machine learning system could increase serious risks. Michael Lones, professor at Heriot-Watt University's School of Mathematical and Computer Sciences, has argued in a new paper that generative AI could expose organizations and the public to unintended harm.

More: Newly published research from a leading computer scientist warns that the use of generative AI to design, train, or perform steps within a machine learning system could increase serious risks.
TL;DR: Newly published research from a leading computer scientist warns that the use of generative AI to design, train, or perform steps within a machine learning system could increase serious risks.
Read original at Phys
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Theoretical framework can predict how complex networks behave

The University of Hong Kong (HKU) has spearheaded an international research collaboration to develop a pioneering theoretical framework that deciphers the predictability of complex networks. A research team including Professor Qingpeng Zhang's group at the HKU Musketeers Foundation Institute of Data Science (HKU IDS) and the HKU Li Ka Shing Faculty of Medicine, together with researchers from Zhejiang University and Sapienza University of Rome, has developed a new theoretical framework to understand the predictability of complex networks.

More: The University of Hong Kong (HKU) has spearheaded an international research collaboration to develop a pioneering theoretical framework that deciphers the predictability of complex networks. A research team including Professor Qingpeng Zhang's group at the HKU Musketeers Foundation Institute of Data Science (HKU IDS) and the HKU Li Ka Shing Faculty of Medicine, together with r…
TL;DR: The University of Hong Kong (HKU) has spearheaded an international research collaboration to develop a pioneering theoretical framework that deciphers the predictability of complex networks.
Read original at Phys
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Q&A: The political calculus—and actual math—of gerrymandering

On April 29, the U.S. Supreme Court struck down Louisiana's voting map on the basis that the state had illegally used race as a consideration when it created a new majority-Black district. Observers say the ruling could have major implications across the country for how future district boundary decisions are made under the Voting Rights Act. Meanwhile, ahead of the November midterms, lawmakers in several states have been redrawing their district maps to favor one party or the other, or are considering such reconfigurations.

More: Q&A: The political calculus—and actual math—of gerrymandering. Supreme Court struck down Louisiana's voting map on the basis that the state had illegally used race as a consideration when it created a new majority-Black district.
TL;DR: Meanwhile, ahead of the November midterms, lawmakers in several states have been redrawing their district maps to favor one party or the other, or are considering such reconfigurations.
Read original at Phys
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Identity traits sharply narrow who becomes friends or marries, model reveals

Our personal identity is composed of many dimensions, such as age, gender, ethnic background, or socioeconomic status. A research team led by Fariba Karimi from the Institute of Human-Centered Computing at Graz University of Technology (TU Graz) and Samuel Martin-Gutierrez from the Complexity Science Hub developed the statistical computational model "MAPS" to calculate the influence of these factors on our social relationships.

More: Our personal identity is composed of many dimensions, such as age, gender, ethnic background, or socioeconomic status. A research team led by Fariba Karimi from the Institute of Human-Centered Computing at Graz University of Technology (TU Graz) and Samuel Martin-Gutierrez from the Complexity Science Hub developed the statistical computational model "MAPS" to calculate the inf…
TL;DR: Our personal identity is composed of many dimensions, such as age, gender, ethnic background, or socioeconomic status.
Read original at Phys
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When noisy decision-making becomes a strategic advantage

A new study shows that apparently erratic or "sloppy" behavior in strategic situations is not necessarily a mistake. Under certain conditions, being less sensitive to one's own gains can become a long-term advantage.

More: When noisy decision-making becomes a strategic advantage. A new study shows that apparently erratic or "sloppy" behavior in strategic situations is not necessarily a mistake. Under certain conditions, being less sensitive to one's own gains can become a long-term advantage.
TL;DR: A new study shows that apparently erratic or "sloppy" behavior in strategic situations is not necessarily a mistake.
Read original at Phys
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'Shoot for the moon?' Aim a bit lower, researchers say

How ambitious should you be? Folk wisdom offers conflicting advice: "Shoot for the moon," but also, "Don't let the perfect be the enemy of the good." A new study by researchers at the University of Wyoming, Stanford University and the University of Colorado-Boulder used a mathematical model to show that ambition lies in the middle—above average but finite.

More: This article has been reviewed according to Science X's editorial process and policies . It does, with some interesting twists." The researchers studied a model of searching for the best available strategy—where a strategy could represent anything from a job to a business idea, to a romantic partner, to a public policy or political campaign.
TL;DR: Folk wisdom offers conflicting advice: "Shoot for the moon," but also, "Don't let the perfect be the enemy of the good." A new study by researchers at the University of Wyoming, Stanford University and the University of Colorado-Boulder used a mathematical model to show that ambition lies in the middle—above average but finite.
Read original at Phys
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2026 World Cup: Spain in the lead, but title race remains wide open

Ahead of major soccer tournaments, a research team led by Achim Zeileis of the University of Innsbruck and Andreas Groll of TU Dortmund University calculates the chances of winning for all participating teams. For the 2026 World Cup in Canada, Mexico, and the United States, their model identifies Spain as the slight favorite with 14.5%. Closely behind are England (12.4%), France (12.4%), and Germany (11.2%). Somewhat further back are Portugal (8.9%) and Argentina (8.2%), as well as the Netherlands (5.6%) and Brazil (4.7%). "Compared to previous tournaments, this year's title race is very tight," confirms Achim Zeileis.

More: 2026 World Cup: Spain in the lead, but title race remains wide open. For the 2026 World Cup in Canada, Mexico, and the United States, their model identifies Spain as the slight favorite with 14.5%. "Compared to previous tournaments, this year's title race is very tight," confirms Achim Zeileis.
TL;DR: Ahead of major soccer tournaments, a research team led by Achim Zeileis of the University of Innsbruck and Andreas Groll of TU Dortmund University calculates the chances of winning for all participating teams.
Read original at Phys
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Mathematicians prove existence of Kaleidocycles then unlock their exact motion

Kaleidocycles are flexible polyhedral structures composed of rigid tetrahedra connected along their edges to form rotating rings. Each tetrahedron is a solid 3D polygon with four triangular faces (like a triangular pyramid), and the hinges connect neighboring units, enabling a smooth rotational motion of the ring without deforming the individual pieces. These mechanisms are often compared with the bubble rings blown by dolphins.

More: Mathematicians prove existence of Kaleidocycles then unlock their exact motion. Each tetrahedron is a solid 3D polygon with four triangular faces (like a triangular pyramid), and the hinges connect neighboring units, enabling a smooth rotational motion of the ring without deforming the individual pieces.
TL;DR: Kaleidocycles are flexible polyhedral structures composed of rigid tetrahedra connected along their edges to form rotating rings.
Read original at Phys
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Mathematical analysis reveals a hidden 'golden rule' in abstract art

A mathematical method borrowed from topology can reveal structural properties of visual art that correspond to how people perceive and respond to them, according to a new study published in PLOS Computational Biology by Jacek Rogala of the University of Warsaw, Poland, Shabnam Kadir of the University of Hertfordshire, UK, and colleagues.

