"Proofs and Refutations"

"Proofs and Refutations" is a philosophical work by Imre Lakatos that explores how mathematical and scientific ideas develop through an ongoing process of testing, questioning, and refining. Instead of viewing proofs as final truths, Lakatos emphasizes that knowledge evolves as hypotheses are challenged and adjusted in light of new evidence or errors. This iterative process involves proposing proofs, attempting to refute or disprove them, and then updating understanding accordingly. Overall, it highlights that progress often comes from critical debate and the refinement of ideas rather than unquestioned acceptance.