In 2024, an AI entered the fray of the International Mathematical Olympiad (IMO). Google’s AlphaProof is part of the same ...

Marijn Heule turns mathematical statements into something like Sudoku puzzles, then has computers go to work on them. His ...

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 ...

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 ...

This is a preview. Log in through your library . Abstract We present a counterexample to the conjecture by Orlik that the restriction of a free hyperplane arrangement to one of its hyperplanes is free ...

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically ...

In a report posted online today, Peter Scholze of the University of Bonn and Jakob Stix of Goethe University Frankfurt describe what Stix calls a “serious, unfixable gap” within a mammoth series of ...