More: This article has been reviewed according to Science X's editorial process and policies . For generations, researchers have tried to understand why certain works of art move us more than others. The researchers further analyzed a broader range of paintings by eminent abstract artists such as Wassily Kandinsky, Mark Rothko, and Jackson Pollock.
TL;DR: A mathematical method borrowed from topology can reveal structural properties of visual art that correspond to how people perceive and respond to them, according to a new study published in PLOS Computational Biology by Jacek Rogala of the University of Warsaw, Poland, Shabnam Kadir of the University of Hertfordshire, UK, and colleagues.
Read original at Phys
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Fair matching systems can still produce unequal outcomes, new research finds

A computerized matching system can be designed to be fair and still produce unequal outcomes if the people using it do not understand how it works, according to new research published in Organization Science that shows that disparities can emerge even when a matching system is designed to reduce bias, discourage gaming and reward honest decision-making.

More: by Rebecca Seel, Institute for Operations Research and the Management Sciences This article has been reviewed according to Science X's editorial process and policies . The study, "Gendered Navigation of Advice and Suboptimal Behavior in Matching Algorithms: Evidence from the Residency Match," examines how medical students navigate the National Residency Matching Program, the h…
TL;DR: A computerized matching system can be designed to be fair and still produce unequal outcomes if the people using it do not understand how it works, according to new research published in Organization Science that shows that disparities can emerge even when a matching system is designed to reduce bias, discourage gaming and reward honest decision-making.
Read original at Phys
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AI makes a major breakthrough in a math problem that had stumped experts for decades

For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the planar unit distance problem. The question posed by the legendary Hungarian mathematician was, on the surface, deceptively simple.

More: AI makes a major breakthrough in a math problem that had stumped experts for decades. For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the planar unit distance problem. The question posed by the legendary Hungarian mathematician was, on the surface, deceptively simple.
TL;DR: For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the planar unit distance problem.
Read original at Phys
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Mathematicians solve decades-old mystery about the hidden order in high-dimensional randomness

Three mathematicians have laid out proof that solves a long-standing problem in mathematics. Even the mathematician—an Abel prize winner—that first posed the problem didn't believe it would ever be solved. The solution provides insight into high-dimensional random structures that could potentially impact data science, machine learning and optimization.

More: Mathematicians solve decades-old mystery about the hidden order in high-dimensional randomness. Even the mathematician—an Abel prize winner—that first posed the problem didn't believe it would ever be solved. The solution provides insight into high-dimensional random structures that could potentially impact data science, machine learning and optimization.
TL;DR: Three mathematicians have laid out proof that solves a long-standing problem in mathematics.
Read original at Phys
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New mathematical model suggests global population crash by 2064

In a new open-access study that I published with my late colleague Kostya Trachenko from Queen Mary University of London, I propose a surprisingly simple nonlinear mathematical equation that unifies 12,000 years of human population growth and points to stark possible futures if global environmental crises intensify.

More: This article has been reviewed according to Science X's editorial process and policies . A simple follow helps independent science journalism stay visible. In some periods, human population expanded slowly and steadily; in others, growth accelerated explosively.
TL;DR: In a new open-access study that I published with my late colleague Kostya Trachenko from Queen Mary University of London, I propose a surprisingly simple nonlinear mathematical equation that unifies 12,000 years of human population growth and points to stark possible futures if global environmental crises intensify.
Read original at Phys
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Researchers develop Bayesian inference for hidden dependence structures in multi-group high-dimensional data

In today's scientific and industrial fields, high-dimensional data in which numerous variables are observed simultaneously, such as genomic, climate, financial, and sensor data, are rapidly increasing. In such data, it is important to learn the dependent structures connecting the variables and to identify a "dependence map" that reveals hidden information in massive data sets.

More: In today's scientific and industrial fields, high-dimensional data in which numerous variables are observed simultaneously, such as genomic, climate, financial, and sensor data, are rapidly increasing. In such data, it is important to learn the dependent structures connecting the variables and to identify a "dependence map" that reveals hidden information in massive data sets.
TL;DR: In today's scientific and industrial fields, high-dimensional data in which numerous variables are observed simultaneously, such as genomic, climate, financial, and sensor data, are rapidly increasing.
Read original at Phys
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An AI solution to an 80‑year‑old problem has shocked mathematicians

Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary Hungarian mathematician Paul Erdős in 1946.

More: This article has been reviewed according to Science X's editorial process and policies . The planar unit distance problem, or Erdős problem 90 , has intrigued mathematicians for decades. At the same time, results like this show us what kind of mathematics current AI models are good at—and where their capabilities are still uncertain.
TL;DR: Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary Hungarian mathematician Paul Erdős in 1946.
Read original at Phys
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Mathematician solves origami donut efficiency challenge with fewest folds

Most people wouldn't think that it would take rigorous mathematical proof to show how many folds it takes to make a donut shape out of paper. Yet, no one could quite figure it out until recently.

More: Mathematician solves origami donut efficiency challenge with fewest folds. Most people wouldn't think that it would take rigorous mathematical proof to show how many folds it takes to make a donut shape out of paper. Yet, no one could quite figure it out until recently.
TL;DR: Most people wouldn't think that it would take rigorous mathematical proof to show how many folds it takes to make a donut shape out of paper.
Read original at Phys
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Mathematicians say 'don't believe hype' on AI capabilities

Dozens of mathematicians signed a declaration Tuesday calling for the discipline to resist beating the drum for artificial intelligence developers.

More: This article has been reviewed according to Science X's editorial process and policies . AI "opens new and exciting opportunities, but it also raises questions that cannot be left unexamined," International Mathematical Union (IMU) vice president Ulrike Tillmann wrote in an endorsement.
TL;DR: Dozens of mathematicians signed a declaration Tuesday calling for the discipline to resist beating the drum for artificial intelligence developers.
Read original at Phys
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Overarming America: Game theory explores how fear and social pressure drive gun purchases

A Dartmouth College study is the first to map the interplay of personal choice and social networks that has led to the United States being one of the world's most heavily armed countries, with 120 firearms for every 100 people. The researchers describe in Science Advances how individual incentives to buy firearms can lead to a phenomenon they call "overarming." In an overarmed society, the collective cost of firearm ownership outweighs the individual benefits of possessing a gun.

More: A Dartmouth College study is the first to map the interplay of personal choice and social networks that has led to the United States being one of the world's most heavily armed countries, with 120 firearms for every 100 people. The researchers describe in Science Advances how individual incentives to buy firearms can lead to a phenomenon they call "overarming.
TL;DR: A Dartmouth College study is the first to map the interplay of personal choice and social networks that has led to the United States being one of the world's most heavily armed countries, with 120 firearms for every 100 people.
Read original at Phys
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What network science can tell us about the 2026 World Cup

Team Australia kicked it long from the goalkeeper. Switzerland took a slower approach and preferred short passes over long drives. Spain, on the other hand, tended to string the ball with sharp, sideways passes across the field. Those are a few of the takeaways from passing-style graphics that Northeastern University's Network Science Institute developed of the top soccer teams at the FIFA World Cup 2022 that showcased their most distinctive passing clusters.

More: What network science can tell us about the 2026 World Cup. Switzerland took a slower approach and preferred short passes over long drives. Those are a few of the takeaways from passing-style graphics that Northeastern University's Network Science Institute developed of the top soccer teams at the FIFA World Cup 2022 that showcased their most distinctive passing clusters.
TL;DR: Team Australia kicked it long from the goalkeeper.
Read original at Phys
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Schrödinger’s color theory finally completed after 100 years

A century after Erwin Schrödinger sketched out a bold vision for how we perceive color, scientists have finally filled in the missing pieces. A Los Alamos team used advanced geometry to show that hue, saturation, and lightness aren’t shaped by culture or experience — they’re built directly into the mathematical structure of how we see color. By defining a crucial missing element known as the “neutral axis,” the researchers repaired a long-standing flaw in Schrödinger’s model and even corrected tricky visual quirks like the way brightness can subtly shift perceived hue.

