MIT Press recently published Fundamental Proof Methods in Computer Science, a book by Konstantine Arkoudas and David Musser, a professor emeritus of computer science at the Rensselaer Polytechnic ...

A mathematician will turn a groundbreaking 100-page proof into computer code. The proof tool, Lean, lets users turn proofs written in prose into rules and logic for testing. Kevin Buzzard already uses ...

Categorical logic and model‐theoretical methods form two complementary approaches to the study of formal structures and their semantics. Categorical logic interprets logical systems as objects and ...

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 ...

Metamathematics investigates the structure and limitations of mathematical theories, with proof theory focusing on the nature of formal proofs and the principles that govern them. In the context of ...

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 ...

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 ...

At a secret meeting in 2025, some of the world's leading mathematicians gathered to test OpenAI's newest large language model, o4-mini. Experts at the meeting were amazed by how much the model's ...