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Tens of millions? You're thinking specifically of the proof of Navier-Stokes. According to https://github.com/openai/math/blob/main/README.md:

"On average, each result used three hours of ChatGPT Pro thinking compute with that model. Over the course of the evaluation, the model was posed approximately 4,000 problems. Aggregating the output into result families and manuscripts and requiring an appropriate level of significance led to the catalog outlined above."

I will note that this includes the Quasi Riemann Hypothesis. The model that solved NS was significantly dumber and less efficient that OpenAIs more recent math-models and you shouldn't over index on "it's expensive now". AI has advanced so quickly that your <2 month old opinion is out of date by 5+ orders of magnitude!

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Question: Have you actually used AI to do research-level math? At the current time, it is not "tackle any problem you wish and you can get headline results in ~3 hours." Their method is spraying-and-praying across the entire mathematical frontier, which is something only AI demonstrators are interested in. And as far as I know, they have never elaborated on what their "average of 3 hours" metric even means (e.g. including or excluding all unsuccessful leads?).
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I would say no. I am just finishing my MS in applied computational math at Johns Hopkins, but am not specialized to a PhD level.
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You shouldn't be so cofindent then, specially since your opinion is based on OpenAI's PR.
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I suspect the AI frontier labs will also soon turn their tools loose on the entire corpus of historical math papers to check for errors. They'll likely find that some major areas of math are built on a very shaky foundation.
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>Have you actually used AI to do research-level math

Being that OpenAI has done most of this on models that are not released, I don't think you have either...

The other thing you're not looking at is mathematics is becoming a means of actual training a model versus just something to try out.

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That sounds close to what human researchers do as well. Big part of getting grants/doing graduate work is finding a tractable problem. It requires constant refinement of what the scope and direction of focus.
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That's not even remotely how human research works.
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I guess this is the part where you claim to have ever done graduate or higher level research before, that wasn’t just a PI just giving you pre defined, contained side project for a summer.
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This is true in experimental sciences, where people who have grants and funding can obtain results using equipment unavailable to others. But their raw data can help much less funded theory groups to formulate new understanding that can lead to new experiments.

As long as the raw proofs, potentially ai generated, are available a lot of less funded mathematicians can still use them to generate understanding and created new programs to be resolved with new ai aided mathematical experiments.

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> As long as the raw proofs, potentially ai generated, are available a lot of less funded mathematicians can still use them to generate understanding and created new programs to be resolved with new ai aided mathematical experiments.

My assumption (based on perceived human nature) is that the raw proofs will not be made available.

If all of the important credit goes to the person who attached understanding to them, I'd assume those with the money to take the first step will keep the AI proofs secret until they believe they have adequately done the follow-up that will give them the lion's share of any credit.

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You're assuming the people with the money care about credit.
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I never had a chance against Terence Tao. Neither did you. There are a few dozen people on the planet who had a giant advantage in math and could do things no one else could do.

It was not some great awesome fair thing that math was dominated by some outrageous outliers on the iq spectrum. It's not some great awesome fair thing now either.

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> I never had a chance against Terence Tao. Neither did you.

I'm not a mathematician at all, so yeah I certainly didn't have a chance.

> It was not some great awesome fair thing that math was dominated by some outrageous outliers on the iq spectrum. It's not some great awesome fair thing now either.

I don't see these as equivalent circumstances. For most people if they get beat by someone smarter or someone stronger, it may be disappointing but they can still respect and admire that they were beat by talent/determination/etc.

Getting beat due to access to money just feels slimy, because at some level we all realize money is not distributed on a meritocratic curve at all, at least not if you are measuring values any well-adjusted person would consider positive.

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You keep saying "meritocracy" and the like, as though it's just by nature a good thing. It is not. High IQ isn't distributed evenly or fairly or anything of that nature, and yet "meritocracy" seems fine with the idea that "some people are just smarter than others, deal with it".

Rawls had a concept of the "veil of ignorance" which is probably better for thinking about fairness rather than "meritocracy". No one should lose sleep over the fact that the tiny number of corporates with enough capital can now beat out the tiny number of 180 iqs at a task (mostly generating proofs) that is not really valuable.

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> Rawls had a concept of the "veil of ignorance" which is probably better for thinking about fairness rather than "meritocracy". No one should lose sleep over the fact that the tiny number of corporates with enough capital can now beat out the tiny number of 180 iqs at a task (mostly generating proofs) that is not really valuable.

This is a weird framing. To begin with you didn't need a 180iq to work with math. What AI is doing though is making it so that an even smaller part of the population can work with intellectual, fun jobs and even more wealth gets concentrated to a small elite. That is absolutely something we should lose sleep over.

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This has unfortunately been the case in experimental academia forever.
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For now. It once took Deep Blue hardware to beat Kasparov. Now most laptops can do it.
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