More: Schrödinger’s color theory finally completed after 100 years. A Los Alamos team used advanced geometry to show that hue, saturation, and lightness aren’t shaped by culture or experience — they’re built directly into the mathematical structure of how we see color.
TL;DR: A century after Erwin Schrödinger sketched out a bold vision for how we perceive color, scientists have finally filled in the missing pieces.
Read original at Sciencedaily
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Arithmetic Without Numbers – How LLMs Do Math

The spiral is a simplified picture of a Fourier-style number code: one part of the vector tracks phase around a circle, while another tracks coarse position.

More: Arithmetic Without Numbers – How LLMs Do Math. Token: one unit the model reads or prints. Higher logit means the model is more likely to print that token.
TL;DR: A language model has none of that.
Read original at Alvaro-videla
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Failing grades soar with AI usage, dwindling math skills in Berkeley CS classes

According to Berkeleytime, 35.3% of CS 10 students and 10.6% of CS 61A students received F’s in spring 2026.

More: Failing grades soar with AI usage, dwindling math skills in Berkeley CS classes. The percentage of failing grades in multiple UC Berkeley computer science classes in spring 2026 is significantly higher than past semesters and marks a departure from the department’s grading guidelines.
TL;DR: According to Berkeleytime, 35.3% of CS 10 students and 10.6% of CS 61A students received F’s in spring 2026.
Read original at Dailycal
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Leiden Declaration on Artificial Intelligence and Mathematics

This declaration calls for action to address the challenges posed by the use of artificial intelligence within mathematics research.

More: Leiden Declaration on Artificial Intelligence and Mathematics. Mathematicians have a choice about whether and how to adopt artificial intelligence in the conduct of their research. This includes work in the broader mathematical sciences, education, mentoring, publishing, funding, science policy, and use of mathematics in the wider world.
TL;DR: This declaration calls for action to address the challenges posed by the use of artificial intelligence within mathematics research.
Read original at Leidendeclaration
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Scientists develop open-source software for modeling soft materials

A team of researchers created Morpho, an open-source programmable environment that enables researchers and engineers to conduct shape optimization and design for soft materials. Applications can be for anything from artificial hearts to robot materials that mimic flesh and soft tissue.

More: Scientists develop open-source software for modeling soft materials. A team of researchers created Morpho, an open-source programmable environment that enables researchers and engineers to conduct shape optimization and design for soft materials. Applications can be for anything from artificial hearts to robot materials that mimic flesh and soft tissue.
TL;DR: A team of researchers created Morpho, an open-source programmable environment that enables researchers and engineers to conduct shape optimization and design for soft materials.
Read original at Sciencedaily
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Smart, energy-efficient robot grippers cut production costs

Energy remains a significant factor in industrial production processes. High levels of energy consumption make production more expensive and exacerbate the climate crisis. A new type of robot technology needs 90% less electricity than conventional systems. The technology uses lightweight, shape memory materials to construct novel, non-pneumatic, industrial gripper systems that function without the need for additional sensors.

More: Smart, energy-efficient robot grippers cut production costs. High levels of energy consumption make production more expensive and exacerbate the climate crisis. A new type of robot technology needs 90% less electricity than conventional systems.
TL;DR: The technology uses lightweight, shape memory materials to construct novel, non-pneumatic, industrial gripper systems that function without the need for additional sensors.
Read original at Sciencedaily
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Researchers successfully prove the solution to Dudeney's 120-year-old dissection puzzle

Over 120 years ago, Henry Ernest Dudeney posed the famous dissection problem of transforming a triangle into a square by cutting it into as few pieces as possible. In a new study, researchers have finally proved that the original solution, which involves only four pieces, is optimal by using a new proof technique. This technique shows for the first time that it is possible to prove the optimality of the solution to a dissection problem.

More: Researchers successfully prove the solution to Dudeney's 120-year-old dissection puzzle. Over 120 years ago, Henry Ernest Dudeney posed the famous dissection problem of transforming a triangle into a square by cutting it into as few pieces as possible.
TL;DR: This technique shows for the first time that it is possible to prove the optimality of the solution to a dissection problem.
Read original at Sciencedaily
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Mini rolling robot takes virtual biopsies

A tiny magnetic robot which can take 3D scans from deep within the body, that could revolutionize early cancer detection, has been developed by researchers. The team say this is the first time it has been possible to generate high-resolution three-dimensional ultrasound images taken from a probe deep inside the gastrointestinal tract, or gut.

More: A tiny magnetic robot which can take 3D scans from deep within the body, that could revolutionize early cancer detection, has been developed by researchers. The team say this is the first time it has been possible to generate high-resolution three-dimensional ultrasound images taken from a probe deep inside the gastrointestinal tract, or gut.
TL;DR: A tiny magnetic robot which can take 3D scans from deep within the body, that could revolutionize early cancer detection, has been developed by researchers.
Read original at Sciencedaily
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Hypersonic simulation in 3D exposes new disturbances

At hypersonic speeds, complexities occur when the gases interact with the surface of the vehicle such as boundary layers and shock waves. Researchers were able to observe new disturbances in simulations conducted for the first time in 3D.

More: Hypersonic simulation in 3D exposes new disturbances. At hypersonic speeds, complexities occur when the gases interact with the surface of the vehicle such as boundary layers and shock waves. Researchers were able to observe new disturbances in simulations conducted for the first time in 3D.
TL;DR: Researchers were able to observe new disturbances in simulations conducted for the first time in 3D.
Read original at Sciencedaily
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A cool fix for hot chips: Advanced thermal management technology for electronic devices

Researchers have demonstrated a significant performance increase in cooling technology for high-power electronic devices. They designed novel capillary geometries that push the boundaries of thermal transfer efficiency. This study could play a crucial role in the development of next-generation technology.

More: A cool fix for hot chips: Advanced thermal management technology for electronic devices. They designed novel capillary geometries that push the boundaries of thermal transfer efficiency. This study could play a crucial role in the development of next-generation technology.
TL;DR: Researchers have demonstrated a significant performance increase in cooling technology for high-power electronic devices.
Read original at Sciencedaily
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Using ChatGPT, students might pass a course, but with a cost

With the assumption that students are going to use artificial intelligence and large language models such as ChatGPT to do their homework, researchers set out to learn how well the free version of ChatGPT would compare with human students in a semester-long undergraduate control systems course.

TL;DR: With the assumption that students are going to use artificial intelligence and large language models such as ChatGPT to do their homework, researchers set out to learn how well the free version of ChatGPT would compare with human students in a semester-long undergraduate control systems course.
Read original at Sciencedaily
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Superconductors: Amazingly orderly disorder

A surprising connection has been found, between two seemingly very different classes of superconductors. In a new material, atoms are distributed irregularly, but still manage to create long-range magnetic order.

More: Superconductors: Amazingly orderly disorder. A surprising connection has been found, between two seemingly very different classes of superconductors. In a new material, atoms are distributed irregularly, but still manage to create long-range magnetic order.
TL;DR: A surprising connection has been found, between two seemingly very different classes of superconductors.
Read original at Sciencedaily
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A chip with natural blood vessels

Miniature organs on a chip could allow us to do scientific studies with great precision, without having to resort to animal testing. The main problem, however, is that artificial tissue needs blood vessels, and they are very hard to create. Now, new technology has been developed to create reproducible blood vessels using high-precision laser pulses. Tissue has been created that acts like natural tissue.

