https://phys.org/science-news/mathematics/ en-us The latest news on mathematics, math, math science, mathematical science and math technology. 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. https://phys.org/news/2026-07-ai-tool-equations-complex.html Mathematics Tue, 07 Jul 2026 12:00:05 EDT news702638959 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. https://phys.org/news/2026-07-free-text-llms-reveal-hidden.html Mathematics Fri, 03 Jul 2026 15:00:01 EDT news702136906 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. https://phys.org/news/2026-06-visual-words-reveals-lip-readers.html Mathematics Fri, 03 Jul 2026 09:20:06 EDT news702053517 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. https://phys.org/news/2026-06-physicists-ai-claude-collaborate-year.html Mathematics Wed, 01 Jul 2026 00:00:02 EDT news701940481 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. https://phys.org/news/2026-06-world-cup-reveals-strategy-teams.html Mathematics Tue, 30 Jun 2026 06:38:59 EDT news702017102 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. https://phys.org/news/2026-06-mathematicians-unleash-multifold-boost-supercomputer.html Mathematics Wed, 24 Jun 2026 14:40:04 EDT news701522521 Many languages recycle words, giving them different meanings. For example, in English, "run" can mean to move quickly but also to manage something, like "run a company." In Spanish, "lengua" is both the word for tongue and language, as in "la lengua española." This type of word reuse is known as colexification. https://phys.org/news/2026-06-languages-recycle-words.html Mathematics Mon, 22 Jun 2026 12:40:02 EDT news701348226 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. https://phys.org/news/2026-06-redefined-conformity-averaging-real-world.html Mathematics Mon, 15 Jun 2026 15:00:09 EDT news700743781 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. https://phys.org/news/2026-06-basketball-mathematics-children-boost-math.html Mathematics Wed, 10 Jun 2026 12:40:04 EDT news700308601 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. https://phys.org/news/2026-06-hidden-geometry-kernel-methods-complex.html Mathematics Mon, 08 Jun 2026 17:50:03 EDT news700156321 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. https://phys.org/news/2026-06-overarming-america-game-theory-explores.html Mathematics Wed, 03 Jun 2026 14:00:10 EDT news699704161 Dozens of mathematicians signed a declaration Tuesday calling for the discipline to resist beating the drum for artificial intelligence developers. https://phys.org/news/2026-06-mathematicians-dont-hype-ai-capabilities.html Mathematics Tue, 02 Jun 2026 12:40:06 EDT news699620965 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. https://phys.org/news/2026-06-richard-feynman-formula-dining-habits.html Mathematics Tue, 02 Jun 2026 12:20:01 EDT news699620074 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. https://phys.org/news/2026-06-mathematician-origami-donut-efficiency-fewest.html Mathematics Mon, 01 Jun 2026 13:03:13 EDT news699537760 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. https://phys.org/news/2026-05-moon-aim-bit.html Mathematics Fri, 29 May 2026 09:00:02 EDT news699176462 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. https://phys.org/news/2026-05-mathematical-global-population.html Mathematics Mon, 25 May 2026 10:00:02 EDT news698921136 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. https://phys.org/news/2026-05-mathematicians-decades-mystery-hidden-high.html Mathematics Sun, 24 May 2026 12:20:01 EDT news698499556 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. https://phys.org/news/2026-05-ai-major-breakthrough-math-problem.html Mathematics Fri, 22 May 2026 13:50:50 EDT news698676636 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. https://phys.org/news/2026-05-noisy-decision-strategic-advantage.html Mathematics Thu, 21 May 2026 13:20:04 EDT news698581921 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. https://phys.org/news/2026-05-physicist-fresh-prisoner-dilemma-reveals.html Mathematics Mon, 18 May 2026 18:00:02 EDT news698339221 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. https://phys.org/news/2026-05-mathematical-analysis-reveals-hidden-golden.html Mathematics Thu, 14 May 2026 14:00:01 EDT news697884781 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. https://phys.org/news/2026-05-mathematicians-kaleidocycles-exact-motion.html Mathematics Thu, 14 May 2026 12:36:18 EDT news697980961 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. https://phys.org/news/2026-05-identity-traits-sharply-narrow-friends.html Mathematics Wed, 13 May 2026 11:00:24 EDT news697888801 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. https://phys.org/news/2026-05-ai-tackles-math-brutal-problems.html Mathematics Fri, 01 May 2026 11:20:05 EDT news696847922 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. https://phys.org/news/2026-04-physics-explanation-elections-wont.html Mathematics Thu, 30 Apr 2026 12:00:07 EDT news696764161 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. https://phys.org/news/2026-04-western-music-simpler-repetitive-day.html Mathematics Wed, 29 Apr 2026 14:00:11 EDT news696675887 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. https://phys.org/news/2026-04-universal-patterns-emerge-languages-vocabularies.html Mathematics Sun, 26 Apr 2026 12:40:01 EDT news695985160 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. https://phys.org/news/2026-04-norms-imitation-deceptively-simple-human.html Mathematics Thu, 23 Apr 2026 18:10:02 EDT news696182101 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. https://phys.org/news/2026-04-world-largest-olympiad-math-problems.html Mathematics Mon, 20 Apr 2026 12:40:03 EDT news695898865 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. https://phys.org/news/2026-04-mental-math-shortcut-pupil-dilation.html Mathematics Sat, 18 Apr 2026 13:50:01 EDT news695482943