Quantum mechanics has at last been formulated exclusively with real numbers, bringing a mathematical puzzle at the heart of ...

In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation ...

If language is what makes us human, what does it mean now that large language models have gained “metalinguistic” abilities?

The theoretical physicist and best-selling author finds inspiration in politics and philosophy for rethinking space and time.

Paulina Rowińska is a science writer with a Ph.D. in mathematics from Imperial College London. Before joining Quanta Magazine as a science writing fellow, she was an editorial intern at ...

Despite their wide variety of sizes, niches and shapes, sharks scale geometrically, pointing to possible fundamental ...

Naomi Saphra thinks that most research into language models focuses too much on the finished product. She’s mining the history of their training for insights into why these systems work the way they ...

The Earth’s atmosphere is nothing but freely roaming molecules. Left alone, they would drift and collide, and eventually even out into a mixture that’s dynamic, yet stable and broadly unchanging. The ...

In cellular automata, simple rules create elaborate structures. Now researchers can start with the structures and reverse-engineer the rules. Alexander Mordvintsev showed me two clumps of pixels on ...

The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures. Hofstadter was ...