More: A chip with natural blood vessels. The main problem, however, is that artificial tissue needs blood vessels, and they are very hard to create. Now, new technology has been developed to create reproducible blood vessels using high-precision laser pulses.
TL;DR: Tissue has been created that acts like natural tissue.
Read original at Sciencedaily
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Study deepens understanding of cell migration, important for potential medical advances

A new study integrated mathematical modeling with advanced imaging to discover that the physical shape of the fruit fly egg chamber, combined with chemical signals, significantly influences how cells move. Cell migration is critical in wound healing, immune responses, and cancer metastasis, so the work has potential to advance a range of medical treatments.

More: A new study integrated mathematical modeling with advanced imaging to discover that the physical shape of the fruit fly egg chamber, combined with chemical signals, significantly influences how cells move. Cell migration is critical in wound healing, immune responses, and cancer metastasis, so the work has potential to advance a range of medical treatments.
TL;DR: A new study integrated mathematical modeling with advanced imaging to discover that the physical shape of the fruit fly egg chamber, combined with chemical signals, significantly influences how cells move.
Read original at Sciencedaily
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Half of today’s jobs could vanish—Here’s how smart countries are future-proofing workers

AI is revolutionizing the job landscape, prompting nations worldwide to prepare their workforces for dramatic changes. A University of Georgia study evaluated 50 countries’ national AI strategies and found significant differences in how governments prioritize education and workforce training. While many jobs could disappear in the coming decades, new careers requiring advanced AI skills are emerging. Countries like Germany and Spain are leading with early education and cultural support for AI, but few emphasize developing essential human soft skills like creativity and communication—qualities AI can't replace.

More: Half of today’s jobs could vanish—Here’s how smart countries are future-proofing workers. A University of Georgia study evaluated 50 countries’ national AI strategies and found significant differences in how governments prioritize education and workforce training. While many jobs could disappear in the coming decades, new careers requiring advanced AI skills are emerging.
TL;DR: Countries like Germany and Spain are leading with early education and cultural support for AI, but few emphasize developing essential human soft skills like creativity and communication—qualities AI can't replace.
Read original at Sciencedaily
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Scientists create a magnetic lantern that moves like it’s alive

A team of engineers at North Carolina State University has designed a polymer “Chinese lantern” that can rapidly snap into multiple stable 3D shapes—including a lantern, a spinning top, and more—by compression or twisting. By adding a magnetic layer, they achieved remote control of the shape-shifting process, allowing the lanterns to act as grippers, filters, or expandable mechanisms.

More: A team of engineers at North Carolina State University has designed a polymer “Chinese lantern” that can rapidly snap into multiple stable 3D shapes—including a lantern, a spinning top, and more—by compression or twisting.
TL;DR: A team of engineers at North Carolina State University has designed a polymer “Chinese lantern” that can rapidly snap into multiple stable 3D shapes—including a lantern, a spinning top, and more—by compression or twisting.
Read original at Sciencedaily
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Entangled spins give diamonds a quantum advantage

UC Santa Barbara physicists have engineered entangled spin systems in diamond that surpass classical sensing limits through quantum squeezing. Their breakthrough enables next-generation quantum sensors that are powerful, compact, and ready for real-world use.

More: Entangled spins give diamonds a quantum advantage. UC Santa Barbara physicists have engineered entangled spin systems in diamond that surpass classical sensing limits through quantum squeezing. Their breakthrough enables next-generation quantum sensors that are powerful, compact, and ready for real-world use.
TL;DR: UC Santa Barbara physicists have engineered entangled spin systems in diamond that surpass classical sensing limits through quantum squeezing.
Read original at Sciencedaily
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AI generates playful, human-like games

A team of scientists has now created a computer model that can represent and generate human-like goals by learning from how people create games. The work could lead to AI systems that better understand human intentions and more faithfully model and align with our goals. It may also lead to AI systems that can help us design more human-like games.

More: AI generates playful, human-like games. A team of scientists has now created a computer model that can represent and generate human-like goals by learning from how people create games. The work could lead to AI systems that better understand human intentions and more faithfully model and align with our goals.
TL;DR: It may also lead to AI systems that can help us design more human-like games.
Read original at Sciencedaily
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AI-based math: Individualized support for schoolchildren

Researchers have developed an AI-based learning system that recognizes strengths and weaknesses in mathematics by tracking eye movements with a webcam to generate problem-solving hints. This enables teachers to provide significantly more children with individualized support.

More: Researchers have developed an AI-based learning system that recognizes strengths and weaknesses in mathematics by tracking eye movements with a webcam to generate problem-solving hints. This enables teachers to provide significantly more children with individualized support.
TL;DR: Researchers have developed an AI-based learning system that recognizes strengths and weaknesses in mathematics by tracking eye movements with a webcam to generate problem-solving hints.
Read original at Sciencedaily
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New computer code could lead to simpler, less costly stellarators for fusion power

Physicists have created a new computer code that could speed up the design of the complicated magnets that shape the plasma in stellarators, making the systems simpler and more affordable to build.

TL;DR: Physicists have created a new computer code that could speed up the design of the complicated magnets that shape the plasma in stellarators, making the systems simpler and more affordable to build.
Read original at Sciencedaily
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Mathematicians uncover the logic behind how people walk in crowds

Mathematicians studied the flow of human crowds and developed a way to predict when pedestrian paths will transition from orderly to entangled. Their findings may help inform the design of public spaces that promote safe and efficient thoroughfares.

More: Mathematicians uncover the logic behind how people walk in crowds. Mathematicians studied the flow of human crowds and developed a way to predict when pedestrian paths will transition from orderly to entangled. Their findings may help inform the design of public spaces that promote safe and efficient thoroughfares.
TL;DR: Mathematicians studied the flow of human crowds and developed a way to predict when pedestrian paths will transition from orderly to entangled.
Read original at Sciencedaily
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A simple way to boost math progress

Scientists investigated whether email interventions informed by behavioral science could help teachers help students learn math.

TL;DR: Scientists investigated whether email interventions informed by behavioral science could help teachers help students learn math.
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BESSY II: Magnetic 'microflowers' enhance local magnetic fields

A flower-shaped structure only a few micrometres in size made of a nickel-iron alloy can concentrate and locally enhance magnetic fields. The size of the effect can be controlled by varying the geometry and number of 'petals'. This magnetic metamaterial developed by Dr Anna Palau's group at the Institut de Ciencia de Materials de Barcelona (ICMAB) in collaboration with her partners of the CHIST-ERA MetaMagIC project, has now been studied at BESSY II in collaboration with Dr Sergio Valencia. Such a device can be used to increase the sensitivity of magnetic sensors, to reduce the energy required for creating local magnetic fields, but also, at the PEEM experimental station, to study samples under much higher magnetic fields than currently possible.

