AI could soon spew out hundreds of mathematical proofs that look "right" but contain hidden flaws, or proofs so complex we can't verify them. How will we know if they're right?

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 ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

It has taken nearly four years, but mathematicians are finally starting to comprehend a mammoth proof that could revolutionise our understanding of the deep nature of numbers. Mathematicians were ...

Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...