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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.
Much like blue-collar workers turned out to be much less exposed to being made obsolete by AI than the white-collars who sneered at them, the 'hard' sciences are on life support after decades of sneering at biologists. Who knew our idiotic nomenclature, awful qualitative methods and black-box approach to running clinical trials were actually the greatest moat against superintelligence a group of mathematically incompetent wordcels could devise.
Interesting to think that AI is a 1000x coder, 10,000x mathematician, but a 2-3x biologist on a good day. At least I'll be afforded the joy of pointlessly pipetting liquids right up until the paperclippers come for me. On the downside, that's all you need to make turboCOVID while falling far short of curing cancer or aging.
LMFAO yes absolutely. Even within physics the areas being dismantled are theoretical physics while the experimental physicists are carrying on doing their jobs just as well or even better before AI, because to them it's literally a complementary assistant that boosts them rather than replacing them. And even within theoretical physics the areas getting blasted the most are the most "rigorous" ones like QFT and GR while the ones that are still sort of saved from the worst of the shelling so far are things like lattice field theory etc. where people randomly go around doing approximations because otherwise nothing works...
I am in experimental nuclear/particle physics, more on the making-stuff-run than paper-writing side of things. For me personally LLMs are a huge boon.
I mean, on the one hand, they have made huge parts of my skillset obsolete. Before I was one of the few people in my department who knew how to run gdb to hunt down a segfault in some terrible ROOT program. This is not an employable skill any more -- Claude can do this far better and more reliably than I ever could at a tiny fraction of my cost.
But as someone lucky enough to have a job, Claude is like having a PhD student who happens to have read every book on every programming language ever working for you. Tasks which would have taken me half a year (because I lacked the specific skills) can now be done in weeks. I have even taken a liking to systemd of all things, because I don't need to learn the syntax myself. Going down some Linux rabbit hole (how do I figure out why an interrupt handler runs at 100% cpu?), which would have taken me days before is now a matter of an hour.
Still, it used to be that in my field, a lot of students were employed in data analysis. Generally, this involved writing terrible ROOT code to get some physics channel out of a dataset, then turning this into a publication and a PhD thesis. In the short term, they also benefit from LLMs -- at least for the code writing part, which used to be a majority of the work.
But solving for equilibrium, it seems unlikely that anyone will employ PhD students for data analysis in the future. They are expensive (compared to LLMs), they suck at programming, they start out with a lot less domain knowledge than the bots, they come with interpersonal conflicts which require management. In the past, there was no way around them (short of employing programmers, which would take larger salaries and require physicists to work interdisciplinarily). These days, a senior physicist can probably use an LLM agent to do some analysis without spending more time mentoring than she would for a PhD student.
Data analysis aside, experimental physics still contain plenty of manual tasks which are not easily automated. We have used PhD students to glue photomultipliers to scintillators before, and these jobs will still require doing.
The other question is the long term career path of physics PhDs. Before, most of them (in my field) ended up in the software industry, which is what kept our system running. Prospects there are probably not so great at the moment.
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