Mathematical logic provides a rigorous framework for analysing the structure of mathematical reasoning, enabling a deep understanding of both formal systems and the nature of proofs. Central to this ...

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 ...

This paper presents a sequent calculus for the positive relevant logic with necessity and a proof that it admits the elimination of cut. Journal Information Studia Logica publishes original papers on ...

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 ...

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 ...

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 ...

Artificial intelligence has formally verified the prizewinning proof that solved the sphere packing problem in eight dimensions, a result closely tied to Maryna Viazovska’s Fields Medal. The ...