Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because ...

In 2024, an AI entered the fray of the International Mathematical Olympiad (IMO). Google’s AlphaProof is part of the same Alpha group that also created AlphaFold and AlphaGo. It solved problems that ...

Hallucination is fundamental to how transformer-based language models work. In fact, it’s their greatest asset: this is the method by which language models find links between sometimes disparate ...

A mathematical proof is irrefutably true, a manifestation of pure logic. But an increasing number of mathematical proofs are now impossible to verify with absolute certainty, according to experts in ...

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 ...

When a top-tier mathematician announced in August that he had proved one of the greatest problems in mathematics, the claim was trumpeted in the New York Times, Nature, Science and the Boston Globe.

Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers. The method can be extended to prove statements about more ...