Intelligent beings learn by interacting with the world. Artificial intelligence researchers have adopted a similar strategy to teach their virtual agents new tricks.

In recreational mathematics, the balance scale is an endless source of puzzles that require precise and elaborate logic and teach the fundamentals of generalization.

Protein buildups like those seen around neurons in Alzheimer’s, Parkinson’s and other brain diseases occur in all aging cells, a new study suggests. Learning their significance may reveal new strategies for treating age-related diseases.

Artificial intelligence has bested humans at problem-solving challenges like chess and Go. Is mathematics research next? Steven Strogatz speaks with mathematician Kevin Buzzard to learn about the effort to translate math into language that computers understand.

The quest to solve cubic equations led to duels, betrayals — and modern mathematics.

A new origins-based system for classifying minerals reveals the huge geochemical imprint that life has left on Earth. It could help us identify other worlds with life too.

With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.

June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.

With Hugo Duminil-Copin, thinking rarely happens without moving. His insights into the flow-related properties of complex networks have earned him the Fields Medal.

On his way to winning a Fields Medal, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

Mark Braverman has spent his career translating thorny problems into the language of information complexity.

Computer scientists have found a new type of problem that quantum computers can solve dramatically faster than their classical counterparts.

Patterns that guide the development of feathers and other features can be set by mechanical forces in the embryo, not just by gradients of chemicals.

Surprisingly, 107 years after the introduction of general relativity, the meanings of basic concepts are still being worked out.

What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide number theorists toward certainty.

In 1973, Paul Erdős asked if it was possible to assemble sets of “triples” — three points on a graph — so that they abide by two seemingly incompatible rules. A new proof shows it can always be done.

Three computer scientists have solved the NLTS conjecture, proving that systems of entangled particles can remain difficult to analyze even away from extremes.

Structural studies of the robust material called sporopollenin reveal how it made plants hardy enough to reproduce on dry land.

Nia Imara is working to understand the mysterious clouds of gas and dust that collapse into stars.

Mathematicians have been studying the distribution of prime numbers for thousands of years. Recent results about a curious kind of prime offer a new take on how spread out they can be.