Proof vs Truth in Mathematics

Abstract

Two crucial concepts of the methodology and philosophy of mathematics are considered: proof and truth. We distinguish between informal proofs constructed by mathematicians in their research practice and formal proofs as defined in the foundations of mathematics (in metamathematics). Their role, features and interconnections are discussed. They are confronted with the concept of truth in mathematics. Relations between proofs and truth are analysed.

Keywords

• formal proof
• informal proof
• truth
• mathematics
• logic
• incompleteness
• jan woleński