It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question.

Inside the proton, quarks and gluons shift and morph their properties in ways that physicists are still struggling to understand. Rithya Kunnawalkam Elayavalli brings to the problem a perspective unlike many of their peers.

Certain grammatical rules never appear in any known language. By constructing artificial languages that have these rules, linguists can use neural networks to explore how people learn.

A new proof marks the first progress in decades on important cases of the so-called kissing problem. Getting there meant doing away with traditional approaches.

Heat is supposed to ruin anything it touches. But physicists have shown that an idealized form of magnetism is heatproof.

Individual cells in the brain light up for specific ideas. These concept neurons, once known as “Jennifer Aniston cells,” help us think, imagine and remember episodes from our lives.

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

The library sorting problem is used across computer science for organizing far more than just books. A new solution is less than a page-width away from the theoretical ideal.

Is the universe flat and infinite, or something more complex? We can’t say for sure, but a new search strategy is mapping out the subtle signals that would reveal if the universe had a shape.

Under the sea ice during the Arctic’s pitch-black polar night, cells power photosynthesis on the lowest light levels ever observed in nature.

Recent results show that large language models struggle with compositional tasks, suggesting a hard limit to their abilities.

By proving a broader version of Hilbert’s famous 10th problem, two groups of mathematicians have expanded the realm of mathematical unknowability.

By treating DNA as a language, Brian Hie’s “ChatGPT for genomes” could pick up patterns that humans can’t see, accelerating biological design.

Emmy Noether showed that fundamental physical laws are just a consequence of simple symmetries. A century later, her insights continue to shape physics.

A young computer scientist and two colleagues show that searches within data structures called hash tables can be much faster than previously deemed possible.

Quantum calculations amount to sophisticated estimates. But in 1931, Hans Bethe intuited precisely how a chain of particles would behave — an insight that had far-reaching consequences.

A new proof reveals the answer to the decades-old “moving sofa” problem. It highlights how even the simplest optimization problems can have counterintuitive answers.

Ten years ago, researchers proved that adding full memory can theoretically aid computation. They’re just now beginning to understand the implications.

Britta Späth has dedicated her career to proving a single, central conjecture. She’s finally succeeded, alongside her partner, Marc Cabanes.

By screening films in a brain scanner, neuroscientists discovered a rich library of neural scripts — from a trip through an airport to a marriage proposal — that form scaffolds for memories of our experiences.

Physicists hope that understanding the churning region near singularities might help them reconcile gravity and quantum mechanics.