https://phys.org/science-news/mathematics/ en-us The latest news on mathematics, math, math science, mathematical science and math technology. Mathematicians have shown that completely fair elections are—in a sense—impossible. No electoral system can guarantee both that local votes translate directly into local seats and that total seat distribution matches overall vote shares—not without an indefinitely growing parliament. https://phys.org/news/2026-07-math-vote.html Mathematics Fri, 31 Jul 2026 05:00:05 EDT news704551291 Encouraging people to contribute to a common good can have a surprising drawback: a risk that rewards become concentrated among a smaller group, putting the rest at a disadvantage. Put more simply, "equality and cooperation are often in conflict," says Joshua Plotkin, Walter H. and Leonore C. Annenberg Professor of the Natural Sciences in the School of Arts & Sciences. https://phys.org/news/2026-07-cautions-spur-inequality.html Mathematics Mon, 27 Jul 2026 16:00:01 EDT news704380802 In May 2026, OpenAI released a new math result that sent shock waves throughout the world of mathematical research. A major unsolved problem called the "unit distance conjecture" had just been resolved by generative AI. https://phys.org/news/2026-07-golden-age-mathematics-dawning-ai.html Mathematics Thu, 23 Jul 2026 19:20:01 EDT news704029562 The world of mathematics handed out its most prestigious awards Thursday at a unique moment for the field, as it faces pressure from AI's potential to outpace human calculation. https://phys.org/news/2026-07-fields-medal-awarded-young-mathematicians.html Mathematics Thu, 23 Jul 2026 13:20:29 EDT news704031607 As millions of people were coming down from the excitement of the FIFA World Cup final at the start of this week, a different kind of excitement was building within the mathematical community. Levent Alpöge, a mathematician who works at the artificial intelligence (AI) company Anthropic, casually announced on X ('hello there the jacobian conjecture is false thanx') that he had found a counterexample to the Jacobian conjecture, a very old and well-known problem in a field of mathematics called algebraic geometry. He had done this using Anthropic's large language model Claude Fable 5, released to the general public only a few weeks ago. https://phys.org/news/2026-07-tiny-social-media-mathematicians-rethinking.html Mathematics Wed, 22 Jul 2026 07:40:03 EDT news703918802 Researchers from the Max Planck Institute for Intelligent Systems (MPI-IS), the Tübingen AI Center and Ellis Institute Tübingen have conducted a study that uncovers a mathematical strategy explaining how digital labor platforms can systematically suppress wages. The research, titled "Stochastic Wage Suppression on Gig Platforms and How to Organize Against It," develops a mathematical model motivated by digital labor markets, including crowdwork, ride-hailing and food delivery. It shows how a buyer that posts prices and can wait for workers to accept them may keep payments very low when some workers are willing to accept tasks at very low prices. https://phys.org/news/2026-07-gig-platforms-simply-workers-slash.html Mathematics Tue, 21 Jul 2026 19:20:01 EDT news703865110 McGill researchers have found that dangerous crowd conditions leading to surges and stampedes may not emerge suddenly but instead develop gradually, as repeated physical contact and pushing accumulate and become synchronized among nearby individuals. Recognizing how these conditions arise could help organizers strengthen security, site management and evacuation planning, reducing the likelihood of injuries during large-scale public events. https://phys.org/news/2026-07-event-crowd-stampedes.html Mathematics Mon, 20 Jul 2026 13:39:03 EDT news703773476 The worry of becoming stupid isn't new; it dates back to the time of the Greek philosopher Socrates, who insisted that writing would destroy memory and weaken the mind. Then came calculators, GPS and computers, all of which again raised concerns that we might forget basic mental skills and lose the battle against cognitive offloading. Cognitive offloading is the act of reducing mental effort by using external tools or aids to handle tasks that have historically relied solely on memory or internal processing. A similar sentiment is being observed with the advent of AI. https://phys.org/news/2026-07-ai-stupid-weaken-skills-built.html Mathematics Mon, 20 Jul 2026 11:10:01 EDT news703760650 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. https://phys.org/news/2026-07-statistical-method-broadens-uncertainty-average.html Mathematics Thu, 16 Jul 2026 11:20:03 EDT news703406752 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. https://phys.org/news/2026-07-statistical-personalization.html Mathematics Tue, 14 Jul 2026 10:00:08 EDT news703232999 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