Terence Tao

Riemann is up there.

P equals NP is a good one because that's a meta problem.

If you solve that in the positive sense that you can find a P equals NP algorithm, then potentially this solves a lot of other problems as well.

If the Riemann hypothesis is disproven, that would be a big mental shock to the number theorists.

But it would have follow-on effects for cryptography.

Because a lot of cryptography uses number theory, uses number theory constructions involving primes and so forth.

And it relies very much on the intuition that number theories have built over many, many years of what operations involving primes behave randomly and what ones don't.

And in particular, encryption methods are designed to turn

text with information on it into text which is indistinguishable from random noise.

And hence, we believe to be almost impossible to crack, at least mathematically.

But if something as core to our beliefs as the Riemann hypothesis is wrong, it means that there are actual patterns at the primes that we are not aware of.

And if there's one, there's probably going to be more.

And suddenly a lot of our crypto systems are in doubt.

Yeah.

You want it to be random.

So more broadly, I'm just looking for more tools, more ways to show that things are random.

How do you prove a conspiracy doesn't happen?

I mean, there's various scenarios.

I mean, there's one where it is technically possible, but in fact, it's never actually implementable.

The evidence is sort of slightly pushing in favor of no, that probably P is not equal to NP.