I was asked in comments about the claimed P != NP proof I posted about last week. This NYT article has a reasonable summary of current opinion. Basically the "proof" appears to have some serious problems. Unfortunately the author may have trouble accepting this verdict.
As for what a proof would mean, the bare fact alone would not change much since many people already assume it is true. However it is likely a valid proof would depend on much greater insight into the theory computation than we currently have.
1 hour ago