More: BESSY II: Magnetic 'microflowers' enhance local magnetic fields. The size of the effect can be controlled by varying the geometry and number of 'petals'. Such a device can be used to increase the sensitivity of magnetic sensors, to reduce the energy required for creating local magnetic fields, but also, at the PEEM experimental station, to study samples under much higher magne…
TL;DR: A flower-shaped structure only a few micrometres in size made of a nickel-iron alloy can concentrate and locally enhance magnetic fields.
Read original at Sciencedaily
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Beyond ambiguous reflections: Bridging optical 3D metrology and computer vision

A new method significantly advances 3D imaging of reflective surfaces. The approach integrates techniques known from high-precision optical 3D metrology and computer vision, and could benefit applications ranging from industrial inspection and medical imaging to virtual reality and cultural heritage preservation.

More: Beyond ambiguous reflections: Bridging optical 3D metrology and computer vision. A new method significantly advances 3D imaging of reflective surfaces. The approach integrates techniques known from high-precision optical 3D metrology and computer vision, and could benefit applications ranging from industrial inspection and medical imaging to virtual reality and cultural herita…
TL;DR: A new method significantly advances 3D imaging of reflective surfaces.
Read original at Sciencedaily
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Physics of irregular objects on inclined planes probed

How gravity causes a perfectly spherical ball to roll down an inclined plane is part of elementary school physics canon. But the world is messier than a textbook. Scientists have sought to quantitatively describe the much more complex rolling physics of real-world objects. They have now combined theory, simulations, and experiments to understand what happens when an imperfect, spherical object is placed on an inclined plane.

More: Physics of irregular objects on inclined planes probed. How gravity causes a perfectly spherical ball to roll down an inclined plane is part of elementary school physics canon. They have now combined theory, simulations, and experiments to understand what happens when an imperfect, spherical object is placed on an inclined plane.
TL;DR: Scientists have sought to quantitatively describe the much more complex rolling physics of real-world objects.
Read original at Sciencedaily
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Study shows addressing working memory can help students with math difficulty improve word problem-solving skills

Working memory is like a mental chalkboard we use to store temporary information while executing other tasks. Scientists worked with more than 200 elementary students to test their working memory, assess its role in word-problem solving and if interventions could boost it and thereby improve their word problem solving skills. Results showed that improving working memory helped both students with and without math difficulties and can help educators more effectively by helping teach the science of math, study authors argue.

More: Study shows addressing working memory can help students with math difficulty improve word problem-solving skills. Working memory is like a mental chalkboard we use to store temporary information while executing other tasks.
TL;DR: Results showed that improving working memory helped both students with and without math difficulties and can help educators more effectively by helping teach the science of math, study authors argue.
Read original at Sciencedaily
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How math helps to protect crops from invasive disease

New research demonstrates how mathematical modeling can predict outbreaks of toxic fungi in Texas corn crops -- offering a potential lifeline to farmers facing billions in harvest losses.

TL;DR: New research demonstrates how mathematical modeling can predict outbreaks of toxic fungi in Texas corn crops -- offering a potential lifeline to farmers facing billions in harvest losses.
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Mathematician solves algebra's oldest problem using intriguing new number sequences

A mathematician has built an algebraic solution to an equation that was once believed impossible to solve.

More: Mathematician solves algebra's oldest problem using intriguing new number sequences. A mathematician has built an algebraic solution to an equation that was once believed impossible to solve.
TL;DR: A mathematician has built an algebraic solution to an equation that was once believed impossible to solve.
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Scientists discover class of crystals with properties that may prove revolutionary

By twisting atom-thin sheets of graphene in just the right way, Rutgers researchers created intercrystals, a new form of matter where geometry alone controls electron behavior. These strange materials could power quantum computers, ultra-efficient circuits, and greener technologies.

More: Scientists discover class of crystals with properties that may prove revolutionary. By twisting atom-thin sheets of graphene in just the right way, Rutgers researchers created intercrystals, a new form of matter where geometry alone controls electron behavior. These strange materials could power quantum computers, ultra-efficient circuits, and greener technologies.
TL;DR: By twisting atom-thin sheets of graphene in just the right way, Rutgers researchers created intercrystals, a new form of matter where geometry alone controls electron behavior.
Read original at Sciencedaily
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AI is good at weather forecasting. Can it predict freak weather events?

Scientists found that neural networks cannot yet forecast 'gray swan' weather events, which might not appear in existing training data but could still happen -- like 200-year floods or massive hurricanes.

TL;DR: Scientists found that neural networks cannot yet forecast 'gray swan' weather events, which might not appear in existing training data but could still happen -- like 200-year floods or massive hurricanes.
Read original at Sciencedaily
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A faster, more reliable method for simulating the plasmas used to make computer chips

Researchers developed a faster, more stable way to simulate the swirling electric fields inside industrial plasmas -- the kind used to make microchips and coat materials. The improved method could lead to better tools for chip manufacturing and fusion research.

More: A faster, more reliable method for simulating the plasmas used to make computer chips. Researchers developed a faster, more stable way to simulate the swirling electric fields inside industrial plasmas -- the kind used to make microchips and coat materials. The improved method could lead to better tools for chip manufacturing and fusion research.
TL;DR: Researchers developed a faster, more stable way to simulate the swirling electric fields inside industrial plasmas -- the kind used to make microchips and coat materials.
Read original at Sciencedaily
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In nature's math, freedoms are fundamental

Scientists have developed a unified theory for mathematical parameters known as gauge freedoms. Their new formulas will allow researchers to interpret research results much faster and with greater confidence. The development could prove fundamental for future efforts in agriculture, drug discovery, and beyond.

More: In nature's math, freedoms are fundamental. Their new formulas will allow researchers to interpret research results much faster and with greater confidence. The development could prove fundamental for future efforts in agriculture, drug discovery, and beyond.
TL;DR: Scientists have developed a unified theory for mathematical parameters known as gauge freedoms.
Read original at Sciencedaily
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The AI that writes climate-friendly cement recipes in seconds

AI researchers in Switzerland have found a way to dramatically cut cement s carbon footprint by redesigning its recipe. Their system simulates thousands of ingredient combinations, pinpointing those that keep cement strong while emitting far less CO2 all in seconds.

More: The AI that writes climate-friendly cement recipes in seconds. AI researchers in Switzerland have found a way to dramatically cut cement s carbon footprint by redesigning its recipe. Their system simulates thousands of ingredient combinations, pinpointing those that keep cement strong while emitting far less CO2 all in seconds.
TL;DR: AI researchers in Switzerland have found a way to dramatically cut cement s carbon footprint by redesigning its recipe.
Read original at Sciencedaily
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Harvard’s ultra-thin chip could revolutionize quantum computing

Researchers at Harvard have created a groundbreaking metasurface that can replace bulky and complex optical components used in quantum computing with a single, ultra-thin, nanostructured layer. This innovation could make quantum networks far more scalable, stable, and compact. By harnessing the power of graph theory, the team simplified the design of these quantum metasurfaces, enabling them to generate entangled photons and perform sophisticated quantum operations — all on a chip thinner than a human hair. It's a radical leap forward for room-temperature quantum technology and photonics.

More: Harvard’s ultra-thin chip could revolutionize quantum computing. This innovation could make quantum networks far more scalable, stable, and compact. It's a radical leap forward for room-temperature quantum technology and photonics.
TL;DR: Researchers at Harvard have created a groundbreaking metasurface that can replace bulky and complex optical components used in quantum computing with a single, ultra-thin, nanostructured layer.
Read original at Sciencedaily
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AI finds hidden safe zones inside a fusion reactor

Scientists have developed a lightning-fast AI tool called HEAT-ML that can spot hidden “safe zones” inside a fusion reactor where parts are protected from blistering plasma heat. Finding these areas, known as magnetic shadows, is key to keeping reactors running safely and moving fusion energy closer to reality.

