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Category: mathematics

How physics and mathematical modeling help us make better clothes

A new paper in the journal Nature Physics offers insights into the physics of liquid droplets—and while many people may not appreciate the mathematical accomplishment, they will benefit from the athletic wear and raincoats it makes possible. The recent article, “Tricky Tension,” explores the intersection of physics and textiles and how wetting is influenced by the structure of tiny individual liquid droplets.

In physics, the cohesive force between two phases is called surface tension. This allows small insects to walk on water.

In a three-phase system—where gas, liquid and solid objects all interact—there is a less-understood phenomenon called the line tension of a liquid droplet. This refers to the force acting at the boundary where the liquid droplet, the air and the solid surface on which the droplet sits all meet. Learning more about the mechanics of droplets on solid surfaces, known as sessile droplets, is important for understanding the wetting and drying of textiles, especially for very small droplets.

A scheme to verify gates of a quantum computer without examining devices

Quantum computers, systems that process information using the principles of quantum mechanics, could solve some problems that cannot be tackled by the classical computers currently used worldwide. Despite their potential, verifying that these computers are working correctly and can reliably perform computations remains challenging.

Shubhayan Sarkar, a researcher at the University of Gdansk, recently introduced a new scheme for certifying that quantum chips (unitary gates) in a quantum computer are operating correctly without relying on assumptions about their internal components. This scheme, introduced in a paper published in Physical Review Letters, uses an approach referred to as almost device-independent (DI) certification.

“Consider the computer you are using right now,” Sarkar told Phys.org. “If it provides the answer to a mathematical problem, how do you know that the computation is correct? In practice, we rarely verify every calculation ourselves.

Astronomers spot an extremely rare galaxy mega-merger

Scale in the universe is hard to understand from a purely human perspective. Many times, the math just doesn’t sit well with our brains, which evolved to capture and process data about the world around us rather than grok the complexities of stellar dynamics and galaxy mergers. But every once in a while, astronomers find something that, if we can wrap our heads around the numbers, gives a sense of just how big the universe is.

That is precisely what a new paper, available on the arXiv preprint server from a group of astronomers led by Z.L. Wen of the Chinese Academy of Sciences, hopes to do when it describes a merger of not one, not two, but six supermassive galaxies and the active dynamics they are subject to.

Admittedly, this paper isn’t the one that originally found the cluster. That was done back in 2018 by several all-sky surveys, including the Two Micron All Sky Survey, WISE and SuperCOSMOS. But it was the first to identify that the cluster contained a group of six merging galaxies at its heart. That tidbit was hidden away in Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys data.

New topology-based biomarkers may improve breast cancer prediction

For decades, pathologists have diagnosed and graded breast cancer by looking at tissue samples under a microscope, searching for telltale signs of disorder in the structure of cells and tissues. Now, researchers at Columbia and their collaborators have developed a new computational approach that transforms those visual patterns into quantitative measurements, potentially improving how clinicians predict breast cancer outcomes and choose therapies.

In a recent study published in Cancer Research, researchers used mathematical tools known as topology to develop biomarkers quantifying the organizational structure of breast cancer tissue. The approach generated continuous numerical scores that predicted patient survival and treatment response more accurately than many traditional biomarkers, while also showing less variation across racial and ethnic groups.

A new ‘library’ for Feynman integrals

Theoretical physicists at Johannes Gutenberg University Mainz (JGU) have developed a new method of ordering Feynman integrals. This critical step in making theoretical predictions for high-energy precision measurements has posed a major computational bottleneck until now.

Scientists in the research group of Professor Stefan Weinzierl from the PRISMA⁺⁺ Cluster of Excellence propose a solution to this longstanding challenge in new articles published in Physical Review Letters and Physical Review D. By ordering the integrals according to their intrinsic geometric properties, they can speed computation times by a factor of about 1,000.

“Feynman integrals are mathematical expressions that researchers must evaluate to make precise predictions,” said Weinzierl. “These are the first pillars for precise predictions for measurements at facilities like the Large Hadron Collider in Switzerland.” The number of these integrals varies from process to process, with some processes needing up to one million.

Doughnut‑shaped topology reveals new way to classify knitting, crochet and other textiles

Fabrics are made by repeatedly intertwining yarns into characteristic patterns. Many of their properties, such as stretchiness, arise not only from the material itself but also from how the yarns are arranged and entangled. Such properties illustrate how topology—the underlying patterns of connectivity and entanglement within a structure—can shape a material’s overall behavior. Understanding these relationships could help researchers design materials with tailored properties through the design of their topology.

A research team led by Dr. Daisuke S. Shimamoto, a senior researcher at the Research Organization of Science and Technology, Ritsumeikan University, Japan, along with Dr. Keiko Shimamoto, an independent researcher from Tokyo, Japan, Dr. Sonia Mahmoudi from Tohoku University, and Dr. Samuel Poincloux from Aoyama Gakuin University, has developed a mathematical framework based on knot theory for characterizing knittability and classifying periodic textile structures based on how defects spread through them. Their findings were published in Physical Review X on July 14, 2026.

DNA origami turns secret messages into nano–Morse code that acts as multiplayer molecular encryption

Mathematics has always been at the core of securing information. From online banking to government communications, modern society relies on cryptography, in which complex mathematical algorithms transform readable information into an unreadable form to keep it secure. But as computing power grows and quantum technology advances, these mathematical safeguards are increasingly vulnerable to being broken. That’s where biology stepped in.

Choosing DNA as their information protector, researchers from China developed a multilayer encryption device that takes advantage of the double-helix molecule’s programmable nature to create an origami structure that can store information with high security.

This new system used tiny, custom-built rectangular structures made of DNA, in which researchers stored the message as dots and dashes, creating a nanoscale version of Morse code. To hide the message further, they turned the flat DNA origami surfaces into tubes, physically blocking the patterns from being read or imaged. With the help of a matching unlocking key, the recipient can trigger a reaction that unrolls the DNA back to its flat form, allowing them to read and verify the message.

Testing the limits of what’s possible (and what isn’t) with AI

When can we trust the results we get from AI, and when is learning impossible? Researchers have shown that there are some problems that even the most powerful AI cannot reliably solve, no matter how much data it is given.

The researchers, from the University of Cambridge and the University of California, Santa Barbara, designed “adversarial” mathematical systems to fool any AI algorithm. Like ethical hackers stress-testing a network’s security, these adversarial systems were designed to map out exactly where and why AI prediction breaks down.

Many real-world systems—like those in the oceans, the human brain or robotics—are too complex to describe neatly with equations, so researchers often learn how they behave by using machine learning. But these AI methods don’t always work well, returning unreliable results or poor predictions.

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