Mathematical proofs getting harder to verify

New Scientist: Mathematical proofs getting harder to verify

'As an example, he points to the Classification of Finite Simple Groups, a claimed proof announced in 1980 that resulted from a collaboration in which members of a group each contributed different pieces. "Twenty-five years later we're still not sure if it's correct or not. We sort of think it is, but no one's ever written down the complete proof," Devlin says.'

Some of the things we've been discussing in my combinatorics course leads down roads like this. The topics lead to statements of uncertainty on some fronts. The problem is even using a computer program to prove or disprove a problem can be impractical because the search space is so massive, it would take years or centuries using current technology and algorithms to complete the program and get a definitive answer (assuming the technology and algorithms are bug-free).

Here's a problem that was massive but modern technology was able to find a definitive answer using only "years" of computer time.

Concordia: The Search for a Finite Projective Plane of Order 10 (it turned out there is no finite projective plane of order 10)

Written on February 20, 2006