https://phys.org/science-news/mathematics en-us The latest news on mathematics, math, math science, mathematical science and math technology. University of Michigan researchers have added a new dimension to the mathematics used to predict the outcomes of all manner of competitions, including sports, games and social hierarchies in both humans and animals. https://phys.org/news/2024-11-shallow-sports-deep-social-hierarchies.html Mathematics Social Sciences Wed, 06 Nov 2024 14:00:01 EST news650106241 Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a public transportation network. Mathematicians have long sought to develop algorithms that can compare any two graphs. https://phys.org/news/2024-11-hard-theory-easy-graph-isomorphism.html Mathematics Wed, 06 Nov 2024 10:54:04 EST news650112841 A new statistical model could help to address the age-old question of how to price non-physical, intangible goods like data, say scientists. https://phys.org/news/2024-11-framework-games-chance-price-intangible.html Mathematics Economics & Business Wed, 06 Nov 2024 09:48:36 EST news650108912 Cause and effect. We understand this concept from an early age. Tug on a pull toy's string, and the toy follows. Naturally, things get much more complicated as a system grows, as the number of variables increases, and as noise enters the picture. Eventually, it can become almost impossible to tell whether a variable is causing an effect or is simply correlated or associated with it. https://phys.org/news/2024-11-mathematics-effect.html Mathematics Fri, 01 Nov 2024 12:19:04 EDT news649682341 A new study reveals it would take far longer than the lifespan of our universe for a typing monkey to randomly produce Shakespeare. So, while the Infinite Monkey Theorem is true, it is also somewhat misleading. https://phys.org/news/2024-10-monkey-unable-hamlet-lifetime-universe.html Mathematics Wed, 30 Oct 2024 10:07:04 EDT news649501597 In 2022, U.S. high school students Calcea Johnson and Ne'Kiya Jackson astonished teachers when they discovered a new way to prove Pythagoras' theorem using trigonometry after entering a competition at their local high school. As a result, both students were awarded keys to the city of New Orleans, and even received personal praise from Michelle Obama. https://phys.org/news/2024-10-high-school-students-ways-pythagoras.html Mathematics Education Mon, 28 Oct 2024 00:10:02 EDT news649068964 Researchers from The University of New Mexico School of Engineering looked to the natural world to explain how synchronized systems can work more efficiently and made a significant discovery. Their results were published in the journal Nature Communications. https://phys.org/news/2024-10-fireflies-drones-uncover-strategy-synchronization.html Mathematics Fri, 25 Oct 2024 09:55:00 EDT news649068898 If you've ever watched a large flock of birds on the wing, moving across the sky like a cloud with various shapes and directional changes appearing from seeming chaos, or the maneuvers of an ant colony forming bridges and rafts to escape floods, you've been observing what scientists call self-organization. https://phys.org/news/2024-10-theory-physics-principle-rattling.html Mathematics Wed, 23 Oct 2024 13:14:03 EDT news648908042 In the fields of physics, mathematics, and engineering, partial differential equations (PDEs) are essential for modeling various phenomena, from heat diffusion to particle motion and wave propagation. While some PDEs can be solved analytically, many require numerical methods, which can be time-consuming and computationally intensive. https://phys.org/news/2024-10-photonic-method-electromagnetic-rapidly-partial.html Mathematics Mon, 21 Oct 2024 11:22:37 EDT news648728553 On October 16, 1843, the Irish mathematician William Rowan Hamilton had an epiphany during a walk alongside Dublin's Royal Canal. He was so excited he took out his penknife and carved his discovery right then and there on Broome Bridge. https://phys.org/news/2024-10-letters-knife-stone-bridge-graffitied.html Mathematics Wed, 16 Oct 2024 12:40:57 EDT news648301247 A Rutgers University-New Brunswick professor who has devoted his career to resolving the mysteries of higher mathematics has solved two separate, fundamental problems that have perplexed mathematicians for decades. https://phys.org/news/2024-10-breakthrough-mathematician-problems.html Mathematics Wed, 09 Oct 2024 14:57:13 EDT news647704628 The COVID-19 pandemic gave the global medical community the opportunity to take giant strides forward in understanding how to develop vaccines and implement public health measures designed to control the spread of disease, but the crisis also offered researchers the chance to learn more about another kind of contagion: ideas. https://phys.org/news/2024-10-ideas-contagious-human-interaction-networks.html Mathematics Social Sciences Wed, 09 Oct 2024 12:54:10 EDT news647697246 Networks, which include nodes and connections, can help researchers model dynamic systems like the spread of disease or how the brain processes information. https://phys.org/news/2024-10-higher-interactions-remodel-landscape-complex.html Mathematics Wed, 02 Oct 2024 14:00:02 EDT news647079501 The theory of indirect reciprocity holds that people who earn a good reputation by helping others are more likely to be rewarded by third parties, but widespread cooperation depends on agreement about reputations. https://phys.org/news/2024-09-method-sustain-social-cooperation.html Mathematics Social Sciences Thu, 26 Sep 2024 10:28:04 EDT news646565282 Election polls often tighten up remarkably as the election date draws near. "Leave" (the European Union) won the UK election of May 2016 with a majority of 51.9%, but earlier the polls weren't nearly as tight—in January 2011 "Remain" was up by about 20 percentage points. In the 2020 presidential election in Poland, Andrzej Duda won with 51.0% of the votes, whereas he was up by about 5 percentage points just eight weeks earlier. https://phys.org/news/2024-09-large-electorates-tend-evenly-results.html Mathematics Political science Mon, 23 Sep 2024 10:00:01 EDT news646304327 Several fields of mathematics have developed in total isolation, using their own "undecipherable" coded languages. In a new study published in