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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 don’t see why mathematicians would be so upset. 99% of professional mathematicians have never contributed to the field of mathematics in any real way.
There are two arguments about AI and employment.
The first and primary one is about mass unemployment. This is a real issue but people obsessed by it also need to understand, as I think @self_made_human increasingly does, that basically all of the surge in white collar labor since 1970 consists of fake make-work very thinly disguised by the laws of classical economics. The invention of the computer literally automated almost all white collar labor as it existed in, say, 1920, and yet instead of an unemployment crisis we just gave ourselves fake titles and decided to spend all day having meetings and making PowerPoint slides. The format in engineering and medicine was very slightly different but vast amounts of both professions, their demand and their provision were and are make-work too. I go to the doctors office and a GP diagnoses the way AI can in 20 seconds or a competent and cheap nobody who could use a search engine could do in 5 minutes even 25 years ago. If society survives the AI X-risk, we will emerge into a world of such unfathomable abundance that it will be trivial to provide every human, certainly in the rich world but eventually the whole world, with a comfortable material life. Dying from an AI engineered virus or a drone war or something is far more likely than starving because AI replaced all jobs and the owners of capital are too tightfisted to share.
The second and more interesting one is about meaning. The mathematician, even though he never meaningfully contributes to the field, imagines that he might. This is why AI makes him depressed. It’s the lack of hope that kills you, but is it? I mean, is it really? Meaning is invented, we’ve spent thousands of years inventing rather arbitrary forms of meaning. We can invent more. We can have kids. We can touch grass. We can compete against each other, if we want to, in games and competitions. Academia is already one such game. If mathematicians still want to play it, all they have to do is change the rules.
I guess I’m more sanguine on this than most. I increasingly converge on one observation, which is that it’s extinction or utopia. Other scenarios (weird AI hell) are plausible but increasingly unlikely. Compute always wins, the bitter lesson is always true, so the only question is whether it destroys us entirely (or someone uses it to) - accidentally or deliberately are really irrelevant - or whether it liberates us from material want entirely.
While AI continuing to be exceptional at mathematics doesn't particularly make me think that it's more likely that most/all labour is imminently automatable, I do agree with your point that if this is truly the case, there's really no point in trying to get rich to avoid dying on the streets when the 0.01% decide to mass unemploy the entire population or whatever. Coordination issues amongst the powers that be aside, it is obviously just not a stable equilibrium for the middle class to be unemployed and starving, while some dude who happened to own the right stocks at the right time is allowed to enjoy a nice lifestyle in perpetuity.
Either most everyone manages to secure material abundance via some combination of make-work and redistribution, which honestly already describes significant swathes of modern economies as you say, and having been rich perhaps confers some marginal status advantages and nothing more, or Something Happens that having a bunch of cash doesn't meaningfully insulate you from: e.g communist overthrow of the state (for real this time), violent state repression and expropriation of most the population, or AI loss of control where everyone dies.
I don't think I'm really all that sanguine re: the question of meaning though. The middle-class in developed countries are already mostly post-scarcity relative to a pre-industrial and a pre-computing basis in nearly all ways (the big exceptions would probably be in zero-sum usage of land and the decay of the body). Yet despite this, most people in the middle class are various flavors of miserable, generally aren't able to generate their own meaning ex nihilo, and mostly drive themselves mad via status comparison and/or the culture war.
If you thought hyper-partisan politics and status competition was bad in 2026, just wait until it's impossible to better your position via actual economic contribution, and the only way to access more resources, status and positional goods is to take it via the political process out of the arms of another. Even if the "utopian" world pans out, I frankly can't see this leading to anything but mass misery even if material needs are met in abundance.
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Wouldn't we expect competition to have optimized this away? This is at the heart of the worldview disagreement between "capitalism is just the invisible hand in action" versus "capitalism is a conspiracy by the powerful to remain in power."
the argument is that markets are more efficient at resource allocation than central planning, not that they’re very efficient.
When Musk bought Twitter and now operates it with 20% of the staff it had, or when Google increases headcount by 1000% in a decade despite operating primarily the same product, this isn’t maximum efficiency. Managers establish fiefdoms. Individual employees care more about themselves than maximizing shareholder returns. Incentives are not fully aligned.
Twitter and Google both had relatively low labor-to-capital ratios to begin with. So, if true, they were increasing headcount by x% from a low base, meaning it might not have been very consequential for their bottom lines. The examples could be cherrypicked anyways, and do not necessarily have bearing on overall patterns. Overall, we've seen the economy restructure itself from a primarily agrarian one, towards a manufacturing one, towards a retail and service based one across the past century or so, and all of that indicates a responsiveness to actual economic demand.
In fact, we've not only seen a shift in employment patterns towards human-necessary roles, but we've also see a rise in economic dominance by companies with relatively small labor footprints. Tech companies, in general, as mentioned, do not employ many people in relation to how much money they rake in, and they've been dominating economic growth and market indices for the past few decades. If they were insensitive to the costs of employing unnecessary labor, and if this was the basis by which the entire economy was organized, we might see them gradually becoming as labor-heavy as other, previous market leaders.
