On: Mathematicians have found a new upper limit to the...

[onetimeuse92304]

I think you are possibly missing the possibility that going from 4^k to 3.993^k might involve learning something new about the problem. Frequently learning something new is more important than the absolute magnitude of the improvement.

[a1369209993 → onetimeuse92304]

> might involve learning something new about the problem

I think that's almost literally what sfink said though:

> > they're creating a whole new form of proof that will almost certainly allow further decreases