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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.
I would argue that a large part of art is connecting with another human being through a shared experience. I think that's why so many artists are up in arms about making art so "easy," because it drops the human connection in many ways. The only human in the loop is prompting.
My view is that things will adapt. The human connection is still needed and there will always be art done the "old fashioned way." People still drag around large-format cameras to take pictures or simply shoot on film. My friend does painting and is trying to make a business of it.
At the same time, things have gotten easier. You don't have to be a "good" photographer to take a good photo with your phone's camera -- because there's already so much AI in that loop making things better. Same with so much other human-made art (and beyond). It's so much easier to get to the joy of creation. With photography, you can be creative with your phone and don't need the traditional thousands of dollars of gear to start creating.
The removal of those gates, both financial and the gate of years of practice, is what allows for that creation. I think we should celebrate that, not regulate it. Why does not "paying your dues" make your contribution invalid?
If your art, regardless of how it's made, helps you connect to others, I say that's a good thing.
I have a lot of other ideas in my head I'm trying to get out and make into a coherent argument, but I'm having trouble. For instance, we've had computer spell-checkers for decades now and no one blinks at that. We've had simple grammar checkers for a while as well, predating the AI everywhere thing we're seeing now, and no one really cares about that. It's only a matter of time before AI does more and people don't care. The only thing that really frustrates me is when people give up their agency to AI and stop thinking for themselves. AI is an amplifier of a human's ideas and abilities. But humans are still important.
A good way to think about artists, writers and the sort is to recognize they're performers who use their specialized mediums as a basis for their performances. This is to say the performers themselves don't fade into the background. Their work isn't judged alone and by itself as technically evolved curiousities. The works are frozen in time like amber, yes, but like in any other performance art, their personalities are fully on display everytime those works are perused, every time they make a public appearance or remark to boost their own publicity. It's those parasocial bonds they create which engender a following. AI would need to become not only competent at manufacturing the underlying goods but fulfilling all the other roles these freelancers take on. For freelancers, the whole operation is a one man show where they must become not only technical experts, but also frontmen who can appeal to crowds, manage public images, deal with other professionals. So an AI would need to be able to cover all of those bases in order to directly replace the individual doing them, or at least to turn them into proxies the AIs can micromanage.
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