But we don't see that. We see them maintaining unprecedentedly lean workforces. That's consummate with a representation of the economy where humans in data-organizing roles are increasingly automated away. These humans don't disappear, but fill in gaps elsewhere, such as in retail and healthcare, providing tangible physical services. Pet grooming has seen a boom in employment.
Some of them do apparently move into roles which are of dubious practical value, but which have been necessitated in large part because of regulation and bureaucracy, such as consultants. However, these regulation regimes have led to decreases in pollution and other harmful things, so the consultants and such can be said to be necessary components of these overall systems' functioning and thus their benefits. Furthermore, they do plausibly provide value in the expertise they are able to provide as well.
Overall, I do not see a basis for thinking the economy is unresponsive to actual supply and demand inputs when it comes to labor organization. The level of its efficiency may be up for debate, but it does appear to shift over time in relation to observable developments.
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Also even maximizing shareholder returns =/= maximizing productivity in every case. A company can make a very share-price friendly move to invest in something unlikely to succeed that is the current recipient of market hype, even if it's unlikely to actually work out.
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We shouldn't have mocked the people from the "What's your job on the leftist commune?" Twitter thread. Seems like they might've been right after all. If we survive as a civilization and do not get made redundant via a BNW-like transition to a tiny humanity.
There's no "we" when you and all your children didn't make it through the cull.
I'm sorry, I don't get it.
Wrong reply, my mistake.
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I don’t think mass automation AI future proves communists correct. Not only because the timely invention of AI required capitalism (yes we don’t have the counterfactual, but I’d say it seems likely) but even more importantly because the only way any kind of ‘from each according to ability, to each according to need’ economy can work is if unlimited ‘ability’ is provided by AI and unlimited ‘need’ can be absorbed by it.
Well, communists did often say that capitalism would bring about its own destruction. Communists also often said that far from capitalism being useless, it is in fact the necessary precursor for communism.
However, it's hard to give them full props for these ideas given that originally these ideas did not envision something like AI being the mechanism.
Right, they envisioned it being because of the tendency of the rate of profit to fall - ie capitalism being so maximally efficient that it turns in on itself - which is actually untrue (capitalism is more efficient than the alternatives but not maximally so; rates of profit ie margins are actually quite high in historical terms right now).
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I'm not saying it proves communists correct. I'm saying the jobs the kumbaya-adjacent leftists envisioned themselves having might be the only source of meaning left in a post-singularity utopia.
I suspect that the main sources of meaning will continue to be things like religion and family / childrearing / marriage that code as trad.
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I'm less sanguine than you. The utopia AI will offer us does have advantages, the biggest being significantly healthier throughout a (neverending?) lifespan. And I, personally, am very excited for the knowledge and discoveries it will have about the universe.
But beyond that, the utopia won't fundamentally change that much. Even today, no one (at least in the USA) is starving for lack of food. The deprivations most people feel are positional and status-related: most people can get a house somewhere, but when people complain about not having access to housing, what they mean is they can't afford a brownstone in Park Slope.
Before AI, society could, at least in part, use merit and economic contribution as a way to allocate those inherently exclusionary goods; that's going away in the utopia. I'm lucky enough to have a almost two-decade-long career during a time where I could convert my intellectual capabilities into something that lets me acquire those resources, but that path won't exist for people like me. I don't have faith that whatever way society decides to allocate status resources will allocate them in a way I like (though I expect I personally am positioned in a place to have the level of exclusionary goods I want; it's more what I'm imagining for future generations).
That's following the optimistic utopia branch. The extinction branch is also quite likely (though I'd guess on the order of decades, not months or years) and much worse.
One reason that matters, though, is because opportunity clusters. If you can't afford a brownstone in Park Slope (wherever that is), that's a problem because you then can't access the high-paying job/networking/cultural opportunities in Park Slope. There is a plausible downward spiral of
couldn't quite afford Park Slope -> moved to the boonies -> could only find low-paying local jobs -> could never even think of moving to Park Slope -> can't even afford the boonies any more
which doesn't quite hold in a utopian society.
Park Slope is a nice neighborhood in Brooklyn. A brownstone in Park Slope is roughly a Victorian in Noe Valley.
In the utopia, how does someone not in Park Slope get their brownstone in Park Slope?
I think the idea is that while some people value a brownstone in Park Slope for its own sake, some value it because it puts them near the job opportunities of NYC and otherwise wouldn't want one.
If the job opportunities of NYC don't matter anymore, that second group no longer wants to be in Park Slope, so while there probably still won't be enough brownstones to go around, there may be less of a gap than there currently is.
We're also seeing some significant declines in fertility rates, and I think more so in the demographics that want to be in Park Slope. So if that trend continues in utopia (which seems reasonable, material abundance if anything seems to get people less interested in children if we look at the modern era), over time there will be fewer people looking for them and the gap might shrink further.
If we get infinite life extension that might be a different matter, but I expect eternal youth will also lead to "eh, I'll get around to making kids later" for some very long definitions of later, and the city-seeking crowd also seems to have a problem with depression that might lead to disinterest in infinite lifespans.
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