Phys.org Mathmatics

• Natural language found more complex than it strictly needs to be—and for good reason

  Human languages are complex phenomena. Around 7,000 languages are spoken worldwide, some with only a handful of remaining speakers, while others, such as Chinese, English, Spanish and Hindi, are spoken by billions. Despite their profound differences, they all share a common function: they convey information by combining individual words into phrases—groups of related words—which are then assembled into sentences. Each of these units has its own meaning, which in combination ultimately form a comprehensible whole.

• Consensus, bias and polarization: How mathematicians study opinions

  How do opinions form and change in large groups of people? That's not just a sociological question, it's a mathematical one. Ph.D. candidate Federico Capannoli studied opinion dynamics. He defended his thesis on November 19.

• Mapping out the hidden mechanics behind why some fads spread like wildfire

  Whether it is a whole friendship group migrating to using iPhones or a swath of classmates wanting the latest Lululemon waterbottle, network scientists have uncovered the hidden mechanics behind social trends.

• One university boosted gender diversity in advanced math by more than 30% in five years—here's how

  As the artificial intelligence (AI) and quantum computing industries explode, trained STEM professionals are in high demand. Mathematics is foundational to these fields.

• Study describes how K-12 teachers used a virtual environment to explore mathematical concepts

  When Old Town High School Math Teacher Kristen Thompson uses TriO—a virtual reality environment developed by researchers at the University of Maine—she envisions a scenario that every teacher dreams about for their students: constant collaboration.

• Interpreting the world through statistics

  If there's one thing that's certain in a digital world, it's that we are surrounded by ever-increasing amounts of data. From your daily step counts to weather reports to global market trends, data is everywhere.

• Algorithm finds smallest dataset that guarantees optimal solutions to complex problems

  Determining the least expensive path for a new subway line underneath a metropolis like New York City is a colossal planning challenge—involving thousands of potential routes through hundreds of city blocks, each with uncertain construction costs. Conventional wisdom suggests extensive field studies across many locations would be needed to determine the costs associated with digging below certain city blocks.

• Is it time to rethink the value of AFL Draft picks?

  With AFL clubs preparing for the Draft, Victoria University (VU) researchers are proposing a new approach to trade draft picks based on their true value according to teams' future performances.

• AI math genius delivers 100% accurate results

  At the 2024 International Mathematical Olympiad (IMO), one competitor did so well that it would have been awarded the Silver Prize, except for one thing: it was an AI system. This was the first time AI had achieved a medal-level performance in the competition's history. In a paper published in the journal Nature, researchers detail the technology behind this remarkable achievement.

• Robust 'Huber mean' for geometric data protects against noise and outliers

  In an era driven by complex data, scientists are increasingly encountering information that doesn't lie neatly on flat, Euclidean surfaces. From 3D medical scans to robot orientations and AI transformations, much of today's data lives on curved geometric spaces, called Riemannian manifolds. Analyzing such data accurately has remained a challenge, especially when noise or outliers distort results.

• Diverse particles form identical geometric patterns when confined, model reveals

  Particles as different as soap bubbles and ball bearings can be made to arrange themselves in exactly the same way, according to a new study that could unlock the creation of brand new materials—including those with promising biomedical applications.

• Scientists find evolutionary explanation for 'irrational' dread risk behavior

  The evolution of the so-called dread risk response has been explained by new research. People often respond to low-probability, high-consequence events like terror attacks or nuclear accidents with a dread risk response. This intense fear of the perceived sources of dread leads to extreme avoidance behavior, which often means that people expose themselves to higher risk of dying in more common incidents like traffic accidents.

• How number systems shape our thinking, and what this means for learning, language and culture

  Most of us have little trouble working out how many milliliters are in 2.4 liters of water (it's 2,400). But the same can't be said when we're asked how many minutes are in 2.4 hours (it's 144).

• Personal resource banks help new math teachers bridge theory and classroom practice

  Teacher education often receives criticism for being too theoretical. Many students lack more training in how to teach in practice when they enter schools. They now receive this at the University of Agder (UiA) through Amalie Sødal's teaching.

• Not-so-model behavior: Popular software tools may give faulty forecasts

  Some of the models used to forecast everything from financial trends to animal populations in an ecosystem are incorrect, according to an Idaho State University statistician.

• Q&A: How mathematics can reveal the depth of deep learning AI

  Artificial intelligence (AI) is increasingly prevalent, integrated into phone apps, search engines and social media platforms as well as supporting myriad research applications. Of particular interest in recent decades is a type of AI machine learning called deep learning, which has a structure inspired by the neural networks of the human brain.

• Unit-free theorem pinpoints key variables for AI and physics models

  Machine learning models are designed to take in data, to find patterns or relationships within those data, and to use what they have learned to make predictions or to create new content. The quality of those outputs depends not only on the details of a model's inner workings but also, crucially, on the information that is fed into the model.

• A rushed new math curriculum doesn't add up. The right answer is more time

  If the recent news of a new mathematics and statistics curriculum for years 0–10 felt familiar, that's because it was.

• How the Mayans were able to accurately predict solar eclipses for centuries

  The Maya Civilization, from Central America, was one of the most advanced ancient civilizations, known for its significant achievements in astronomy and mathematics. This includes accurate calendars and detailed celestial records, but scientists don't fully understand all the details of their calculations. However, new research is shedding light on how they predicted future eclipses with remarkable accuracy.

• Declining rates of high-level math in VCE contributing to nation's widening skills gap

  Australia's engineering skills gap and labor shortage is the highest it's been for more than a decade. New Swinburne research could explain why.

• Human ingenuity outpaces AI in finding new 'kissing number' bounds

  How many coins can touch one coin, or how many basketballs can "kiss" one basketball at the same time? This seemingly playful question lies at the heart of the famous kissing number problem, a mathematical riddle that becomes almost supernaturally difficult to work out in dimensions beyond 4D. Despite its whimsical name, similar problems have practical applications in areas such as mobile communications and satellite navigation.

• Using math to ensure AI systems can operate safely

  As artificial intelligence (AI) takes on increasingly critical roles—from managing power grids to piloting autonomous vehicles—making sure these systems are safe has never been more important. But how can we be certain that the AI controlling them can be trusted?

• Algorithmic outreach can lead to information inequality

  Algorithms that identify influential people in social networks can help maximize the reach of messages, but a modeling study published in PNAS Nexus shows that those same algorithms can disseminate information inequitably, potentially exacerbating existing social inequalities.

• A mathematical 'Rosetta Stone' translates and predicts the larger effects of molecular systems

  Penn Engineers have developed a mathematical "Rosetta Stone" that translates atomic and molecular movements into predictions of larger-scale effects, like proteins unfolding, crystals forming and ice melting, without the need for costly, time-consuming simulations or experiments. That could make it easier to design smarter medicines, semiconductors and more.

• Time-delay snapshots enable scientists to identify dynamics in chaotic systems

  Many of the world's most important systems, such as the atmosphere, turbulent fluids, and even the motion of planets, behave unpredictably due to chaos and noise. Scientists often study these systems through their "invariant" measures, long-term statistical behaviors, rather than individual paths. While useful, these measures have a fundamental limitation: completely different systems can share the same statistics, making it impossible to identify the underlying dynamics.