Large language models (LLMs) have astounded the world with their capabilities, yet they remain plagued by unpredictability and hallucinations – confidently outputting incorrect information. In ...

A team led by mathematician Thomas Hales has delivered a formal proof of the Kepler Conjecture, which is the definitive resolution of a problem that had gone unsolved for more than 300 years. The ...

DeepMind’s AlphaProof system solved four out of six problems at the 2024 International Mathematical Olympiad, generating formally verified proofs through reinforcement learning trained on millions of ...

(Phys.org) —A team of researchers led by the man, Thomas Hales, who came up with written proof of the Kepler conjecture is now reporting that they have constructed a formal proof of the conjecture, ...