How could I objectively judge that?

To me, it is not at all obvious that the "level" of the training set is an upper limit to the capabilities of an LLM.

Sure, the LLM hasn't been exposed to material more advanced than the most capable human domain experts have produced. However, it has seen and learned from a vast amount of information that these domain experts are completely unaware of. Why shouldn't the LLM be able to use that information to produce output that's beyond the capability of a domain expert?

Yup, the e2e proof of FLT (estimated effort of 5 years & 1M$ by the best human in the field) and a counter example for a millennium prize (similarly valued at 1m$.

I hadn't seen anything three years ago produced by an LLM that looked better than the most mediocre humans. The argument here isn't about today's output, it's about the potential of LLMs to outperform humans. And it's far from clear that the architecture is bound this way, or that it only repeats stuff it's already heard.

Recent mathematical breakthroughs?