Proceedings of the National Academy of Sciences, Tamás Hausel, professor of mathematics at the Institute of Science and Technology Austria (ISTA), presents "big algebras," a two-way mathematical 'dictionary' between symmetry, algebra, and geometry, that could strengthen the connection between the distant worlds of quantum physics and number theory. https://phys.org/news/2024-09-mathematical-dictionary-quantum-physics-theory.html Mathematics Thu, 12 Sep 2024 10:28:58 EDT news645355732 In a world where organizing a simple meeting can feel like herding cats, new research from Case Western Reserve University reveals just how challenging finding a suitable meeting time becomes as the number of participants grows. https://phys.org/news/2024-09-mathematical-explores-statistical-mysteries-successfully.html Mathematics Mon, 09 Sep 2024 15:12:55 EDT news645113572 Darwin was puzzled by cooperation in nature—it ran directly against natural selection and the notion of survival of the fittest. But over the past decades, evolutionary mathematicians have used game theory to better understand why mutual cooperation persists when evolution should favor self-serving cheaters. https://phys.org/news/2024-09-mathematicians-puzzling-breakdown-cooperative-behavior.html Mathematics Tue, 03 Sep 2024 08:30:01 EDT news644512757 Computer graphics and geometry processing research provide the tools needed to simulate physical phenomena like fire and flames, aiding the creation of visual effects in video games and movies as well as the fabrication of complex geometric shapes using tools like 3D printing. https://phys.org/news/2024-08-framework-parabolic-partial-differential-equations.html Mathematics Wed, 28 Aug 2024 17:11:03 EDT news644083861 The summer holidays are ending, which for many concludes with a long drive home and reliance on GPS devices to get safely home. But every now and then, GPS devices can suggest strange directions or get briefly confused about your location. But until now, no one knew for sure when the satellites were in a good enough position for the GPS system to give reliable direction. https://phys.org/news/2024-08-mathematicians-debunk-gps-assumptions.html Mathematics Wed, 28 Aug 2024 13:19:04 EDT news644069941 A new applied mathematical theory could enhance our understanding of how sea ice affects global climate, potentially improving the accuracy of climate predictions. https://phys.org/news/2024-08-cold-math-hot-topic-theory.html Mathematics Tue, 27 Aug 2024 19:10:01 EDT news643978742 Mathematicians at Loughborough University have turned their attention to a fascinating observation that has intrigued scientists and cocktail enthusiasts alike: the mysterious way ouzo, a popular anise-flavored liquor, turns cloudy when water is added. https://phys.org/news/2024-08-mathematicians-secrets-ouzo-cloudy.html Mathematics Thu, 22 Aug 2024 13:27:40 EDT news643552049 Statistical analysis of classic literature has shown that the way punctuation breaks up text obeys certain universal mathematical relationships. James Joyce's tome "Finnegans Wake," however, famously breaks the rules of normal prose through its unusual, dreamlike stream of consciousness. New work in chaos theory, published in the journal Chaos, takes a closer look at how Joyce's challenging novel stands out, mathematically. https://phys.org/news/2024-08-finnegans-spacing-punctuation.html Mathematics Other Tue, 20 Aug 2024 11:00:01 EDT news643302781 In just a few months, voters across America will head to the polls to decide who will be the next U.S. president. A new study draws on mathematics to break down how humans make decisions like this one. https://phys.org/news/2024-08-biggest-biases-math.html Mathematics Political science Mon, 12 Aug 2024 11:05:40 EDT news642679532 Whether it's physical phenomena, share prices or climate models—many dynamic processes in our world can be described mathematically with the aid of partial differential equations. Thanks to stochastics—an area of mathematics which deals with probabilities—this is even possible when randomness plays a role in these processes. https://phys.org/news/2024-06-mathematical-proof-equations-random-components.html Mathematics Mon, 24 Jun 2024 08:59:03 EDT news638438341 By rapidly analyzing large amounts of data and making accurate predictions, artificial intelligence (AI) tools could help to answer many long-standing research questions. For instance, they could help to identify new materials to fabricate electronics or the patterns in brain activity associated with specific human behaviors. https://phys.org/news/2024-06-merging-ai-human-efforts-tackle.html Mathematics Mon, 24 Jun 2024 08:50:02 EDT news638437425 Direct reciprocity facilitates cooperation in repeated social interactions. Traditional models suggest that individuals learn to adopt conditionally cooperative strategies if they have multiple encounters with their partner. However, most existing models make rather strong assumptions about how individuals decide to keep or change their strategies. https://phys.org/news/2024-06-cooperation-evolve-limited-payoff-memory.html Mathematics Social Sciences Wed, 19 Jun 2024 10:33:15 EDT news638011991 Ever wondered how your friends shape your music taste? In a recent study, researchers at the Complexity Science Hub (CSH) demonstrated that social networks are a powerful predictor of a song's future popularity. By analyzing friendships and listening habits, they've boosted machine learning prediction precision by 50%. https://phys.org/news/2024-06-power-social-songs.html Mathematics Social Sciences Tue, 11 Jun 2024 10:26:03 EDT news637320362 A research article published June 10 in the Proceedings of the National Academy of Sciences highlights the importance of careful application of high-tech forensic science to avoid wrongful convictions. https://phys.org/news/2024-06-wire-forensic-unreliable-court.html Mathematics Political science Mon, 10 Jun 2024 15:00:01 EDT news637227541 How can disaster response teams benefit from understanding how people most efficiently pick strawberries together, or how they choose the perfect ice cream shop with friends? https://phys.org/news/2024-06-good-decisions-videogame.html Mathematics Social Sciences Tue, 04 Jun 2024 12:19:34 EDT news636722369