If LLMs really solved hard problems by 'trying every single solution until one works', we'd be sitting here waiting until kingdom come for there to be any significant result at all. Instead this is just one of a few that has cropped up in recent months and likely the foretell of many to come.

In other words, it's solving a problem.

The link has an entire section on "The infeasibility of finding it by brute force."

But this is exactly how we do math.

We start writing all those formulas etc and if at some point we realise we went th wrong way we start from the begignning (or some point we are sure about).

How do you think mathematicians solve problems?

No, that's precisely solving a problem.

Shotgunning it is an entirely valid approach to solving something. If AI proves to be particularly great at that approach, given the improvement runway that still remains, that's fantastic.

That's also the only way how humans solve hard problems.