https://phys.org/science-news/mathematics/ en-us The latest news on mathematics, math, math science, mathematical science and math technology. 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 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. https://phys.org/news/2026-05-fair-unequal-outcomes.html Mathematics Fri, 15 May 2026 14:00:07 EDT news698069461 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 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. https://phys.org/news/2026-05-qa-political-calculus-actual-math.html Mathematics Thu, 07 May 2026 16:40:01 EDT news697389301 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. https://phys.org/news/2026-05-theoretical-framework-complex-networks.html Mathematics Thu, 07 May 2026 16:00:04 EDT news697387982 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. https://phys.org/news/2026-04-generative-ai-cyber.html Mathematics Sun, 03 May 2026 14:30:03 EDT news696579687 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 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. https://phys.org/news/2026-04-opinions-maximally-insights.html Mathematics Tue, 28 Apr 2026 14:00:03 EDT news696597084 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 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. https://phys.org/news/2026-04-crowd-reveal-hidden-slowdowns-standstills.html Mathematics Wed, 15 Apr 2026 19:40:01 EDT news695488142 Recently, a cheerful 100-year-old message in a bottle was found on the south-west coast of Australia. In it, a World War One soldier proclaimed to be "as happy as Larry." https://phys.org/news/2026-04-chance-message-bottle.html Mathematics Mon, 13 Apr 2026 16:00:07 EDT news695304991 A University of Houston researcher and his collaborators have developed a mathematical model that helps identify whether a competitive environment is healthy, stagnant or skewed. Published in the journal npj Complexity, the study led by UH Computer Science Professor Ioannis Pavlidis presents a general, falsifiable framework for assessing competition quality and fairness. The model works by analyzing the statistical pattern of repeated success and reverse-engineering the kind of competitive system that produced it. https://phys.org/news/2026-04-mathematical-signature-competition-fair-winner.html Mathematics Thu, 09 Apr 2026 13:20:05 EDT news694954861 As organizations increasingly rely on algorithms to rank candidates for jobs, university spots, and financial services, a new method, named hyperFA*IR, offers a more principled approach when picking candidates based on a limited pool of applicants, especially if minorities are few. The new interactive visualization, "Ranks of Disparity," makes these complex dynamics visible. https://phys.org/news/2026-04-disparity-approach-flaw-fairness-algorithms.html Mathematics Tue, 07 Apr 2026 13:20:01 EDT news694778667 Many drivers will know the feeling: you pull ahead of the slower car you've been stuck behind and cruise the open road ahead at your own, faster speed. By the time you reach the next stop light, you're sure that you've left the slower car far behind you—but to your surprise, you see that same car cruise up right behind you in the mirror. Horror buffs might even recall scenes from "Friday the 13th," where masked villain Jason Voorhees always catches up to his sprinting victims—despite himself walking at a leisurely pace. https://phys.org/news/2026-04-voorhees-law-slower-car.html Mathematics Tue, 07 Apr 2026 11:00:03 EDT news694772674 Debates over how geometry is understood and learned date back at least to the days of Plato, with more recent scholars concluding that only humans possess the foundations of this understanding. However, a new analysis by New York University psychology professor Moira Dillon concludes that geometry's foundations are shared by humans and a variety of other animals—from rats to chickens to fish. https://phys.org/news/2026-04-analysis-geometric-human-math-module.html Mathematics Mon, 06 Apr 2026 16:10:06 EDT news694709581 When people are talking, they can start to unconsciously mirror each other, for instance, in the words they use, their sentence structures and even hand gestures. This tendency to mirror others can lead to smoother conversations, while also fostering empathy and collaboration. https://phys.org/news/2026-04-alignment-conversations-highly-situation.html Mathematics Mon, 06 Apr 2026 10:20:01 EDT news694687707 Many people have likely found themselves watching oddly satisfying videos of random objects being squashed by a powerful hydraulic press, but rarely do people consider why things squash the way they do. One object that caught the eye of researchers at The University of Manchester was a simple drink can. When crushed while filled with liquid, it behaves completely differently from an empty one. Instead of collapsing suddenly, it produces an ordered sequence of circular rings that appear one by one. https://phys.org/news/2026-03-soda-cans-mathematics-corrugation-formation.html Mathematics Tue, 31 Mar 2026 18:00:05 EDT news694186021 When you go out to run errands on the weekend, you're on a "tour" as defined by human mobility researchers. Same if you book a guided tour of a famous city or take a trip on a cruise boat that reaches multiple ports. A characteristic of such tours is that you begin and end up in the same place and take intermediate stops along the way. The number of stops is the tour's "length." https://phys.org/news/2026-03-science-delivery.html Mathematics Mon, 30 Mar 2026 14:20:02 EDT news694089403 When we learn something new, that information does not exist in isolation. It integrates into the complex landscape of our knowledge, forging connections with existing ideas and opening up possibilities for new learning. In a study in Nature Communications, Dartmouth researchers report a mathematical technique for mapping the unique landscape of a student's conceptual knowledge from their performance on short multiple-choice quizzes. https://phys.org/news/2026-03-mathematical-framework-landscape-student-knowledge.html Mathematics Tue, 24 Mar 2026 06:00:02 EDT news693488653