Theorems which later turned out to be vacuous

274 Views Asked by At

Has it ever happened that a theorem of the form

If $P$, then $Q$

was proven and published, perhaps with great difficulty, only for someone to realize later that the condition $P$ of the theorem is never satisfied, or, worse, that the conclusion $Q$ of the implication is false?

For example, if the Generalized Riemann Hypothesis were disproved tomorrow, I would have a large supply of examples on my hands, as so many results are conditional on GRH. But surely, this must have happened before, in the long history of mathematics?

1

There are 1 best solutions below

1
On

In the proof of FLT, was essential the fact that nontrivial FLT solution $\implies$ $\exists$ weird elliptical curve. Wiles proved that there isn't weird elliptical curve. See A question on FLT and Taniyama Shimura.