https://phys.org/science-news/mathematics en-us The latest news on mathematics, math, math science, mathematical science and math technology. Number theory, the study of the properties of positive integers, is perhaps the purest form of mathematics. At first sight, it may seem far too abstract to apply to the natural world. In fact, the influential American number theorist Leonard Dickson wrote, "Thank God that number theory is unsullied by any application." https://phys.org/news/2023-08-scientists-uncover-theory-evolutionary-genetics.html Mathematics Tue, 01 Aug 2023 12:26:44 EDT news610111601 Around the world, political violence increased by 27% last year, affecting 1.7 billion people. The numbers come from the Armed Conflict Location & Event Data Project (ACLED), which collects real-time data on conflict events worldwide. https://phys.org/news/2023-08-scientists-method-armed-conflicts.html Mathematics Political science Tue, 01 Aug 2023 12:26:35 EDT news610111592 In addition to describing biological interactions, evolutionary theory has also become a valuable tool to make sense of the dynamics of social norms. Social norms determine which behaviors should be regarded as positive, and how community members should act towards each other. https://phys.org/news/2023-07-evolution-double-sided-social-norms-cooperative.html Mathematics Social Sciences Thu, 27 Jul 2023 12:05:18 EDT news609678315 In the quest to unravel the underlying mechanisms of natural systems, accurately identifying causal interactions is of paramount importance. Leveraging the advancements in time-series data collection through cutting-edge technologies, computational methods have emerged as powerful tools for inferring causality. https://phys.org/news/2023-07-gobi-breakthrough-package-inferring-causal.html Mathematics Tue, 25 Jul 2023 09:39:36 EDT news609496773 In the face of existential dilemmas that are shared by all of humanity, including the consequences of inequality or climate change, it is crucial to understand the conditions leading to cooperation. A new game theory model developed at the Institute of Science and Technology Austria (ISTA) based on 192 stochastic games and on some elegant algebra finds that both cases—available information and the lack thereof—can lead to cooperative outcomes. https://phys.org/news/2023-07-game-theory-people-decisions-environments.html Mathematics Social Sciences Mon, 24 Jul 2023 09:31:05 EDT news609409862 Everyone knows that 2 + 2 = 4, but why do we have arithmetic in the first place, and why is it true? Researchers at the University of Canterbury have recently answered these questions by "reverse engineering" arithmetic from a psychological perspective. To do this, they considered all possible ways that quantities could be combined, and proved (for the first time in mathematical terms) that addition and multiplication are the simplest. https://phys.org/news/2023-07-psychological-arithmetic-biologically-based-natural-consequence.html Mathematics Social Sciences Tue, 18 Jul 2023 11:10:40 EDT news608897439 Putting off college math could improve the likelihood that students remain in college. But that may only be true as long as students don't procrastinate more than one year. This is what colleagues and I found in a study published in 2023 of 1,119 students at a public university for whom no remedial coursework was required during their first year. https://phys.org/news/2023-07-college-math-good-idea.html Mathematics Education Mon, 10 Jul 2023 12:48:03 EDT news608212082 Board games based on numbers, like Monopoly, Othello and Chutes and Ladders, make young children better at math, according to a comprehensive review of research published on the topic over the last 23 years. https://phys.org/news/2023-07-board-games-boost-math-ability.html Mathematics Education Fri, 07 Jul 2023 00:00:01 EDT news607862535 Life, from the perspective of thermodynamics, is a system out of equilibrium, resisting tendencies towards increasing their levels of disorder. In such a state, the dynamics are irreversible over time. This link between the tendency toward disorder and irreversibility is expressed as the 'arrow of time' by the English physicist Arthur Eddington in 1927. https://phys.org/news/2023-07-team-solution-temporal-asymmetry.html Mathematics Wed, 05 Jul 2023 10:44:52 EDT news607772689 Recently, an international team of four, that includes Cheriton School of Computer Science professor Dr. Craig