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Category: mathematics – Page 3

Fast but error-prone AI assists in solving a decades-old fluid mechanics problem in five weeks

An AI assistant helped University of Colorado Boulder researchers solve a mathematical problem that had challenged their lab for a year and a half, though it made subtle errors along the way. The breakthrough could improve how scientists study nanoparticles—tiny particles about 1,000 times thinner than a human hair—but it reveals both the promise and limitations of AI as a scientific research partner.

The new study, published in the Journal of Fluid Mechanics, details the solution to a decades-old fluid mechanics problem and explains how researchers combined AI with human expertise to reach the answer.

The research was led by Ankur Gupta, an assistant professor of chemical and biological engineering, and his graduate student, Arkava Ganguly, who spent a year and a half working on the problem. With help from Anthropic’s Claude AI, they discovered that changing a nanoparticle’s shape, such as by stretching it from a circle to a football shape, changes how fast it moves in an electric field, while adding finer features, such as bumps or ripples, does not.

How high scores in an online brain teaser made mathematicians lie for three years

It might not yet be the phenomenon that is Wordle, but for hundreds of thousands of players, Digit Party has scratched the itch of a casual brain teaser to break up their day.

Players arrange numbers on a 5-by-5 grid, earning points whenever identical numbers touch on adjacent or diagonally connected squares. They can then compare their score to the puzzle’s maximum score that the game spits out at the end of a round.

There’s just one problem: The game was lying. Or rather, its creators were. For more than three years, Vincent Vatter, Ph.D., at the University of Florida and Robert Brignall, Ph.D., at The Open University in the United Kingdom didn’t know how to calculate the true high scores.

IIoT Platform Consolidation: Schneider’s $3.1B Cognite Bet

Schneider Electric agreed to pay $3.1 billion, roughly 18 times 2025 revenue, for Cognite, an industrial data and AI software company with $170 million in revenue. Cognite will be absorbed into AVEVA CONNECT, folding a third independent IIoT data layer under one corporate roof. The deal reflects real growth math: AI-driven industrial analytics is expanding more than 40% annually while core automation hardware grows in single digits. It also means buyers get fewer independent vendors to negotiate with.

IIoT platform consolidation just got an explicit price tag, and it’s steep enough to explain why the wave of industrial software acquisitions isn’t slowing down. Schneider Electric agreed to acquire Cognite Holding B.V. in an all-cash transaction valued at $3.1 billion, adding industrial data contextualization and agentic AI capabilities to its automation business, according to Drives&Controls’ coverage of the announcement. Cognite reported revenue exceeding $170 million in 2025. That price works out to roughly 18 times revenue, a multiple that says more about where the growth is than about Cognite’s current size.

Cognite’s core technology, a unified data model and knowledge graph called Data Fusion, plus an agentic layer called Atlas AI, will be absorbed directly into AVEVA’s CONNECT platform once the deal closes, according to ARC Advisory Group’s analysis. IIoT platform consolidation at this price only makes financial sense against IoT Analytics’ 2026 finding that AI-driven applications and advanced analytics are growing more than 40% annually from a smaller base, compared with single-digit growth for core industrial hardware and established automation segments. Schneider isn’t paying for Cognite’s current revenue. It’s paying to own the fastest-growing layer of the stack before someone else does.

New Monte Carlo method accelerates simulations of densely entangled polymer melts

Long polymer chains are everywhere: in synthetic materials, soft matter, biological systems such as chromosomes, and mathematical models of filaments and knots. When many such chains are densely packed, they form what physicists call a polymer melt. In this crowded environment, each chain is constrained by the others around it. These entanglements are central to the behavior of polymeric materials, but they also make the systems extremely difficult to simulate. As chain length increases, the time needed to obtain a new independent configuration grows very rapidly. For very large systems, conventional simulations can therefore become computationally prohibitive.

For more than 70 years, scientists have used many “tricks” to speed up this process, including so-called Monte Carlo methods with ingenious moves designed to accelerate the evolution of the system. These methods helped, but the basic problem remained: In a dense melt, changes still had to propagate through a highly tangled system, slowing down the simulation.

A New Quantum Blueprint Could Make States Easier To Tell Apart

MIT and University of Ferrara researchers created a mathematical blueprint for designing distinguishable non-Gaussian quantum states.

Researchers worldwide are working to develop quantum systems for sensing, communications, computing, and control that could outperform today’s technologies. A major challenge is creating quantum states that are stable, measurable, and easy to distinguish, since these states are the foundation of any practical quantum device.

Quantum states have unique characteristics that make them attractive for advanced information processing. However, achieving both stability and distinguishability remains difficult. Recovering information from a quantum system depends on how well its quantum states can be distinguished, a property tied to orthogonality. Because no two Gaussian states (a widely studied class of quantum states) are orthogonal, some level of error is unavoidable when trying to tell them apart.

New Technique Could Slash AI’s Memory Energy Use by Thousands of Times

The microscopic magnetic flips behind digital memory could soon use thousands of times less energy, offering a new way to shrink AI’s rapidly growing power footprint.

Artificial intelligence is creating and processing data on an enormous scale. Searches, recommendations, generated images, scientific simulations, and large language models all depend on information that must be repeatedly stored, transferred, retrieved, and rewritten. Each operation consumes energy, and those costs multiply across the billions of devices and sprawling data centers that support the digital world.

Researchers at the University of Edinburgh have now developed a mathematical framework designed to slash the energy required to write information in future magnetic memory. Rather than creating a new memory material, the approach changes how the magnetic state representing a digital bit is flipped.

Universal pattern revealed in quantum matter

When different materials transition from one phase to another, such as water coming to a boil or a magnet losing its ability to attract metals, something remarkable can happen: They begin to behave identically, following the same mathematical rules. “Physicists call this trait universality—the messy, microscopic details wash out and only a few essential features survive,” explains Jason Alicea, William K. Davis Professor of Theoretical Physics. The math underlying these universal traits is commonly described by a theoretical framework called conformal field theory.

Reporting in the journal Nature, a collaboration between the experimental group of Caltech’s Manuel Endres, professor of physics, and Alicea’s theory group, together with theorists at Université Paris-Saclay and the Technical University of Munich, performed first-of-their-kind experiments on two different conformal field theories using quantum simulators, which are simplified versions of quantum computers tailored for specific tasks.

Using new technology developed for these quantum simulators, the team reports the first direct measurement of energy levels in synthetic quantum matter as predicted by the Ising and tricritical Ising conformal field theories. (Ising refers to Ernst Ising, a physicist who, in the 1920s, solved an early model of magnetism.) Both theories describe universal behavior that emerges when a quantum system—exhibiting exotic traits such as entanglement and superposition—is placed at a tipping point between two states, one of which is more ordered than the other.

Long-range magnetic interactions govern how a ferrimagnet approaches its phase transition

Close to a phase transition, very different materials can follow the same mathematical rules. The concept of universality, which groups seemingly distinct systems based on their common properties, was developed to describe this phenomenon.

In magnetic systems, ferromagnets, ferrimagnets and antiferromagnets fall into the same universality class when short-range interactions dominate and their spatial and spin dimensionalities coincide. However, this universality has not been established when long-range interactions dominate.

In insulating magnets, long-range coupling may originate from dipole-dipole interactions. However, dipolar-driven mean-field criticality has only been firmly established in ferromagnets, leaving the ferrimagnetic and antiferromagnetic cases unexplored.

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