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 ...

A mathematical proof has finally debunked the idea that we live in a simulation, according to a group of international researchers. The theory that the universe could be a computer programme has been ...

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 ...

The one source of truth is mathematics. Every statement is a pure logical deduction from foundational axioms, resulting in absolute certainty. Since Andrew Wiles proved Fermat’s Last Theorem, you’d be ...

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 ...

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 ...

You enter a cave. At the end of a dark corridor, you encounter a pair of sealed chambers. Inside each chamber is an all-knowing wizard. The prophecy says that with these oracles’ help, you can learn ...

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 ...

Forbes contributors publish independent expert analyses and insights. Dr. Lance B. Eliot is a world-renowned AI scientist and consultant. In today’s column, I examine an insightful AI research study ...

A mathematical proof has finally debunked the idea that we live in a simulation, according to a group of international researchers. The theory that the universe could be a computer programme has been ...