https://phys.org/science-news/mathematics/ en-us The latest news on mathematics, math, math science, mathematical science and math technology. Kaushik Bhattacharya is an engineer and materials scientist, but he has always been fascinated by seashells. Part of the draw is the "beautiful" idea that even simple organisms like mollusks can construct wonderfully complex structures over and over again, even in differing environments. He marvels at nature's engineering capabilities. https://phys.org/news/2026-10-mathematics-shell-recreating-diverse-mollusk.html Mathematics Tue, 27 Oct 2026 10:40:24 EDT news712312261 A few short years ago, asking AI to add two four-digit numbers together for a third-grade math assignment would have been a bad idea. Over half the time, the answer would be wrong, studies have shown. Long division or a "leaky tank" problem, an algebra class staple? Forget about it. https://phys.org/news/2026-10-ai-math-problems-stumped-humans.html Mathematics Fri, 23 Oct 2026 13:40:14 EDT news711975424 Announcements over recent months that artificial intelligence models have cracked previously unsolvable problems are shaking top-level mathematicians to the core, and they are now asking themselves: Where do we come in? https://phys.org/news/2026-10-ai-math-unsolvable.html Mathematics Tue, 20 Oct 2026 15:10:02 EDT news711723447 AI models are good at finding answers to mathematical puzzles but are not as good at research judgment, according to theoretical computer scientists. https://phys.org/news/2026-10-ai-math-advance-highlights-gap.html Mathematics Wed, 14 Oct 2026 16:50:01 EDT news711214201 People who tackled arithmetic problems while stressed by a countdown clock, error buzzers and an observer nearby later gave potential losses less weight when deciding whether to accept a gamble. This finding from a new study suggests that pressure may change the balance between how people perceive what they could stand to gain and what they could lose. https://phys.org/news/2026-10-math-pressure-gamble-downside-smaller.html Mathematics Wed, 14 Oct 2026 09:00:18 EDT news711115765 Software developer Ioannis Tsiokos has reported the discovery of a three-dimensional shape, which roughly resembles a chair, that can fill space infinitely without repeating a pattern. The shape follows certain mathematical rules that make it the first of its kind in three dimensions. The AI-assisted findings are described in an arXiv preprint paper. https://phys.org/news/2026-10-newly-3d-chair-space-patterns.html Mathematics Tue, 13 Oct 2026 11:30:01 EDT news711105176 Earlier this week, OpenAI published a trove of hundreds of mathematical results it claimed could "push the frontier of human knowledge." Produced largely by an unreleased artificial intelligence (AI) model, the 722 papers relate to 372 open problems covering everything from algebra and geometry to theoretical computer science. https://phys.org/news/2026-10-mathocalypse-openai-latest-results-dump.html Mathematics Fri, 09 Oct 2026 08:00:02 EDT news710749202 Societal changes do not follow a linear path—this also holds true for Neolithic Europe, approximately 8,000 to 4,000 years ago. Two researchers from the National Academy of Sciences of Ukraine (NASU) and the Leibniz-Zentrum für Archäologie (LEIZA) in Germany have looked at factors driving these dynamics. Using a mathematical model, they analyzed the interplay between population size, production capacity and information exchange. https://phys.org/news/2026-10-pottery-styles-reveal-contrasting-paths.html Mathematics Thu, 08 Oct 2026 09:20:14 EDT news710668621 Why do some students dread math class while others look forward to it? New research offers a closer look at the thinking skills that may help explain differences in math ability. https://phys.org/news/2026-10-people-good-math-struggle.html Mathematics Wed, 07 Oct 2026 09:40:06 EDT news710579642 In 1960, Science, one of the world's leading science journals, published an article with an unambiguous title: Doomsday: Friday, 13 November, A.D. 2026. It predicted that on this future date—just over a month from today—the human population would approach infinity and effectively annihilate itself. https://phys.org/news/2026-09-scientists-friday-november-doomsday.html Mathematics Wed, 30 Sep 2026 17:10:01 EDT news710004362 A research team at the University of Vienna, led by pharmaceutical chemist Johannes Kirchmair, has developed a statistical method to identify hidden anomalies in scientific datasets. The method can be applied automatically to large datasets, making it easier for researchers to pinpoint those that need closer scrutiny. The approach improves the quality of data-driven research and supports the development of reliable AI applications. https://phys.org/news/2026-09-statistical-method-flag-hidden-anomalies.html Mathematics Tue, 29 Sep 2026 11:00:08 EDT news709895821 A shape can be considered complex because it has many sides. A complex melody may feature varied pitches and rhythms. Does the mind treat these as separate features, or can it recognize something common beneath their differences? https://phys.org/news/2026-09-intricate-favor-complex-melodies.html Mathematics Wed, 23 Sep 2026 15:44:42 EDT news709396896 A new decision-making tool developed by Queensland University of Technology researchers could help governments, businesses and organizations make more reliable decisions for such projects as major infrastructure and public policy development. Developed by Ph.D. researchers Omid Motamedisedeh and Faranak Zagia from the QUT School of Architecture and Built Environment, the model addresses a major challenge in group decision-making: Small differences in expert judgments can sometimes lead to dramatically different outcomes. https://phys.org/news/2026-09-expert-consensus-complex-decision-stable.html