This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...

Artificial intelligence has formally verified the prizewinning proof that solved the sphere packing problem in eight dimensions, a result closely tied to Maryna Viazovska’s Fields Medal. The ...

Stephen has degrees in science (Physics major) and arts (English Literature and the History and Philosophy of Science), as well as a Graduate Diploma in Science Communication. Stephen has degrees in ...

Two years ago, a couple of high school classmates each composed a mathematical marvel, a trigonometric proof of the Pythagorean theorem. Now, they’re unveiling 10 more. For over 2,000 years, such ...

Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major problem in algebraic geometry. Other mathematicians had their doubts. Now he says ...

The quest to make mathematics rigorous has a long and spotty history — one mathematicians can learn from as they push to formalize everything in the computer program Lean. In ancient Greece, Euclid ...

Mathematicians have made lots of recent progress on a question called the Mordell conjecture, which was posed a century ago Faltings’s proof answered a question that had been open since the early ...

The original version of this story appeared in Quanta Magazine. Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the ...

The original version of this story appeared in Quanta Magazine. At the turn of the 20th century, the renowned mathematician David Hilbert had a grand ambition to bring a more rigorous, mathematical ...