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I made a comment recently speculating that Terence Tao may be a paid promoter of AI. After some off-site discussion elsewhere, our resident shaman on whom the mods cast a long-duration silence posted my comment as a circus exhibit on Twitter to demonstrate a dangerous form of psychosis. Fortunately, OpenAI deemed this a worthy time to intervene and publish an ad featuring Terence Tao, who has taken time out of his busy schedule to assist this struggling non-profit with their promotional.
I want to dissect what I think is really going on.
For starters, every time I sit down to watch WoW on YouTube, I'm greeted with my favourite streamer telling me about the super fun game Raid Shadow Legends, which I should definitely download and play because it's super fun. Is the OpenAI-Terence Tao relationship like this? Not really. Terence Tao does appear to actually spend some time playing around with LLMs. Further, he's not exactly saying a bunch of empty marketing blather, either. In fact, probably to the annoyance of some readers here, I want to take a couple paragraphs for a technical aside, because there is actually subtlety here. I'll bound this in horizontal bars so non-technical readers can skip it:
The main talking point is that automated theorem proving is a perfect fit for LLMs precisely because it's not vulnerable to their main catastrophic failure mode: hallucination. The model can hallucinate whatever it wants, but the text still goes into the theorem prover, and if it's bullshit, well, the prover just rejects it and you query the LLM again. Do this in a loop, burn whatever unholy amount of compute you want, and if the loop stops, you've got yourself a proof! (Well, or a bug in the theorem prover. Or a "You've run out of tokens on your budget" error message. But I digress). This story is largely true. There's a giant asterisk of "Uh, so how much compute we talkin' about?", and the answer is "As much as you need or can afford, whichever comes first!" Which is, of course, the business model.
I will point out one additional technical nit-pick that annoys me because Terence Tao is working in Lean 4, which is a dependently-typed theorem prover. In classical mathematics, one is concerned solely with whether a theorem is true or false, and the structure of the proof is basically irrelevant as long as it's valid. Lean 4 is not based on this model. Rather, it's based on a more computationally-motivated model of mathematics pioneered by Brouwer in the early 1900s called "constructivism." In this world, the question isn't the boolean notion of "Is this theorem true or false?" but rather the related but distinct notion of "Which proof do you have?" To ground this in practical terms, consider the following example: I can prove that True|False and Yes|No are isomorphic, but I can do so in multiple ways: I can map True to Yes and False to No, or I can map True to No and False to Yes (and then show that there are respective inverses which preserve identity, obviously). It is in this sense that one can meaningfully say "Which proof of isomorphism?" when I say I have a proof of isomorphism. Perhaps this all sounds like technobabble, but to connect it to the preceding paragraph: you can immediately see how this does reveal some cracks into the narrative being sold there. It does actually matter which proof is produced, not merely in a social sense of "can any human understand this wall of text the LLM spit out", but in a technical, computationally-relevant sense. For pure mathematics, this distinction is often not considered important -- in fact, many classical mathematicians aren't even aware of the difference, and will be confused if you try to explain it to them and think this is all a bit silly. However, it's not a silly or minor distinction for the following reason: one of the motivations of this computational model for "theorem provers" (it's really a programming language + compiler, rebranded for mathematicians) like Lean is so that formal methods can be applied not just to classical mathematics, but to software in general. And as soon as you enter software formalisation, this distinction is no mere intellectual curiosity, but of paramount relevance. The classical-style logic in the preceding paragraph does not apply to constructivist logic used for software formalisation! I'm sure this distinction is not lost on Terence Tao. But that doesn't concern OpenAI. OpenAI is more concerned with whether the distinction will be lost on the MBAs listening to Terence Tao, and the answer is "absolutely."
Ok, no more technical details like that, I promise. Back to the social level:
So, I mentioned Raid Shadow Legends is a poor metaphor for the OpenAI-Tao relationship. Let me propose some better ones: Michael Phelps and Wheaties (with the added benefit that Terence Tao never smokes weed. See, this is why mathematicians are better than athletes), or better yet, attending Harvard University. This may seem like a strange juxtaposition, but I've done so intentionally, because the marketing is obvious in one but subtle in the other, but it's actually the same trick: the goal is to misattribute performance. With Wheaties, the goal is to sell the notion that Michael Phelps is a great swimmer because he has a healthy diet of stuff like Wheaties, and if you eat Wheaties, maybe you'll perform well, too! Of course, in reality, he was eating sugar-coated french toast and chocolate chip pancakes because he needed 10k Calories/day just to break even on energy, and the reason he's such an awesome swimmer is in large part genetics. Wheaties, or anything similar to it, has virtually no relevance to Michael Phelps at all. But what about Harvard?