More: AI finds hidden safe zones inside a fusion reactor. Scientists have developed a lightning-fast AI tool called HEAT-ML that can spot hidden “safe zones” inside a fusion reactor where parts are protected from blistering plasma heat. Finding these areas, known as magnetic shadows, is key to keeping reactors running safely and moving fusion energy closer to reality.
TL;DR: Scientists have developed a lightning-fast AI tool called HEAT-ML that can spot hidden “safe zones” inside a fusion reactor where parts are protected from blistering plasma heat.
Read original at Sciencedaily
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Scientists discover forgotten particle that could unlock quantum computers

Scientists may have uncovered the missing piece of quantum computing by reviving a particle once dismissed as useless. This particle, called the neglecton, could give fragile quantum systems the full power they need by working alongside Ising anyons. What was once considered mathematical waste may now hold the key to building universal quantum computers, turning discarded theory into a pathway toward the future of technology.

More: Scientists discover forgotten particle that could unlock quantum computers. This particle, called the neglecton, could give fragile quantum systems the full power they need by working alongside Ising anyons.
TL;DR: Scientists may have uncovered the missing piece of quantum computing by reviving a particle once dismissed as useless.
Read original at Sciencedaily
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A strange quantum effect could power future electronics

Rice University physicists confirmed that flat electronic bands in kagome superconductors aren’t just theoretical, they actively shape superconductivity and magnetism. This breakthrough could guide the design of next-generation quantum materials and technologies.

More: A strange quantum effect could power future electronics. Rice University physicists confirmed that flat electronic bands in kagome superconductors aren’t just theoretical, they actively shape superconductivity and magnetism. This breakthrough could guide the design of next-generation quantum materials and technologies.
TL;DR: Rice University physicists confirmed that flat electronic bands in kagome superconductors aren’t just theoretical, they actively shape superconductivity and magnetism.
Read original at Sciencedaily
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Scientists just found a hidden quantum geometry that warps electrons

A hidden quantum geometry that distorts electron paths has finally been observed in real materials. This “quantum metric,” once thought purely theoretical, may revolutionize electronics, superconductivity, and ultrafast devices.

More: Scientists just found a hidden quantum geometry that warps electrons. A hidden quantum geometry that distorts electron paths has finally been observed in real materials. This “quantum metric,” once thought purely theoretical, may revolutionize electronics, superconductivity, and ultrafast devices.
TL;DR: A hidden quantum geometry that distorts electron paths has finally been observed in real materials.
Read original at Sciencedaily
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Tiny magnetic spirals unlock the future of spintronics

Scientists in Korea have engineered magnetic nanohelices that can control electron spin with extraordinary precision at room temperature. By combining structural chirality and magnetism, these nanoscale helices can filter spins without complex circuitry or cooling. The breakthrough not only demonstrates a way to program handedness in inorganic nanomaterials but also opens the door to scalable, energy-efficient spintronic devices that could revolutionize computing.

More: Tiny magnetic spirals unlock the future of spintronics. By combining structural chirality and magnetism, these nanoscale helices can filter spins without complex circuitry or cooling. The breakthrough not only demonstrates a way to program handedness in inorganic nanomaterials but also opens the door to scalable, energy-efficient spintronic devices that could revolutionize com…
TL;DR: Scientists in Korea have engineered magnetic nanohelices that can control electron spin with extraordinary precision at room temperature.
Read original at Sciencedaily
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Shocking study exposes widespread math research fraud

A sweeping investigation has revealed widespread fraud in mathematics publishing, where commercial metrics and rankings have incentivized the mass production of meaningless or flawed papers. The study highlights shocking distortions—such as a university without a math department ranked as having the most top mathematicians—and the explosion of megajournals willing to publish anything for a fee.

More: A sweeping investigation has revealed widespread fraud in mathematics publishing, where commercial metrics and rankings have incentivized the mass production of meaningless or flawed papers. The study highlights shocking distortions—such as a university without a math department ranked as having the most top mathematicians—and the explosion of megajournals willing to publish a…
TL;DR: A sweeping investigation has revealed widespread fraud in mathematics publishing, where commercial metrics and rankings have incentivized the mass production of meaningless or flawed papers.
Read original at Sciencedaily
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AI-powered smart bandage heals wounds 25% faster

A new wearable device, a-Heal, combines AI, imaging, and bioelectronics to speed up wound recovery. It continuously monitors wounds, diagnoses healing stages, and applies personalized treatments like medicine or electric fields. Preclinical tests showed healing about 25% faster than standard care, highlighting potential for chronic wound therapy.

More: AI-powered smart bandage heals wounds 25% faster. It continuously monitors wounds, diagnoses healing stages, and applies personalized treatments like medicine or electric fields. Preclinical tests showed healing about 25% faster than standard care, highlighting potential for chronic wound therapy.
TL;DR: A new wearable device, a-Heal, combines AI, imaging, and bioelectronics to speed up wound recovery.
Read original at Sciencedaily
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A strange quantum metal just rewrote the rules of electricity

In a remarkable leap for quantum physics, researchers in Japan have uncovered how weak magnetic fields can reverse tiny electrical currents in kagome metals—quantum materials with a woven atomic structure that frustrates electrons into forming complex patterns. These reversals amplify the metal’s electrical asymmetry, creating a diode-like effect up to 100 times stronger than expected. The team’s theoretical explanation finally clarifies a mysterious phenomenon first observed in 2020, revealing that quantum geometry and spontaneous symmetry breaking are key to this strange behavior.

More: A strange quantum metal just rewrote the rules of electricity. These reversals amplify the metal’s electrical asymmetry, creating a diode-like effect up to 100 times stronger than expected. The team’s theoretical explanation finally clarifies a mysterious phenomenon first observed in 2020, revealing that quantum geometry and spontaneous symmetry breaking are key to this strang…
TL;DR: In a remarkable leap for quantum physics, researchers in Japan have uncovered how weak magnetic fields can reverse tiny electrical currents in kagome metals—quantum materials with a woven atomic structure that frustrates electrons into forming complex patterns.
Read original at Sciencedaily
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Quantum simulations that once needed supercomputers now run on laptops

A team at the University at Buffalo has made it possible to simulate complex quantum systems without needing a supercomputer. By expanding the truncated Wigner approximation, they’ve created an accessible, efficient way to model real-world quantum behavior. Their method translates dense equations into a ready-to-use format that runs on ordinary computers. It could transform how physicists explore quantum phenomena.

More: Quantum simulations that once needed supercomputers now run on laptops. Their method translates dense equations into a ready-to-use format that runs on ordinary computers. It could transform how physicists explore quantum phenomena.
TL;DR: A team at the University at Buffalo has made it possible to simulate complex quantum systems without needing a supercomputer.
Read original at Sciencedaily
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New prediction breakthrough delivers results shockingly close to reality

Researchers have created a prediction method that comes startlingly close to real-world results. It works by aiming for strong alignment with actual values rather than simply reducing mistakes. Tests on medical and health data showed it often outperforms classic approaches. The discovery could reshape how scientists make reliable forecasts.