Kaplan, discovered a single shape that tiles the plane—an infinite, two-dimensional surface—in a pattern that can never be made to repeat. https://phys.org/news/2023-07-tiles-plane-aperiodically.html Mathematics Wed, 05 Jul 2023 10:08:23 EDT news607770498 It's a dilemma that many a regular bettor probably faces often—deciding when to place a sports bet. In a study entitled, "A statistical theory of optimal decision-making in sports betting," Jacek Dmochowski, Associate Professor in the Grove School of Engineering at The City College of New York, provides the answer. His original finding appears in the journal PLOS One. https://phys.org/news/2023-06-science-sports.html Mathematics Social Sciences Thu, 29 Jun 2023 10:51:11 EDT news607254669 Children do better at math when music is a key part of their lessons, an analysis of almost 50 years of research on the topic has revealed. https://phys.org/news/2023-06-combining-math-music-higher-scores.html Mathematics Education Thu, 29 Jun 2023 00:00:01 EDT news607180274 In a time of income inequality and ruthless politics, people with outsized power or an unrelenting willingness to browbeat others often seem to come out ahead. https://phys.org/news/2023-06-game-theory-bullies.html Mathematics Social Sciences Tue, 27 Jun 2023 13:57:04 EDT news607093021 Making history with 42 digits, scientists at Paderborn University and KU Leuven have unlocked a decades-old mystery of mathematics with the so-called ninth Dedekind number. https://phys.org/news/2023-06-ninth-dedekind-scientists-long-known-problem.html Mathematics Mon, 26 Jun 2023 15:25:04 EDT news607011901 Do you know someone who knows someone? We have all played this game, often to be amazed that despite the extreme scale of human society, random people can be linked through very small chains of acquaintances—typically, around six. Recently, a group of researchers from across the globe discovered that this magic of six degrees can be explained mathematically. The intriguing phenomenon, they show, is linked to another social experience we all know too well—the struggle of cost vs. benefit in establishing new social ties. https://phys.org/news/2023-06-veracity-degrees.html Mathematics Social Sciences Mon, 26 Jun 2023 13:11:32 EDT news607003887 On June 23, 1993, the mathematician Andrew Wiles gave the last of three lectures detailing his solution to Fermat's last theorem, a problem that had remained unsolved for three and a half centuries. Wiles' announcement caused a sensation, both within the mathematical community and in the media. https://phys.org/news/2023-06-mathematicians-bridges-discipline-fermat-theorem.html Mathematics Thu, 22 Jun 2023 16:54:13 EDT news606671649 In a new study, researchers of the Complexity Science Hub highlight the connecting elements between traditional financial market research and econophysics. "We want to create an overview of the models that exist in financial economics and those that researchers in physics and mathematics have developed so that everybody can benefit from it," explains Matthias Raddant from the Complexity Science Hub and the University for Continuing Education Krems. https://phys.org/news/2023-06-bridging-traditional-economics-econophysics.html Mathematics Economics & Business Mon, 19 Jun 2023 13:51:03 EDT news606401461 When faced with difficult choices, we often rank the alternatives to see how they stack up. This approach is ubiquitous, used from major business and policy decisions, through to personal choices such as the selection of a university course, place to live, or political voting preference. https://phys.org/news/2023-06-decisionsusing-scoring.html Mathematics Economics & Business Fri, 16 Jun 2023 12:42:03 EDT news606138121 In science, the explanation with the fewest assumptions is most likely to be true. Called "Occam's Razor," this principle has guided theory and experiment for centuries. But how do you compare between abstract concepts? https://phys.org/news/2023-06-sharpening-occam-razor-perspective-complexity.html Mathematics Wed, 14 Jun 2023 03:58:09 EDT news605933877 Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title "On the invariant subspace problem in Hilbert spaces." The paper is just 13 pages long and its list of references contains only a single entry. https://phys.org/news/2023-06-mathematician-invariant-subspace-problem.html Mathematics Mon, 12 Jun 2023 13:20:01 EDT news605794272 David Smith, a retired print