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Category: mathematics

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.

Sia Performs “Unstoppable” To Close the 2025 Breakthrough Prize Ceremony

Multi-platinum recording artist Sia closed the Breakthrough Prize ceremony with an inspiring rendition of “Unstoppable” as all prize laureates returned to the stage to a standing ovation.
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The eleventh Breakthrough Prize awards celebrated outstanding scientific achievements, honoring scientists driving remarkable discoveries in gene editing, human diseases, the search for the fundamental laws of the Universe and pure mathematics. Held at the Barker Barker Hangar in Santa Monica, CA, presentations were given by Christina Aguilera, Drew Barrymore, MrBeast, Lily Collins, Vin Diesel, Jodie Foster, Gal Gadot, Salma Hayek Pinault, Ke Huy Quan, Gayle King, Edward Norton, Gwyneth Paltrow, Seth Rogen, Lauren Sanchez, Jeremy Strong, will.i.am, and more. With live performances by Katy Perry and Sia. Continued at https://breakthroughprize.org/News/92.

Full show: • 2025 Breakthrough Prize Ceremony: Full Show.

https://breakthroughprize.org

‘Complex numbers are not needed for quantum mechanics’: Physicists develop quantum model that uses only ‘real’ numbers for first time ever

For the first time, physicists have built a working version of quantum mechanics without complex numbers — numbers that have been considered essential to the theory for nearly a century.

Complex numbers combine a regular “real” number with an “imaginary” one — a multiple of the square root of-1, represented by the symbol i — into a single value, like 3 + 4i. The square root of-1 doesn’t correspond to any quantity you could count or measure directly (you can’t have negative one apple, for instance), which is why mathematicians call it imaginary.

Is AI making us stupid?

Not exactly—but how we use it matters.

A new Trends in Cognitive Sciences perspective argues that AI doesn’t inherently erode human intelligence. Instead, it highlights a well-known principle in cognitive psychology: cognitive offloading.

When we let AI perform tasks that require reasoning, writing, memory, or problem-solving, we reduce the amount of mental practice our brains receive. Like physical exercise, cognitive skills strengthen through use and weaken through disuse.

Skills: learned abilities such as writing, mathematical reasoning, diagnosis, or programming. These are most vulnerable if AI consistently replaces the learning process.

Basic cognitive abilities: foundational functions like working memory, attention, and executive control. Current evidence suggests these may be more resistant to decline, although more research is needed.

The key message isn’t that AI makes people “stupid.” Rather: AI can improve immediate performance. Overreliance may reduce long-term learning and skill retention.

AI is most beneficial when it augments human thinking instead of replacing it. This fits with decades of neuroscience showing that practice drives neuroplasticity. The brain adapts to the cognitive demands we place on it. If.

Continue reading “Is AI making us stupid?” | >

New test certifies quantum measurements that simpler methods cannot mimic

Proving that one quantum measurement is more powerful than another has long been difficult. Physicists from Heinrich Heine University Düsseldorf, Lund University and the University of Innsbruck have now developed and demonstrated a simple technique to certify that a certain class of measurements has properties that cannot be mimicked by simpler means. Their paper is published in the journal PRX Quantum.

Measurements are central to all quantum technologies. They are said to “collapse” the quantum state they act on, destroying its quantum properties and serving as the bridge to the classical world. Curiously, quantum mechanics allows for measurements that are more general than the ones we can directly associate with classical properties of a system.

These generalized measurements, or POVMs, short for Positive Operator Valued Measures, are not just a mathematical curiosity. They are known to improve performance in tasks like distinguishing between quantum states that would otherwise be indistinguishable, extracting more information from quantum sensors and securing quantum communication.

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