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Notes -
A Big Day in the Culture War
Apologies for any incoherency or grammatical errors; today's events led me to down more than my usual share of booze.
Earlier today, big things happened in math. No, not Claude providing a sub quadratic 3SUM. OpenAI released hundreds of notable math results, in a GitHub repo.
Fun results:
Hilbert's tenth problem over (\mathbb{Q}) is undecidable
The quasi-Riemann hypothesis
The rational Hodge conjecture holds for every CM abelian variety
Integer multiplication can be done in sub-log-linear time. Oh, there's also a sub-log linear DFT.
Thoughts and observations:
Mathematicians are big mad. View the relevant subreddit on our progenitor site. Most there are probably, at best, adjuncts at community colleges desperately coping with the downward trajectory of already marginal careers, but it's fair to say that the writing is on the wall for mathematicians. There's probably a double digit number of grad students staring into a glass of whiskey tonight and thinking of hanging themselves.
My immediate question was about whether this closer to the current peak of performance, or just a lazy demonstration of OpenAI's power. So, I took one of the particularly interesting preprints to me (memory and precision in Gaussian models) and tested whether it's at the edge of capabilities or not. 30 minutes of back and forth with Astra (itself behind OAI's internal model) resulted in a significantly stronger result, on multiple dimensions. While I finished my first bottle, I spent a fair amount of time convincing myself of the result; I was convinced the strengthened results were plausible. Write this off as AI psychosis if you want, but try it yourself; I'm genuinely curious for what you get. (The back and forth, here, was entirely me saying "you can do it!", "keep at it, I believe in you", and "you've got this, finish it!")
Probably the most important line in OAI's announcement post is "The average result used the equivalent compute of roughly three hours of ChatGPT Pro thinking." This isn't a case of OAI spending millions for a marketing bump. My bet is a kind of Pareto distribution: most took minutes, not hours, with a long tail around Riemann-level results pulling up the average significantly.
Notably, ML related results are nearly entirely absent from this batch of proofs; maybe a half dozen touch on it, distantly. Some problem indices are skipped in overview.md. Conspiratorially, my inclination was to think they filtered them out for competitive advantage. I can't find any evidence of that in the GitHub repo or any of the preprints (equally plausible: deduping), so maybe they judiciously decided not to point their mathematical ballista at ML. ML also doesn't have a meaningful bank of rigorous conjectures, so given the conjecture sources, maybe they're not yet digging into ML math. But color me skeptical.
Does math matter? Is it something to advance civilization and technology, or an artistic pasttime for humans to create logical beauty? Likely both, today, but this is an almost nuclear detonation against the latter.
Doomer responses to this is just so sad. I'm an artist and designer and with every improvement of ai art/creativity I welcome it as augmenting possibilities of creativity rather than thinking my own creativity is worthless. Math people should be so happy they have new knowledge of math opening up to them and excited about the new answers rather than sad that a computer did it better than them. Surely there are now tons of new applications of knowledge and information from the new findings they can work from, I don't understand why they'd be upset about it. I'm sure it's very much like in art where most of the good artists are curious about the new AI tools while the bad ones worry.
Centaurs (humans using AI tools) don't last forever. They are a transitional stage until the AI gets good enough to replace the humans entirely.
And maybe that would be fine if we had figured out a way to compensate the losers with money and sexual access, but here in the real world, going from being an artist to being unemployed because now suddenly everyone has an artist in their laptop is a huge blow. It's not just envy and greed that other people now have access to your talents; it has real material consequences.
Most artists are artists because they love art, not because of the money (it's a notoriously badly-paid field). Telling them, "nope, sorry, you can't even keep earning a marginal living by drawing now, you will have to take some other job flipping burgers or sweeping floors and maybe draw in your spare time if you want but keep in mind you will never be as good as the machine and nobody will ever look at your drawings because everyone can have infinite high-quality drawings of whatever their niche interest is created on demand" is soul-crushing.
You could say that about photography as well, that the humans controlling cameras are a transitional stage until the cameras get so good that they don't need people. Yet it's been over a century, there's uncountable hours of photography being captured at all times all over the planet all the time and yet almost none of it is interesting outside of like the nature wildlife automated photography that some people like to look at. I could probably find beauty in automated traffic cameras if I felt like it but I'm in the minority and most people would rather see a human produced and curated series of photographs than a randomly generated or algorithmically curated series of photographs
Again I am an artist and designer and no one is telling me I'll have to flip burgers right now, I can think of 50 other more creative tasks I could monetize before I'm going to sweep a floor. lol. Besides that the bottle neck in the economics of art has never been supply side but rather demand side and AI has NO answer for the demand problem. I could already produce thousands of t-shirt designs a day if I wanted ten years ago, the technology was already there, but the demand for this variety of t-shirts does not exist.
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