A Mathematician with early access to XAI Grok 4.20, found a new Bellman function for one of the problems he had been working ...

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 ...

For centuries, the Pythagorean Theorem has occupied a unique position in mathematics: both elementary and profound. Its ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry. In 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 ...

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

Find out how and why mathematics is used in microeconomics, its limitations, and the math skills that economics students need.