As a plot device I need some kind of conjecture that is used in lot proofs and widely assumed true. Something like many papers in computer science start with "Assuming P != NP ...".

In my story for dramatic purposes my heroine disproves it.

It doesn't matter how, or is it plausible in real world, I just need a lot of esteemed work and many careers in tatters. The story is basically about a complicated proof, and those who could understand it due to working in same or nearby fields must choose between the truth or their prestige.

I would prefer something from pure math, so the damage would be contained to academia. Breaking cryptography would make three letter agencies very interested. Anything related to relativity and or quantum mechanics would gain too much attention.