Phys.org Mathmatics

• Mathematical framework uncovers key to decoupling economic growth from pollution in developing countries

  Balancing environmental conservation with economic progress is one of the most pressing challenges of our time. This is particularly difficult for many developing countries, which urgently need to lift their populations out of poverty while grappling with the increasing degradation of their environment. Unfortunately, a common belief is that these nations have to choose between economic growth and a clean environment—a situation made more complex by their reliance on foreign aid.

• How do we get more Year 12s doing math?

  Mathematics has been the broccoli of school subjects for generations of Australian teenagers.

• A hidden simplicity behind how people move: Study reveals geography's role in relocation

  In a new paper, published in Nature Human Behaviour, scientists from DTU (the Technical University of Denmark) examine how geography shapes human mobility and propose a way to separate physical constraints from behavioral patterns. A result that may improve urban planning, transportation design as well as epidemiology models.

• Breaking the code in network theory: Bimodularity reveals direction of influence in complex systems

  As summer winds down, many of us in continental Europe are heading back north. The long return journeys from the beaches of southern France, Spain, and Italy once again clog alpine tunnels and Mediterranean coastal routes during the infamous Black Saturday bottlenecks. This annual migration, like many systems in our world, forms a network—not just of connections, but of communities shaped by shared patterns of origin and destination.

• Q&A: Math education and the importance of memory and problem solving

  From classrooms to kitchen tables, debates about math education are never far away. Should teachers drill multiplication facts or encourage creative strategies to solve problems? The answer, especially among educators, is constantly evolving.

• Using game theory to explain how institutions arise naturally to manage limited resources

  A simple model developed by a RIKEN researcher and a collaborator predicts the emergence of self-organized institutions that manage limited resources such as fisheries or irrigation water. This model provides a window into the mechanism behind the emergence of such institutions. The results are published in PNAS.

• Self-reinforcing cascades: How ideas, beliefs, and innovations spread in the digital age

  It might start as a joke, a belief, or a rumor. At first, it's easy to dismiss. But then it gains a twist, builds momentum, and spreads like wildfire. What causes some ideas to die out while others take over the internet?

• Cities obey the same laws of living systems, researchers claim

  An EPFL study has found that urban areas follow the same universal rules observed in the natural world. From population size to carbon emissions and road networks—could the key to sustainable urbanization lie in the very "metabolism" of our cities?

• A universal rhythm guides how we speak: Global analysis reveals 1.6-second 'intonation units'

  Have you ever noticed that a natural conversation flows like a dance—pauses, emphases, and turns arriving just in time? A new study has discovered that this isn't just intuition; there is a biological rhythm embedded in our speech.

• The poetry of ancient math

  Add zero and one to get one, one and one to get two, one and two to get three, two and three to get five. Most of us know this—that each successive number is the sum of the two numbers that came before it—as the Fibonacci sequence, named after a 12th-century Italian mathematician. But as early as 200 BCE, an Indian poet and mathematician named Acharya Pingala used that sequential concept to analyze poetry, and 7th-century scholar Virahanka later described it in more detail.

• Catching a 'eureka' before it strikes: New research spots the signs

  They feel like lightning—sudden, brilliant and seemingly impossible to predict. But according to new research, those mind-flashing "aha" moments of insight may leave detectable traces before they strike.

• The shape of the universe revealed through algebraic geometry

  How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the mathematicians Claudia Fevola from Inria Saclay and Anna-Laura Sattelberger from the Max Planck Institute for Mathematics in the Sciences, recently published in the Notices of the American Mathematical Society.

• Numerical simulations characterize 'matrix tides' and other complex wave patterns seen in Qiantang River

  During 2024, onlookers observed a startling sight on China's Qiantang River: waves forming a grid-like pattern. Dubbed the "matrix tide," this complex wave pattern was caused by the river's famed tidal bores that surge upstream against the current. Specifically, two shockwave-like tidal bores, known as undular bores, spread along two different directions like ripples on a pond and collided with each other.

• Students' image tool offers sharper signs, earlier detection in the lab or from space

  A group of UBC Okanagan students has helped create technology that could improve how doctors and scientists detect everything from tumors to wildfires.

• How do scientists estimate crowd sizes at public events—and why are they often disputed?

  Last Sunday, tens of thousands marched across the Sydney Harbor Bridge in support of Gaza. But exactly how many people were there depends on whom you ask.

• Mathematical proof provides new perspectives on the effects of blending

  What happens when things combine? This question lies at the heart of the Borell-Brascamp-Lieb inequality (BBL), a mathematical relation widely applied across many fields of mathematics, science and beyond.

• Beyond words: Study maps the cognitive force of metaphor

  Metaphors are a fundamental aspect of human language and cognition, allowing us to understand complex concepts and relationships by mapping them onto more familiar and concrete domains. However, the nature of metaphors and how they work is still not well understood.

• Scientists find 'speed limit' for innovation networks to prevent system collapse

  Research shows that while connections between innovations speed discovery, they also sharply increase the risk of total system collapse—with the sweet spot for sustainable innovation proving surprisingly narrow.

• Searching for Artificial Memory Systems in ancient humans with spatial statistics

  Université de Bordeaux-led research reports that spatial statistics can discriminate potential Paleolithic Artificial Memory Systems from butchery and art, aligning prehistoric marked objects with memory devices in Africa and Europe.

• Comparing baseball greats across eras, who comes out on top?

  An interdisciplinary study co-authored by researchers from the statistics and history departments at the University of Illinois Urbana-Champaign introduces a novel statistical framework for comparing baseball players across different eras.

• Humans beat AI at international math contest despite gold-level AI scores

  Humans beat generative AI models made by Google and OpenAI at a top international mathematics competition, despite the programs reaching gold-level scores for the first time.

• Mathematicians reveal factors driving gun sales in America

  As gun sales in the United States continue to soar, researchers at Georgia State University have uncovered insights into what drives Americans to buy firearms. A new study published in PNAS Nexus journal reveals the complex interaction among media coverage, social media activity and firearm purchases.

• Mathematical model clarifies scaling regimes in Lagrangian turbulence evolution

  A sneeze. Ocean currents. Smoke. What do these have in common? They're instances of turbulence: unpredictable, chaotic, uneven fluid flows of fluctuating velocity and pressure. Though ubiquitous in nature, these flows remain somewhat of a mystery, theoretically and computationally.

• I'm a statistics professor who became embroiled in the world of online chess drama

  As a mild-mannered statistics professor, it's not often that I get contacted directly by the CEO of a multi-million-dollar company, much less regarding allegations of cheating and malfeasance among world champions.

• Hybrid model reveals people act less rationally in complex games, more predictably in simple ones

  Throughout their everyday lives, humans are typically required to make a wide range of decisions, which can impact their well-being, health, social connections, and finances. Understanding the human decision-making processes is a key objective of many behavioral science studies, as this could in turn help to devise interventions aimed at encouraging people to make better choices.