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

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 ...

After more than three centuries, a geometry problem that originated with a royal bet has been solved. Imagine you’re holding ...

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 ...

Imagine that someone gives you a list of five numbers: 1, 6, 21, 107 and — wait for it — 47,176,870. Can you guess what comes next? If you’re stumped, you’re not alone. These are the first five busy ...

Randomness is a source of power. From the coin toss that decides which team gets the ball to the random keys that secure online interactions, randomness lets us make choices that are fair and ...

In math, the search for optimal patterns never ends. The sphere-packing problem — which asks how to cram balls into a (high-dimensional) box as efficiently as possible — is no exception. It has ...