New computer tools have the potential to revolutionize the practice of mathematics by providing more-reliable proofs of mathematical results than have ever been possible in the history of humankind.

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 ...

A new computer program fashioned after artificial intelligence systems like AlphaGo has solved several open problems in combinatorics and graph theory. “I was very happy to have the question answered.

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 ...

A pair of mathematicians has solved the first chunk of one of the most famous conjectures about the additive properties of whole numbers. Proposed more than 60 years ago by the legendary Hungarian ...

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Scientists and mathematicians often describe facts, theories and proofs as “beautiful,” even using aesthetics to help guide their work. Their criteria might seem opaque to nonexperts, but new research ...