The point is they have less algebraic structure than things like elliptic curves. If you want "math resistant" properties, this is a good thing.

> My gut is telling me pushing security model to hashes seems like a far far worse bet if you are worried about advances in maths.

Aren't hashes far less reliant on math tricks?

My understanding is the problem with public-key crypto is it extremely reliant on a single math trick (e.g. the factoring problem), so if it turns out that trick was weaker than was assumed, the whole thing crumbles.

That's the opposite of what my gut is telling me.

Hashes are so simple. There's no place for these crazy math attacks, which rely on rethinking long-standing and otherwise reasonable assumptions, to hide.

Surely we can all agree that there's no way to reverse a modulus.