Well, Harvard sells the image so well that most people outside this forum outright believe the illusion. The illusion is, of course, that attending Harvard makes you smart and likely to succeed, rather than Harvard accepting only people who were smart and likely to succeed in the first place and thus redirecting credit for these future achievements to Harvard. Mark Zuckerberg may see Harvard as a pointless waste of time, but the world sees Harvard as "The university that made Mark Zuckerberg happen!"
I like the Harvard analogy because this is surely the intent with Terence Tao. There's a high chance sooner or later Terence Tao will prove something cool "using" ChatGPT, and if he does, it would be really awesome if we could make it sound like the secret ingredient in the ChatGPT-Terence Tao alliance was ChatGPT, when obviously the actual secret ingredient is Terence Tao. The analogy I always use for this is stone soup, a European folktale where starving travelers dupe gullible townsfolk into helping them make soup from stones by requesting "extra" ingredients bit by bit until they've just made actual soup, thus astonishing the gullible townsfolk.
There are a lot of other things I could say on this, especially on the technical side, as there are a lot of clever tricks you can pull to make it look like a model is doing more than it really is, but I'll stop for now and conclude with this:
Just be cognizant that OpenAI, and all the other LLM vendors, do marketing. They have an enormous budget that dwarfs anything you have ever seen before. Remember the reality distortion field of Black Lives Matter? Or trans people? Imagine that, but like... two orders of magnitude larger. That is the level of persuasive pressure we're dealing with here.
Just take it all with a grain of salt.
Let's suppose AI models aren't so great for mathematics and it's Terence Tao doing most of the work.
The primary commercial usecase for AI isn't mathematics, it's coding, as you say.
I cannot code beyond the most basic Khan Academy beginner sense, my actual end to end abilities are completely worthless. And yet I can make useful AI tools for work, processing documents in various ways that saves lots of human time. In a certain sense, I'm providing most of the 'secret ingredient' since you cannot just tell an AI to do these fiddly tasks and expect them done properly in oneshot. It will usually not work the first time. So I give it some counsel and tell it what to troubleshoot, errors, differences from expected output, clarify my intentions and ultimate usefulness. Eventually it works and then I refine it to work better and better by getting AI to handle all these edgecases and Word-induced BS.
And how could I make a (still under development) 4X game with AI if I can't code? There's a fair bit going on. Space battles, ground battles, culture, technologies, buildings, resources, goods, markets, map generation, turn order, trade between provinces (intra faction), trade between factions, freighters, pops and social classes, loans, diplomacy and war plotting, coalition building... Some things are not well fleshed out but there is quite a bit there.
I was just now getting it to make an evolutionary testing system to refine ship designs and fleet compositions and so define the meta. First time it worked OK, then when trying to make it better (too many bad mutations!) it broke, then I overhauled it and now it works great and with multicore processing too. Apparently the dominant strategy is getting hundreds of incredibly cheap and terrible warships to act as chaff for a small core of high-tech warships to exploit the targeting and reinforcement logic. So clearly I need to change how reinforcement and targeting works, raise minimum costs for ships.
It was my idea to make this tool, my idea behind the overhaul and my ideas behind every mechanic but I could never have done it myself. The secret ingredient is clearly the AI.
I don't know, my experience is kinda the opposite, but I have been programming since childhood. I find AI very frustrating to use, and rarely consult it.
Keep in mind that it has all of Github in its training data. It can go a long way by basically feeding you an existing project and not mentioning where it got it. I don’t mean to oversimplify and say that this is all models do and that there’s no reasoning, but I think people underestimate just how much is memorised: you can get mainstream models to recite entire books like Harry Potter almost word-for-word, with upwards of 95% accuracy, and to the extent that you can't, it's usually due to active sabotage by the model vendor to prevent people from getting free Harry Potter, not because the model doesn't have Harry Potter memorised. Vendors really do not want it to look like everything is getting memorised, but to a large extent it is. I just tried it with some random books I'm reading now and… yeah, they definitely have every book I'm trying memorised, even though they're very coy about it. And some of these are quite obscure books that I'm confident less than 1% of people would even recognise the name of. I then tried it on a snippet from a random library I published ten years ago on Github and… yeah, it has it memorised, down to the exact word. Amusingly, unlike the books, it does not go out of its way to tell me where this quote is from and lecture me about the importance of copyright. When I explicitly ask it where it got that, it just says it made it up—that it’s not a quote from any published book.
EDIT: to drive the point home, it is not so good at predicting the text of an unpublished library I have sitting on my PC! I suppose it's some consolation that this vendor does not appear to have access to my computer.
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