More: New prediction breakthrough delivers results shockingly close to reality. Tests on medical and health data showed it often outperforms classic approaches. The discovery could reshape how scientists make reliable forecasts.
TL;DR: Researchers have created a prediction method that comes startlingly close to real-world results.
Read original at Sciencedaily
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Architects gain a new superpower for complex curved designs

A researcher from the University of Tokyo and a U.S.-based structural engineer developed a new computational form-finding method that could change how architects and engineers design lightweight and free-form structures covering large spaces. The technique specifically helps create gridshells, thin, curved surfaces whose members form a networked grid. The method makes use of NURBS surfaces, a widely used surface representation format in computer-aided design (CAD). It also drastically reduces computation cost — a task that previously took 90 hours on a high-end GPU completes in about 90 minutes on a standard CPU.

More: Architects gain a new superpower for complex curved designs. The technique specifically helps create gridshells, thin, curved surfaces whose members form a networked grid. The method makes use of NURBS surfaces, a widely used surface representation format in computer-aided design (CAD).
TL;DR: A researcher from the University of Tokyo and a U.S.-based structural engineer developed a new computational form-finding method that could change how architects and engineers design lightweight and free-form structures covering large spaces.
Read original at Sciencedaily
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Ramanujan’s 100-year-old pi formula is still revealing the Universe

Ramanujan’s elegant formulas for calculating pi, developed more than a century ago, have unexpectedly resurfaced at the heart of modern physics. Researchers at IISc discovered that the same mathematical structures behind these formulas also describe real-world phenomena like turbulence, percolation, and even black holes. What once seemed like pure mathematics now appears deeply intertwined with the physical laws governing the universe.

More: Ramanujan’s 100-year-old pi formula is still revealing the Universe. Researchers at IISc discovered that the same mathematical structures behind these formulas also describe real-world phenomena like turbulence, percolation, and even black holes. What once seemed like pure mathematics now appears deeply intertwined with the physical laws governing the universe.
TL;DR: Ramanujan’s elegant formulas for calculating pi, developed more than a century ago, have unexpectedly resurfaced at the heart of modern physics.
Read original at Sciencedaily
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This AI finds simple rules where humans see only chaos

A new AI developed at Duke University can uncover simple, readable rules behind extremely complex systems. It studies how systems evolve over time and reduces thousands of variables into compact equations that still capture real behavior. The method works across physics, engineering, climate science, and biology. Researchers say it could help scientists understand systems where traditional equations are missing or too complicated to write down.

More: This AI finds simple rules where humans see only chaos. A new AI developed at Duke University can uncover simple, readable rules behind extremely complex systems. The method works across physics, engineering, climate science, and biology.
TL;DR: Researchers say it could help scientists understand systems where traditional equations are missing or too complicated to write down.
Read original at Sciencedaily
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These mesmerizing patterns are secretly solving hard problems

Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly reflecting shapes to tile a surface, researchers uncovered a method that links geometry, symmetry, and problem-solving. The technique works in both ordinary flat space and curved hyperbolic worlds used in theoretical physics. Its blend of beauty and precision could influence everything from engineering to digital design.

More: These mesmerizing patterns are secretly solving hard problems. By repeatedly reflecting shapes to tile a surface, researchers uncovered a method that links geometry, symmetry, and problem-solving. Its blend of beauty and precision could influence everything from engineering to digital design.
TL;DR: Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems.
Read original at Sciencedaily
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This AI spots dangerous blood cells doctors often miss

A generative AI system can now analyze blood cells with greater accuracy and confidence than human experts, detecting subtle signs of diseases like leukemia. It not only spots rare abnormalities but also recognizes its own uncertainty, making it a powerful support tool for clinicians.

More: This AI spots dangerous blood cells doctors often miss. A generative AI system can now analyze blood cells with greater accuracy and confidence than human experts, detecting subtle signs of diseases like leukemia. It not only spots rare abnormalities but also recognizes its own uncertainty, making it a powerful support tool for clinicians.
TL;DR: A generative AI system can now analyze blood cells with greater accuracy and confidence than human experts, detecting subtle signs of diseases like leukemia.
Read original at Sciencedaily
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How everyday foam reveals the secret logic of artificial intelligence

Foams were once thought to behave like glass, with bubbles frozen in place at the microscopic level. But new simulations reveal that foam bubbles are always shifting, even while the foam keeps its overall shape. Remarkably, this restless motion follows the same math used to train artificial intelligence. The finding hints that learning-like behavior may be a fundamental principle shared by materials, machines, and living cells.

More: How everyday foam reveals the secret logic of artificial intelligence. Foams were once thought to behave like glass, with bubbles frozen in place at the microscopic level. But new simulations reveal that foam bubbles are always shifting, even while the foam keeps its overall shape.
TL;DR: Remarkably, this restless motion follows the same math used to train artificial intelligence.
Read original at Sciencedaily
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Scientists discover hidden geometry that bends electrons like gravity

Researchers have discovered a hidden quantum geometry inside materials that subtly steers electrons, echoing how gravity warps light in space. Once thought to exist only on paper, this effect has now been observed experimentally in a popular quantum material. The finding reveals a new way to understand and control how materials conduct electricity and interact with light. It could help power future ultra-fast electronics and quantum technologies.

More: Scientists discover hidden geometry that bends electrons like gravity. Once thought to exist only on paper, this effect has now been observed experimentally in a popular quantum material. It could help power future ultra-fast electronics and quantum technologies.
TL;DR: Researchers have discovered a hidden quantum geometry inside materials that subtly steers electrons, echoing how gravity warps light in space.
Read original at Sciencedaily
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Scientists create smart synthetic skin that can hide images and change shape

Inspired by the shape-shifting skin of octopuses, Penn State researchers developed a smart hydrogel that can change appearance, texture, and shape on command. The material is programmed using a special printing technique that embeds digital instructions directly into the skin. Images and information can remain invisible until triggered by heat, liquids, or stretching.

More: Scientists create smart synthetic skin that can hide images and change shape. The material is programmed using a special printing technique that embeds digital instructions directly into the skin. Images and information can remain invisible until triggered by heat, liquids, or stretching.
TL;DR: Inspired by the shape-shifting skin of octopuses, Penn State researchers developed a smart hydrogel that can change appearance, texture, and shape on command.
Read original at Sciencedaily
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Brain inspired machines are better at math than expected

Neuromorphic computers modeled after the human brain can now solve the complex equations behind physics simulations — something once thought possible only with energy-hungry supercomputers. The breakthrough could lead to powerful, low-energy supercomputers while revealing new secrets about how our brains process information.

More: Neuromorphic computers modeled after the human brain can now solve the complex equations behind physics simulations — something once thought possible only with energy-hungry supercomputers. The breakthrough could lead to powerful, low-energy supercomputers while revealing new secrets about how our brains process information.
TL;DR: Neuromorphic computers modeled after the human brain can now solve the complex equations behind physics simulations — something once thought possible only with energy-hungry supercomputers.
Read original at Sciencedaily
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A tiny twist creates giant magnetic skyrmions in 2D crystals

Twisting atomically thin magnetic layers does more than reshape their electronics—it can create giant, topological magnetic textures. In chromium triiodide, researchers observed skyrmion-like patterns stretching far beyond the expected moiré scale, reaching hundreds of nanometers. Even more surprising, their size doesn’t simply follow the twist pattern but peaks at a specific angle. This twist-controlled magnetism could pave the way for low-power spintronic devices built from geometry alone.