technician from the north of England, was pursuing his hobby of looking for interesting shapes when he stumbled onto one unlike any other in November. https://phys.org/news/2023-06-uk-hobbyist-stuns-math-world.html Mathematics Sat, 10 Jun 2023 05:56:07 EDT news605595358 An international team led by researchers at Nankai University in China and at University of Zagreb in Croatia, along with team at the Institut national de la recherche scientifique (INRS) in Canada, led by Roberto Morandotti has made an important breakthrough in the study of topological phases. Their findings were recently published in Nature Physics. https://phys.org/news/2023-06-global-symmetry-topological-boundary-states.html Mathematics Thu, 08 Jun 2023 12:23:10 EDT news605445777 Cooperation is a guiding principle of everyday life. It's as simple as following the rules of the road when driving or holding a door for a stranger; cooperation is a fundamental aspect of human societies and has long intrigued evolutionary biologists. But how do people reach a consensus on whether, and with whom, to cooperate? https://phys.org/news/2023-06-exploring-community-based-social-norms-evolve.html Mathematics Social Sciences Thu, 08 Jun 2023 12:21:47 EDT news605445703 A George Washington University research team has created a novel formula that demonstrates how, why, and when hate speech spreads throughout social media. The researchers put forth a first-principles dynamical theory that explores a new realm of physics in order to represent the shockwave effect created by bigoted content across online communities. https://phys.org/news/2023-06-online-speech-shockwave-formula.html Mathematics Social Sciences Tue, 06 Jun 2023 16:50:41 EDT news605289039 In the 18th century, the philosopher David Hume observed that induction—inferring the future based on what's happened in the past—can never be reliable. In 1997, SFI Professor David Wolpert with his colleague Bill Macready made Hume's observation mathematically precise, showing that it's impossible for any inference algorithm (such as machine learning or genetic algorithms) to be consistently better than any other for every possible real-world situation. https://phys.org/news/2023-06-implications-no-free-lunch-theorems.html Mathematics Mon, 05 Jun 2023 13:32:21 EDT news605190738 Researchers at the Universidad Carlos III de Madrid (UC3M) and the Universidad Complutense de Madrid (UCM) have discovered a phase shift between chaotic states that can appear in herds of animals and, in particular, in swarms of insects. This advance may help to better understand their behavior or be applied to the study of the movement of cells or tumors. https://phys.org/news/2023-06-butterfly-chaos-effect-swarms-herds.html Mathematics Mon, 05 Jun 2023 10:57:09 EDT news605181424 Mathematicians from Yorkshire University, the University of Cambridge, the University of Waterloo and the University of Arkansas have one-upped themselves by finding a close relative of "the hat," a unique geometric shape that does not repeat itself when tiled, that is a true chiral aperiodic monotile. David Smith, Joseph Samuel Myers, Craig Kaplan and Chaim Goodman-Strauss have published a paper outlining their new find on the arXiv preprint server. https://phys.org/news/2023-06-aperiodic-tile-hat-true-chiral.html Mathematics Fri, 02 Jun 2023 10:00:56 EDT news604918848 Australian students' performance and engagement in mathematics is an ongoing issue. https://phys.org/news/2023-05-whiteboard-random-groups-simple-students.html Mathematics Education Wed, 31 May 2023 11:10:04 EDT news604749153 Consider an auction. You have two types of main protagonists or agents: a seller (or auctioneer) and many potential buyers. There are, of course, certain ground rules. For instance, one objective may be to design the auction in such a way that the person buying the item(s) up for sale is the buyer "who values that good the most." https://phys.org/news/2023-05-exploring-compellingness-mechanism.html Mathematics Economics & Business Fri, 26 May 2023 13:13:43 EDT news604325621 Theoretical string theory in theoretical physics predicts the existence of parallel worlds (mirror symmetry prediction). These two worlds (A-side and B-side) are supposed to differ in terms of the six-dimensional spaces (A and B) hidden in each world. https://phys.org/news/2023-05-theoretical-proof-parallel-world-extremely.html Mathematics Fri, 19 May 2023 12:51:54 EDT news603719513