The International Mathematical Olympiad (IMO) is probably the most prestigious competition for preuniversity students. Every year students from around the world compete for its coveted bronze, silver ...

J. R. Brown, Philosophy of mathematics: an introduction to the world of proofs and pictures, Routledge (1999). 2. R. B. Nelsen, Proofs without words I: exercises in ...

A system developed by Google’s DeepMind has set a new record for AI performance on geometry problems. DeepMind’s AlphaGeometry managed to solve 25 of the 30 geometry problems drawn from the ...

The original version of this story appeared in Quanta Magazine. In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an ...

Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs ...

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing ...

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 ...