More: A tiny twist creates giant magnetic skyrmions in 2D crystals. Even more surprising, their size doesn’t simply follow the twist pattern but peaks at a specific angle. This twist-controlled magnetism could pave the way for low-power spintronic devices built from geometry alone.
TL;DR: Twisting atomically thin magnetic layers does more than reshape their electronics—it can create giant, topological magnetic textures.
Read original at Sciencedaily
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Scientists built the hardest AI test ever and the results are surprising

As AI systems began acing traditional tests, researchers realized those benchmarks were no longer tough enough. In response, nearly 1,000 experts created Humanity’s Last Exam, a massive 2,500-question challenge covering highly specialized topics across many fields. The exam was engineered so that any question solvable by current AI models was removed. Early results show even the most advanced systems still struggle — revealing a surprisingly large gap between AI performance and true expert-level knowledge.

More: Scientists built the hardest AI test ever and the results are surprising. The exam was engineered so that any question solvable by current AI models was removed. Early results show even the most advanced systems still struggle — revealing a surprisingly large gap between AI performance and true expert-level knowledge.
TL;DR: As AI systems began acing traditional tests, researchers realized those benchmarks were no longer tough enough.
Read original at Sciencedaily
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New light trap design supercharges atom-thin semiconductors

Scientists have found a clever way to supercharge ultra-thin semiconductors by reshaping the space beneath them rather than altering the material itself. By placing a single-atom-thick layer of tungsten disulfide over tiny air cavities carved into a crystal, they created miniature “light traps” that dramatically boost brightness and optical effects—up to 20 times stronger emission and 25 times stronger nonlinear signals. These hollow structures, called Mie voids, concentrate light exactly where the material sits, overcoming a major limitation of atomically thin devices.

More: New light trap design supercharges atom-thin semiconductors. By placing a single-atom-thick layer of tungsten disulfide over tiny air cavities carved into a crystal, they created miniature “light traps” that dramatically boost brightness and optical effects—up to 20 times stronger emission and 25 times stronger nonlinear signals.
TL;DR: Scientists have found a clever way to supercharge ultra-thin semiconductors by reshaping the space beneath them rather than altering the material itself.
Read original at Sciencedaily
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This simple change stops robot swarms from getting stuck

In crowded environments, more robots don’t always mean faster results—in fact, too many can bring everything to a standstill. Harvard researchers discovered a surprising fix: adding a bit of randomness to how robots move can actually prevent gridlock and boost efficiency. By allowing robots to “wiggle” slightly instead of marching in straight lines, they can slip past each other and keep tasks flowing smoothly.

More: This simple change stops robot swarms from getting stuck. Harvard researchers discovered a surprising fix: adding a bit of randomness to how robots move can actually prevent gridlock and boost efficiency. By allowing robots to “wiggle” slightly instead of marching in straight lines, they can slip past each other and keep tasks flowing smoothly.
TL;DR: In crowded environments, more robots don’t always mean faster results—in fact, too many can bring everything to a standstill.
Read original at Sciencedaily
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This donut-shaped discovery just shattered a 150-year math rule

A 150-year-old rule in geometry has been proven wrong. Mathematicians found two different doughnut-shaped surfaces that look identical when measured locally but are actually different overall. For decades, researchers suspected this might be possible but couldn’t prove it—until now. The breakthrough reshapes how mathematicians understand the relationship between local measurements and global form.

More: This donut-shaped discovery just shattered a 150-year math rule. Mathematicians found two different doughnut-shaped surfaces that look identical when measured locally but are actually different overall. For decades, researchers suspected this might be possible but couldn’t prove it—until now.
TL;DR: The breakthrough reshapes how mathematicians understand the relationship between local measurements and global form.
Read original at Sciencedaily
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Scientists just captured a mysterious quantum “dance” inside superconductors

In a breakthrough experiment, scientists directly imaged how particles pair up in a system that mimics superconductors. Instead of behaving independently, the pairs moved in a synchronized, dance-like pattern—something never predicted before. This suggests a major gap in the classic theory of superconductivity.

More: Scientists just captured a mysterious quantum “dance” inside superconductors. Instead of behaving independently, the pairs moved in a synchronized, dance-like pattern—something never predicted before. This suggests a major gap in the classic theory of superconductivity.
TL;DR: In a breakthrough experiment, scientists directly imaged how particles pair up in a system that mimics superconductors.
Read original at Sciencedaily
Further reading: MathSciNetQuanta MagazineAMS Math NewsWikipedia

New AI method tackles one of science’s hardest math problems

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing “mollifier layers” that smooth noisy data, they’ve made these calculations more stable and far less computationally demanding. This could transform fields like genetics, where understanding how DNA behaves is key to disease research.

More: New AI method tackles one of science’s hardest math problems. By introducing “mollifier layers” that smooth noisy data, they’ve made these calculations more stable and far less computationally demanding. This could transform fields like genetics, where understanding how DNA behaves is key to disease research.
TL;DR: Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects.
Read original at Sciencedaily
Further reading: Stack Exchange MatharXiv MathQuanta MagazineWikipedia

Scientists discover hidden math secret inside Chinese money plant leaves

Scientists have uncovered a hidden mathematical secret inside the leaves of the Chinese money plant: a naturally occurring geometric pattern known as a Voronoi diagram, something typically associated with city planning, computer science, and network design. By mapping tiny pores and looping veins in the plant’s leaves, researchers discovered that the plant organizes itself using the same kind of elegant spatial logic humans use to solve complex distance problems — without ever “measuring” anything.

More: Scientists discover hidden math secret inside Chinese money plant leaves. Scientists have uncovered a hidden mathematical secret inside the leaves of the Chinese money plant: a naturally occurring geometric pattern known as a Voronoi diagram, something typically associated with city planning, computer science, and network design.
TL;DR: By mapping tiny pores and looping veins in the plant’s leaves, researchers discovered that the plant organizes itself using the same kind of elegant spatial logic humans use to solve complex distance problems — without ever “measuring” anything.
Read original at Sciencedaily
Further reading: Stack Exchange MatharXiv MathQuanta MagazineWikipedia

Key Chemistry Question Answered, No Quantum Computer Required

Do we need quantum computers to fully understand complex chemical reactions? A new result, decades in the making, shows the surprising power of ordinary “classical” machines. The post Key Chemistry Question Answered, No Quantum Computer Required first appeared on Quanta Magazine

More: Key Chemistry Question Answered, No Quantum Computer Required. Do we need quantum computers to fully understand complex chemical reactions? The post Key Chemistry Question Answered, No Quantum Computer Required first appeared on Quanta Magazine
TL;DR: Do we need quantum computers to fully understand complex chemical reactions?
Read original at Quantamagazine
Further reading: arXiv MathQuanta MagazineQuanta MagazineWikipedia

Citing 'severe' math deficits, UC faculty demand a return to SAT tests for STEM

More than 600 University of California faculty members, led by mathematicians at UC Berkeley, are calling on the system to reinstate standardized testing requirements for science, technology, enginee…

More: Citing 'severe' math deficits, UC faculty demand a return to SAT tests for STEM. Without standardized testing in admissions, professors said they don’t know whether incoming students can handle college-level math.
TL;DR: The open letter, addressed to top UC leaders, asks for SAT or ACT exams to be required beginning in fall 2027 and for STEM faculty to be given formal oversight of readiness standards in their majors.
Read original at Latimes
Further reading: arXiv MathQuanta MagazineQuanta MagazineWikipedia

Math-to-Manim

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Read original at Github
Further reading: arXiv MathQuanta MagazineQuanta MagazineWikipedia