Proofs and Refutations: The Logic of Mathematical Discovery
| Author | Imre Lakatos; edited by John Worrall and Elie Zahar |
|---|---|
| Published | 1976 |
| Format | Book |
TL;DR — Lakatos’s dialogue, set in an imaginary classroom, showing mathematics growing through conjectures, proofs and counterexamples rather than by pure deduction.
Published posthumously by Cambridge University Press in 1976, edited by John Worrall and Elie Zahar from Lakatos’s doctoral work and articles of the early 1960s. This copy is an image-only scan with no text layer.
Most of the book is a dialogue between a teacher and students working through the history of Euler’s conjecture about polyhedra (vertices − edges + faces = 2). As counterexamples appear, the class tries different responses — “monster-barring” the counterexample, adjusting definitions, restricting the conjecture, or analysing which lemma of the proof failed — and the method of “proof and refutation” emerges from that process. Footnotes trace the real mathematicians who made each move. Appendices extend the analysis to uniform convergence and bounded variation and contrast the “deductivist” and “heuristic” styles of presenting mathematics.
What it is: a classic of the philosophy of mathematics, from an in-print academic book.
Where this came from
- A copy saved in October 2026.
184 pages. A PDF copy is held in Kyle’s private archive; it is not linked or shared here.