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Category: mathematics – Page 2

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.

‘Silly sprinklers’ put in reverse to further unravel decades-old physics puzzle

Each summer, lawns are marked by a familiar addition: “silly sprinklers,” whose loops and spirals spew water in creative ways. While seemingly frivolous in their construction, a team of mathematicians has used their design to address a long-standing mystery surrounding the laws of physics.

For decades, scientists have been trying to solve Feynman’s Sprinkler Problem: How does a sprinkler running in reverse—in which the water flows into the device rather than out of it—work? Through a series of experiments on custom-designed sprinklers with different shapes, the researchers arrived at a clear answer and, more generally, determined how flowing fluids exert forces and move structures.

“This work provides the experimental answer for Feynman’s Sprinkler Problem by showing, across several sprinkler types, how the angular momentum of water flows drives sprinklers’ rotation,” explains Leif Ristroph, an associate professor at New York University’s Courant Institute School of Mathematics, Computing, and Data Science and the senior author of the paper, which appears in the journal Proceedings of the National Academy of Sciences.

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