Mathematics Wed, 23 Sep 2026 08:40:01 EDT news709368122 When is a billiard ball not a billiard ball? When mathematicians get involved and view a popular game as a model computer. https://phys.org/news/2026-09-billiard-balls-reveal-limits.html Mathematics Tue, 22 Sep 2026 13:40:01 EDT news709302881 Perfection is overrated—at least when it comes to complex systems like the power grid, food webs and advanced materials. For decades, scientists generally assumed that networks function most reliably when their individual components are as similar as possible. But real-world networks are rarely uniform. https://phys.org/news/2026-09-finely-tuned-mess-disorder-networks.html Mathematics Thu, 17 Sep 2026 19:40:04 EDT news708874381 Artificial intelligence programs used to classify images could be trained much more cheaply using a surprisingly simple method inspired by the childhood game of 20 Questions, according to new research posted to the arXiv preprint server by a team from the University of Bristol. https://phys.org/news/2026-09-simple-game-ai-future.html Mathematics Thu, 17 Sep 2026 13:40:01 EDT news708858636 One of Athens' crowning jewels is the Parthenon, a classical temple on the Acropolis that overlooks the Greek capital. According to legend, many historians, textbooks and tour guides say the ancient Greek architects who designed it added subtle curves and other variations to correct optical illusions that would have disturbed the building's clean lines. https://phys.org/news/2026-09-mathematician-year-legend-parthenon-optical.html Mathematics Wed, 16 Sep 2026 10:30:01 EDT news708772079 OpenAI said Tuesday that one of its unreleased artificial intelligence models had solved a mathematical puzzle that has eluded mathematicians for generations, a claim that also drew a fight with rival researchers over credit. https://phys.org/news/2026-09-openai-ai-agents-math-hardest.html Mathematics Wed, 09 Sep 2026 06:45:12 EDT news708155096 When humans are making decisions, they are known not to rely solely on their own considerations and the evidence available to them. Past behavioral science and psychology studies have shown that people are often also influenced by the choices and opinions of others. https://phys.org/news/2026-09-disagreement-groups-trustworthy-mathematical-framework.html Mathematics Sat, 05 Sep 2026 10:00:04 EDT news707734830 Jeffrey Rosenthal was a young professor at the University of Toronto when he discovered he was born on a Friday—though not just any Friday. https://phys.org/news/2026-09-full-moon-bad-luck-friday.html Mathematics Fri, 04 Sep 2026 09:20:03 EDT news707730421 Hawking radiation causes black holes to eventually evaporate. This is because particle pairs are spontaneously created near the event horizon (the position of the last ray of light that can escape the black hole's gravitational pull). A particle and its antiparticle are created for a brief moment and disappear immediately afterward. But sometimes a particle falls into the black hole, allowing the other particle to escape: This is Hawking radiation. According to Stephen Hawking, this would ultimately mean that no black holes would remain in the universe. https://phys.org/news/2026-09-gravity-particles-mathematical.html Mathematics Tue, 01 Sep 2026 15:00:05 EDT news707483446 It might not yet be the phenomenon that is Wordle, but for hundreds of thousands of players, Digit Party has scratched the itch of a casual brain teaser to break up their day. https://phys.org/news/2026-08-high-scores-online-brain-teaser.html Mathematics Wed, 26 Aug 2026 13:05:56 EDT news706968321 From the daily weather forecast to a baseball player's batting average to an individual's risk of developing lung cancer, understanding statistics can help people in the United States navigate their lives, according to Mark Ramos, assistant research professor of health policy and administration at Penn State. However, more than half of adults in the U.S. reported knowing little or nothing about basic statistical concepts, according to a recent study led by Ramos. https://phys.org/news/2026-08-adults-lack-basic-statistical.html Mathematics Fri, 21 Aug 2026 11:20:03 EDT news706525741 It took nearly 15 years, researchers around the world and enough computing power to search through a universe of possibilities to answer one question: Who goes first? https://phys.org/news/2026-08-dice-board-gaming-complex-problem.html Mathematics Mon, 17 Aug 2026 16:20:01 EDT news706188830 Latin squares are arrangements of symbols in a grid in which every symbol appears exactly once in each row and column. These symbol arrangements, which were first studied more than three centuries ago, are now widely used to optimize experimental designs and develop secure cryptographic systems, puzzles or other complex combinatorial structures. https://phys.org/news/2026-08-quantum-latin-squares-euler-officers.html Mathematics Fri, 14 Aug 2026 08:00:02 EDT news705745989 A vaccine only protects a whole community if enough people get it, including those who would stay safe anyway once their neighbors are covered. The same tension runs through climate action and social movements: The shared payoff arrives only when enough people pitch in. https://phys.org/news/2026-08-based-rewards-cooperation-free-riders.html Mathematics Tue, 11 Aug 2026 17:00:03 EDT news705681417 In his 1927 paper, "A law of comparative judgment," the American psychologist L. L. Thurstone proposed that when people select one option among multiple alternatives, they are picking the one that has the highest value to them, even though they cannot assign a particular number to that choice. https://phys.org/news/2026-08-people-pays-power.html Mathematics Mon, 10 Aug 2026 18:00:02 EDT news705595141 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