If such a simulation were possible, the simulated universe could itself give rise to life, which in turn might create its own simulation. This recursive possibility makes it seem highly unlikely that ...

Mathematicians explore ideas by proposing conjectures and proving them with theorems. For centuries, they built these proofs line by careful line, and most math researchers still work like that today.

A few months before the 2025 International Mathematical Olympiad (IMO) in July, a three-person team at OpenAI made a long bet that they could use the competition’s brutally tough problems to train an ...