Show Summary Details

p. 353. Proofslocked

  • Timothy Gowers

Abstract

‘Proofs’ is concerned with the concept of a proof, that is, an argument that puts a statement beyond all possible doubt. One of the most famous proofs in mathematics shows that the square root of two is irrational. It illustrates a technique known as reductio ad absurdum, or proof by contradiction. Further examples of mathematical induction and proofs are provided using the irrationality of the golden ratio, regions of a circle, Pythagoras' theorem, and the problem of tiling a square grid with the corners removed. Finally, three obvious-seeming statements that need proofs are outlined.

Access to the complete content on Very Short Introductions online requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.

Please subscribe or login to access full text content.

If you have purchased a print title that contains an access token, please see the token for information about how to register your code.

For questions on access or troubleshooting, please check our FAQs, and if you can't find the answer there, please contact us.