Q&A: Why are Simpler Proofs Not Given Credit?

Cross-posted from here.

Question

If a mathematician proved Fermat’s Last Theorem in fewer pages than Andrew Wiles, shouldn’t they be credited for proving Fermat’s Last Theorem, since their proof is better?

Answer

That would, of course, be a very impressive accomplishment.

But solving an unsolved problem at all, especially a long-standing well-known problem like Fermat’s Last Theorem, is generally way harder than coming up with a simpler solution to an already-solved problem.

Which proof would be “better”? The simpler one.

Who should get the credit for solving FLT? Andrew Wiles.

Does that mean there’s no point in striving for a simpler proof? No – when you come up with a simpler proof, you’re generally doing so by developing a better understanding of the “core” of the problem. And that better understanding can helpful for solving other unsolved problems, which is beneficial regardless of whether you’re thinking altruistically (what’s in it for the field of mathematics as a whole) or selfishly (what’s in it for you in particular).