Formal Proofs
Thursday, November 6th, 2008A very interesting issue of the American Mathematical Society on formal proofs.
Most people don’t realize it but mathematical proofs are usually written in a very condensed way, that allows other mathematicians to understand what is being said, but which are not formal complete statements, since lots of things are implied. Proof verification is essentially a social process by which other mathematicians convince themselves that the proof is correct. This doesn’t sound very reassuring but it has (in most cases) worked until now. Off course new challenges are appearing, with proofs 500 pages long or that use computer programs to to part of the job (like testing cases), that’s why formal proofs are becoming more and more pertinent.
