The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum ...

The quest to find the longest-running simple computer program has identified a new champion. It’s physically impossible to write out the numbers involved using standard mathematical notation.

A decade ago, Karen Lloyd discovered single-celled microbes living beneath the seafloor. Now she studies how they can survive ...

New studies of the ‘platypus of materials’ help explain how their atoms arrange themselves into orderly, but nonrepeating, ...

Patchen Barss is a Toronto-based science journalist and author. He has contributed to Scientific American, the BBC and Nautilus, among others. His latest book is The Impossible Man: Roger Penrose ...

For decades, mathematicians have struggled to understand matrices that reflect both order and randomness, like those that ...

The new science of “emergent misalignment” explores how PG-13 training data — insecure code, superstitious numbers or even ...

Strong new evidence suggests that primordial material from the planet’s center is somehow making its way out. Continent-size entities anchored to the core-mantle boundary might be involved.

A small but enthusiastic group of neuroscientists is exhuming overlooked experiments and performing new ones to explore whether cells record past experiences — fundamentally challenging what memory is ...

Fan Chung, who has an Erdős number of 1, discusses the importance of connection — both human and mathematical.