it often disproves the viability of often very promising venues of thought.
For example, a lot of linguists have been caught up in Chomsky's generative ideas about language, that the surface expressions (infinite in number) are generated on the basis of innate rules (finite in number)... but game theory supposedly has very rude things to say about that.

I don't know if the OP of this subthread is correct, but it seems to say that maths is seeing itself not applying to the case at hand. Which is funny, at least to me.

Regardless of whether it's true.