Computers make it possible for a mathematical proof to run as long as several thousand full-length novels combined. But human beings alone cannot verify such immense proofs. That, according to Ian ...

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 ...

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

Computer-assisted of mathematical proofs are not new. For example, computers were used to confirm the so-called 'four color theorem.' In a short release, 'Proof by computer,' the American Mathematical ...

Peter Scholze wants to rebuild much of modern mathematics, starting from one of its cornerstones. Now, he has received validation for a proof at the heart of his quest from an unlikely source: a ...

There’s a curious contradiction at the heart of today’s most capable AI models that purport to “reason”: They can solve routine math problems with accuracy, yet when faced with formulating deeper ...

Despite multiple conferences dedicated to explicating Mochizuki’s proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 ...

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