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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.
I did. Most of the top comments do not have an angry tone. It's more like, a mix of resignation and excitement. With some mad mixed into it.
Anyway and more importantly, it might be time to start thinking harder about the key question of our time: is it over for humancels?
Not any time soon, I think, but I tell you this: social positions in which being human is an inherent part of the value proposition are starting to seem like much more appealing things to devote one's time to than STEMing it up.
I'm thinking positions like prostitute, politician, athlete, stage actor, bartender, socialite, rock star, cult leader, man who makes money by befriending rich people, or man who makes money for taking the fall when an organization gets in trouble.
If y'all got any other ideas, share 'em. Cause it's time to strategize. Unless you're rich already, in which case: all good. Unless Skynet scenario.
I hope the AI-boosted productivity gains soon outstrip the job losses and we get the utopian diseases-cured Star Trek scenario instead of the Great Depression or Skynet ones.
I'm lucky enough to have had a career in STEM, so I'm rich already, but I'm not confident that's going to "matter" in the long run. Where the long run might be, uh, a few years. In an economy where all real work is done by AI, are we even going to honour the increasingly-fake number that is the size of your bank account? In an AI world, does it make sense for me to be able to commandeer 1000x the resources of my never-working friends?
You might say that this would cause upheaval, but there are an awful lot more poor people who'd be in favour of this upheaval than rich people who'd be against it.
No, and it's magical thinking based on a heuristic to think otherwise. People really need to start seeing past this. Your stuff isn't your stuff. You're just renting it. Pray the deal isn't altered.
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