Terence Tao, Professor of Mathematics at UCLA and Fields Medalist, on why nobody can fully explain why LLMs work: Tao starts with the mechanics, which are no mystery at all. You gather an enormous amount of text and you fit a curve to it. "The magic of LLMs is that if you train these LLMs on enough data — so trillions and trillions of data points — and you really try to fit as good a curve as possible, and this takes like millions and millions of dollars of computing power and months and months of time, then suddenly, even when you iterate, it stays coherent. It begins to sound not like monkeys but it actually sounds like a human speaking." That is the entire recipe: data, compute, time, curve-fitting. None of it obviously adds up to fluent English. Then Tao says the part that most people building these systems move past quickly: "And somehow we don't fully understand why that's the case." The admission comes from one of the most capable living mathematicians, and the gap he describes sits at the centre of the field. His best account of what's happening puts the mystery in the language rather than the machine: "What seems to be true is that language, like English or other natural languages, contains a lot of hidden patterns that we're not consciously aware of. I mean, we know some of the laws of English, there's laws of grammar and things, but there are sort of unspoken, unwritten rules of language that humans pick up." It relocates the question: the structure was always latent in the text, and the model found it. Why enough curve-fitting surfaces that structure is still unanswered. Tao reaches for a child to explain it: "A human child, even though they're not taught what a noun is, what a verb is or whatever, they can pick up what order English words go in just by continual exposure to the language." Which is honest about the limits of the explanation, because we can't fully account for how children do it either. From there, the unexplained behaviour compounds. Exposure to language turns out to be enough to produce something that looks like reasoning: "It seems like you can teach these models to also pick up patterns in language to the point where you can give them math questions. The answer to 2 plus 3 is — and they will say five." And once a model handles language at all, you can push it into resembling self-correction: "Once you have a little bit of ability to speak English, you can kind of go in loops and sort of check your work and make fewer mistakes, and you can prompt these models to proceed step by step and not say something unless it's been double checked and so forth. And so they become a little bit smarter, quote unquote, to the point where they can solve many, many complicated tasks." The scare quotes around "smarter" carry the whole argument. Tao does not concede that the unexplained fluency implies anything underneath it: "But they're still just guessing the next word to say. It's not really grounded in any deep understanding of the real world. It's just that they have seen the patterns in the English language or other language that they've absorbed so well."