The aim of this paper is to provide epistemic reasons for investigating the notions of informal rigour and informal provability. I argue that the standard view of mathematical proof and rigour yields ...

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 ...

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 ...

Vol. 133, No. 1/2, Foundations of the Formal Sciences I (Oct. - Nov., 2002), pp. 237-255 (19 pages) We give an overview of recent results in ordinal analysis. Therefore, we discuss the different ...

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 ...