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Comment by sebzim4500 | Hacker News Reader

Surely by the time of the IPO we will know whether the main results are correct, if only because a different AI will have produced a lean proof or found a logical flaw (the second case would be hard to verify but probably not impossible).

Also from what I can tell from the few fields I understand, the proofs aren't that long or complicated they are just terribly written.

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Why should that make material difference to the IPO? What is the economic value of those results?

The entire US federal budget for math research is something like $100M annually. And mathematicians in other countries are hardly making bank either. How does one reconcile how the market has historically valued mathematics with the cash-strapped frontier labs ploughing so much money into that enterprise?

The market works in mysterious ways. What companies do for marketing is often irrational, what companies do to attract investors is likewise often irrational, and why investors invest in companies is also often irrational.

Why should that make a material difference to the IPO? Because of the vibes, and investors are indeed all about the vibes.

It works in mysterious ways, but you know exactly it will behave certain way "Because of the vibes, and investors are indeed all about the vibes."?

The first paragraph is describing a general trend over multiple events across multiple agents. Between zero and three of these can be true for any transaction across every transaction.

The second paragraph is specific to OpenAIs behavior.

> what companies do to attract investors is likewise often irrational, and why investors invest in companies is also often irrational.

Note that the cool thing about rationality is that it does not depend on transitivity. If what companies do to attract investors works, then it is in fact rational of them, regardless of the rationally of investors.

And neither is rationality absolute nor consistent. One company can exhibit rational behavior while attracting investors, while a different company does not. A single companies can be rational at times and irrational at other times. And quite often companies will behave in extremely dumb ways. Especially in our current economic system where the cost of being dumb is negatively correlated with the amount of money available to you, and that cost goes down on a sigmoid curve.

They're burying any doubt that the models are capable of superhuman performance on intellectual tasks. Neural nets aren't calculators, and were notably poor at mathematical reasoning tasks for a long time. Now they're not, and the labs are proving that by chewing through what would ordinarily be decades of progress in a month. And the reason to go for math in particular is because there's no wiggle room. You can't just dismiss it as hallucination.

If the models can do this, they're almost certainly good at just about everything, because the reasoning and creativity required to solve these problems will translate. And even if they were only good at this stuff, that's still a tremendously valuable thing, because quantitative reasoning and analysis is the bedrock for many, many industries.

oAI is gunning for the largest IPO in history at this point, and they might actually get there.

> If the models can do this, they're almost certainly good at just about everything, because the reasoning and creativity required to solve these problems will translate.

The "then" in your "if-then" bears a heavy load. Why would society assign so little economic value to pure mathematics if the skills for proving math theorems translate to massive value in "just about everything"? Would you expect top mathematicians to cure cancer if you transplanted them from the math department to a medical research lab?

Do you think mathematicians are not already working on cancer research? There's quite a bit of heavy math in biostatistics, medical imaging, machine learning, etc.

I'd assume that the majority of people who study math take their skills and move onto some related STEM career that isn't pure math. Academia is incredibly small and competitive.

Because research mathematics is a subset of all quantitative work that gets done, but it's by far the most technically difficult subset. If the models can handle research grade math and produce ironclad proofs, they can probably handle the quantitative side of just about any discipline in a trustworthy fashion. Think about how many dinky spreadsheets have gone on to become critical tooling for large organizations. Even if you consider that many disciplines hide technically demanding work behind tooling (e.g. essentially no one is writing a stiffness matrix FE routine by hand), this model would be capable of writing a direct competitor from scratch to produce the same result.

All of STEM relies on mathematical analysis, and new models are now superhuman at that. And yeah, I'd go a step further and say that the reasoning and creativity required to solve cutting edge math problems probably does translate to other tasks like interpretation of the law, or medical diagnosis, or accounting, etc., for the same reasons that I think most top tier mathematicians would excel at those tasks were they so inclined.

That sort of worked for Eric Lander but as he moved higher up in the bureaucracy, he found himself suddenly having to manage people who weren't nerds like him. He was bad at that had to step down.

American mathematician Jim Simons was worth some $31 billion at the time of his death in 2024. The lack of economic value in pure math doesn't mean that applied math is of little value. Physicists and mathematicians with PhDs "sell out" to join Wall Street as quants and make a killing there, Jane Street is full of them.

> If the models can do this, they're almost certainly good

I would argue that "good at math" was a short hand for "good at X" because mathematicians were historically good at engaging with very complex ideas, distilling them and coming up with precise and concise answers they could validate by themselves.

Given that AI solutions are described as "psychedelical" and they rely on the outside source to validate the result, I don't think the same logic could apply to them.

I don't see anything stopping the models from getting to that point, though. So far we've gone from the models not being able to do math at all, to improving on progressively more difficult problems, to claims of "it's just a counterexample", to now producing constructive proofs and new mathematics on the hardest problems we currently have. All within less than two years.

Being able to do a task well and explain what you're doing in an organized way are fairly orthogonal, even in humans. I don't see why the skills the models currently have wouldn't transfer, even if the results look psychedelic. The next step would obviously be to improve trust by improving the way in which results are communicated.

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