https://phys.org/science-news/mathematics en-us The latest news on mathematics, math, math science, mathematical science and math technology. 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 Perpetual American strangle options (PASOs) offer investors a method for minimizing risk during highly volatile market scenarios by allowing them to buy or sell options at any date without an expiration date. In a new study, researchers investigated the pricing of PASOs under a stochastic volatility model with fast mean reversion which better captures real markets compared to traditional models. https://phys.org/news/2024-09-precise-pricing-formula-perpetual-american.html Mathematics Economics & Business Mon, 16 Sep 2024 16:48:04 EDT news645724081 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 Tiles that fill two- and three-dimensional spaces with no gaps—including triangles, squares, hexagons, cubes, and other polyhedra—are typically designed with sharp corners and flat faces (straight edges). https://phys.org/news/2024-09-soft-cells-rounded-tile-echo.html Mathematics Tue, 10 Sep 2024 13:35:02 EDT news645194101 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 The way we memorize information—a mathematical problem statement, for example—reveals the way we process it. A team from the University of Geneva (UNIGE), in collaboration with CY Cergy Paris University (CYU) and Bourgogne University (uB), has shown how different solving methods can alter the way information is memorized and even create false memories. https://phys.org/news/2024-08-mathematical-methods-affect.html Mathematics Education Fri, 30 Aug 2024 10:25:43 EDT news644232338 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 Number theoretic transform (NTT) is widely recognized as the most efficient method for computing polynomial multiplication with high dimension and integral coefficients, due to its quasilinear complexity. https://phys.org/news/2024-08-generalized-theoretic.html Mathematics Wed, 28 Aug 2024 11:59:14 EDT news644065147 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 past years, elections in the U.S. have been marked by stories of long waiting lines at the voting polls. Add other barriers, like long commutes and inadequate transportation, and voting can become inaccessible. But these voting deserts are difficult to quantify. https://phys.org/news/2024-08-topological-analysis-voting.html Mathematics Political science Mon, 12 Aug 2024 13:26:02 EDT news642687961 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 Math education outcomes in the United States have been unequal for decades. Learners in the top 10% socioeconomically tend to be about four grade levels ahead of learners in the bottom 10%—a statistic that has remained stubbornly persistent for 50 years. https://phys.org/news/2024-07-real-equity-math-good-grades.html Mathematics Education Wed, 31 Jul 2024 10:10:04 EDT news641637738 Researchers at The University of Western Australia's ARC Industrial Transformation Research Hub for Transforming Energy Infrastructure through Digital Engineering (TIDE) have made a significant mathematical breakthrough that could help transform ocean research and technology. https://phys.org/news/2024-07-mathematical-method-spectral-density-ocean.html Mathematics Fri, 05 Jul 2024 12:58:50 EDT news639403128 How can you figure out which points lie on a certain curve? And how many possible curves do you count by a given number of points? These are the kinds of questions Pim Spelier of the Mathematical Institute studied during his Ph.D. research. Spelier received his doctorate with distinction on June 12. https://phys.org/news/2024-07-mathematical-magic.html Mathematics Fri, 05 Jul 2024 11:37:02 EDT news639398221 "We wanted to investigate how second pillar pension funds react to financial crises and how to protect them from the crises," says Kaunas University of Technology (KTU) professor Dr. Audrius Kabašinskas, who, together with his team, discovered a way to achieve this goal. The discovery in question is the development of stress tests for pension funds. Lithuanian researchers were the first in the world to come up with such an adaptation of the stress tests. https://phys.org/news/2024-06-stress-pension-funds-technique-based.html Mathematics Economics & Business Wed, 26 Jun 2024 12:44:50 EDT news638624676 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 Bob Moses, who helped register Black residents to vote in Mississippi during the Civil Rights Movement, believed civil rights went beyond the ballot box. To Moses, who was a teacher as well as an activist, math literacy is a civil right: a requirement to earning a living wage in modern society. In 1982, he founded the Algebra Project to ensure that "students at the bottom get the math literacy they need." https://phys.org/news/2024-06-access-algebra-civil-rights.html Mathematics Education Thu, 20 Jun 2024 11:40:01 EDT news638099508 The purpose of education is to ensure that students acquire the skills necessary for succeeding in a world that is constantly changing. Self-assessment, or teaching students how to examine and evaluate their own learning and cognitive processes, has proven to be an effective method, and this competence is partly based on metacognitive knowledge. https://phys.org/news/2024-06-students-awareness-cognitive-math.html Mathematics Education Wed, 19 Jun 2024 13:09:03 EDT news638021342 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 The good news is that—statistically speaking—there is reason to believe Edmonton Oilers goalie Stuart Skinner will improve against the Florida Panthers in the Stanley Cup final. https://phys.org/news/2024-06-held-cognitive-illusion-hockey-goaltenders.html Mathematics Thu, 13 Jun 2024 09:09:21 EDT news637488554 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 Human society includes various minority groups. However, it is often difficult to know whether someone is a minority member simply by looking at the person, as minority traits may not be visually apparent (e.g., sexual orientation, color vision deficiency). In addition, minorities may hide their minority traits or identities. Consequently, we may have been unaware of the presence of minorities in daily life. Probabilistic thinking is critical in such uncertain situations. https://phys.org/news/2024-06-people-underestimate-probability-minority-member.html Mathematics Social Sciences Wed, 05 Jun 2024 15:09:40 EDT news636818978 The classic "secretary problem" involves interviewing job candidates in a random order. Candidates are interviewed one by one, and the interviewer ranks them. After each interview, the interviewer must either accept or reject the candidate. If they accept a candidate, the process stops; otherwise, the next candidate is interviewed and so on. https://phys.org/news/2024-06-decision-analysis-variant-classical-secretary.html Mathematics Economics & Business Tue, 04 Jun 2024 14:53:03 EDT news636731582