They estimated $40M of agent costs (it was a large fleet of them). Using the number in the post its closer to ~880,000 hours × $150/hour = $132 million for the human case. Still an amazing feat not quite "four orders of magnitude". The comparison is obviously pointless because coordinating 1M hours of intellectual labor isn't easy to say the least.
> If they were, then their big speed advantage over us would mean that there would be much more of a flood of results.
Is this true right now? Just recently Jarred Sumner tweeted [1] that he managed to make some progress on the Riemann hypothesis while on a jog. Managed to get somewhere by encouraging the llm to “keep going” and “believe in yourself”.
This raised a few questions for me. Had no one at Anthropic thought to try this earlier? It's an interesting footnote that a software engineer there pursued this. How many people in the world can actually verify a proof? How many would we need to sit around and do the right incantations to get a proof out of it? How many would we need to verify and give those proofs value and meaning? What happens when there are more proofs than verifiers? How many will be around in 100 years?
I think it just turns out that a lot this stuff is more socially useful than anything else. The 10 proofs drop came and went in the daily news cycle. Perhaps math is already in it's chess like "for fun" period. I am interested in when we find a very high real-world utility breakthrough math/physics, some space where we've already poured our best human resources at it.
The result in [1] is not progress on the Riemann Hypothesis. It's another fine result, but it's not progress on the Riemann Hypothesis. You could prove 100% of zeros are on the line and it wouldn't show the Riemann Hypothesis. 100% of natural numbers are composite in this same asymptotic density sense, and yet that doesn't prove that all natural numbers are composite.
> Still not sure what that means, but some analytic number theorists seem excited
ie, I prompted AI and it put out a giant pile of tokens. I dont know what it means, but I hope someone gets excited. Mathematicians are now the priests and shamans chanting incantations and taking the holy blessings from the AI gods.
A real-world high-value breakthrough in physics would be to find some substantially cheaper (than the giant tokamak approach) arrangement of matter that can create sustained nuclear fusion with energy out to energy in factors over 10, which can also feasibly be built within a decade or two.
Advances in astrophysics or fundamental models are all very cool but won't be of much real-world applicability, at least in the short or medium term.
Why don't they?