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PaperclipPerfector  2d ago (text post)   7365 thread views

Culture War Roundup for the week of September 7, 2026

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AI largely autonomously solving open problems is bad, because the solution itself isn't very important, but the techniques (advances, insights, etc.) developed to find the solution and failed attempts are. These techniques assist future problems including ones with practical applications.

Well the technique in this case seems to be 'smash the problem with $10 million worth of compute.'

From Tao:

But there is now a scenario in which an autonomous AI harness, backed by an enormous amount of computational resources, performs this entire iteration internally, and ends up producing the final ansatz, and thence the solution to the Navier-Stokes regularity problem, while the AI company running the harness keeps the process to arrive at that ansatz almost completely out of public view. Technically, one of the most prominent open problems in mathematics would now be solved; but there would be almost no value added to mathematics as a consequence. It is theoretically possible that with some herculean (and heavily AI-assisted) additional effort by a third party, some portion of the process could be reverse-engineered to recover some actual insight and understanding from the solution; but this would be a far less efficient process than if the solution had been obtained via a diverse combination of both human mathematicians and machine assistance as mentioned above.

How would it be more efficient? We can read the trend on the chart. OpenAI's agent swarm apparently needed a human to put them on the right direction today, that seems possible. I don't understand bounded v unbounded or what exactly is going on here, the subtleties of different proofs. I don't trust OpenAI.

Say they gleaned a few insights off the other mathematician. What about in 6 months or 1 year? Unleash the swarm on both the practical problems and the theoretical problems, smash them all one after the last. More algorithmic improvement (the practical money-making kernels and AI algorithms, data techniques), more compute as Rubin starts being deployed, more money to spend as the ROI rises... An 'enormous amount of computational resources' will shift up 10x or 100x in absolute scale.

What does he think ASI is, what does he think OpenAI is trying to do?

Human mathematicians, even Terence Tao, need not worry about diminishing progress in mathematics in the medium term by AI eating the seed corn. Tao's actual insight and understanding will have no more value than Kasparov's in chess.

It hinges on whether the techniques humans learn to solve open problems can be applied to areas that LLMs can’t. If LLMs can apply their own techniques, or solve more open problems with more time and scaling that continues to be feasible, human-readable proofs won’t matter beyond niche curiosity. But even then, curiosity and learning for its own sake are intrinsically important to some people. Moreover, I think these techniques sometimes lead to insights (that, for example, lead to new inventions) which today’s LLMs lack the creativity to apply themselves.

It hinges on whether the techniques humans learn to solve open problems can be applied to areas that LLMs can’t

Fair enough but I think that window is closing. 'LLMs can't' is just going to shrink and shrink. It's already perilously small! If they can do Millennium problems, what can't they do in maths? They can't answer the other Millennium problems just yet? Judging by past trends, that's about six months to a year away!

OK, they can't deliver real gamechangers like quantum gravity or room temperature superconductors. But what are the chances that humans understanding whatever insane techniques the AIs used would help us get to quantum gravity before the AIs do that?

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