I'm sorry but you don't actually need the mathematical community to check any of this. You just need autonomous verification, which already exists at scale and speed vastly beyond the entire human mathematical establishment. OpenAI simply rushed these out without completing that for every paper. These mistakes have nothing at all to do with the mathematical community and are 100% just the result of market pressure incentivizing speed at 1,000,000x the pace of human mathematicians. Frankly, a couple mistakes, trivially found not by humans but by humans using AI, is almost completely irrelevant. Human mathematicians have essentially nothing to contribute to this effort aside from prompting verification agents, which any of us can do if we cared to spend the time (most of us don't).
There is no such thing as knowledge that has never even been written down a single time by anyone or anything. Those are simply called ideas, they are not unique to humans, and they are more likely to be wrong than right compared to anything OpenAI just produced. It would be bold and almost certainly spectacularly wrong to assume that multi-trillion-parameter AI models could not possess their own such ideas, generated during the training process as part of their internal model of the world. Beyond that, if we assume that such knowledge does exist in humans, its marginal value is clearly nearly zero now, as AI systems without access to it are vastly outperforming all human mathematicians combined by multiple orders of magnitude.
This feels like a very rigid ontology. I know what type of food my dog prefers. An executive assistant has intimate knowledge of their boss’s needs. Neither of these would become knowledge if they were written down for the first time; they already are.
You’re distinguishing “knowledge” from “idea” in a particular way that doesn’t correspond to common usage (see my counter examples). Without you being explicit about your definitions, I can’t tell whether what you’re saying is meaningful. It feels tautological.
Given that an executive assistant has unwritten knowledge that is necessary to do their job, where your evidence that no mathematician has analogous knowledge (using the word in the common way, not whatever way you mean it)?
It’s possible, but it’s not as obvious as you seem to think.
I don't know that any of this really matters. I could just as well say that you don't know anything at all about the internal experience of your dog's mind. All you can do is read behavioral patterns and attempt to make inferences. At best you have an approximation, and approximations tend to be wrong. Math is correct knowledge, not approximations of reality. Correctness is not a property of the idea or inference itself, since ideas and inferences can be wrong; it's the result of a verification process which you cannot possibly carry out in its entirety relating to the internal conscious experience of your dog.
We can dig into the philosophy of these definitions, but I think the far more interesting point is that even if we grant the existence of this kind of knowledge in the minds of human mathematicians, we have passed the threshold where that "knowledge" can keep up with systems that do not have access to it. Moreover, to claim humans have a "vast amount of mathematical knowledge" that is apparently valuable and that AI systems don't have, you'd have to prove that this "knowledge" is not implied or cannot be reverse engineered from the entire corpus of mathematical writing on which AI systems are trained. You'd also have to demonstrate that this "knowledge" leads to actual results that AI systems cannot generate without it. Given the results AI systems are producing, which are far beyond human ability at this point, it is more likely that AI systems have already internalized the entirety of this so-called "tacit knowledge" and then went much further, much faster, without humans in the loop at all.
As a response to my overall position, no, I think you threw out almost all of it.
On the question of a single word out of my entire position, that is a reasonably fair statement for mathematics (which is the topic under discussion). The fact that you think it's tautological supports both that you agree with its correctness and that this is a mostly irrelevant side conversation. And whatever you think the answer should be is not somehow not subject to the constraints of logic.
Apologies, I was referring only to your idiosyncratic and non-explicit definition of what knowledge is and isn’t, and it’s tautological and dubious nature.
Not your contention that LLMs likely have something analogous to what you call “ideas” (you’re almost certainly right).
Mostly irrelevant? Dunno, maybe according to your rigid ontology ;-p
Those are simply called ideas, they are not unique to humans, and they are more likely to be wrong than right compared to anything OpenAI just produced. It would be bold and almost certainly spectacularly wrong to assume that multi-trillion-parameter AI models could not possess their own such ideas, generated during the training process as part of their internal model of the world. Beyond that, if we assume that such knowledge does exist in humans, its marginal value is clearly nearly zero now, as AI systems without access to it are vastly outperforming all human mathematicians combined by multiple orders of magnitude.
They aren't just ideas, i read that in semiconductor manufacturing these old heads have a tremendous amount of process knowledge that's never been written down.
I'd need to see specific examples. It's not clear to me that I'd consider this knowledge about the world but rather agreed upon conventions for how humans work together.
I do research on programming languages. There are many facts about programming languages that (1) nobody else knows and (2) I have not written down because I just haven’t had the time / opportunity.
I think his grain of truth is that human private knowledge is a) not special and AIs can/will do it too, and b) AIs will vastly outstrip human capacity for this type of knowledge.
You scoff, but when I watched my theoretical computer science professor in a YouTube seminar (the kind that barely anyone watches) just at the start of the LLM news basically he too saw that humans were done. That was years ago. Academics see things on a different timescale. The issues are deeper than the hype.
At the minimum you ought recognize that world class experts would disagree with your dismissiveness. Trying to explain the differing positions should not earn such immediate dismissal.
I am personal friends with famous, world-class TCS professors who have specifically asked me for my opinion on where AI is headed and respected my responses.
"lol no" is not a respectable response period. Need I remind you, you called the other guy "absolutely ridiculous". The fact that you are buddy buddy with some elites does not excuse you from intellectual obnoxiousness. And you are further ignoring the specific fact given that there are TCS academics who likely disagree with your opinion and disingenuously conflating that fact with the personal fact of a few others having had entertained your personal views on the matter in order to dig into your positionality on this forum with a total stranger. That toxic ad hominem and status-based behavior tells me you are not of their caliber as a responsible intellectual. If you yourself are an academic you should be ashamed of the immature and unenlightened move you just made, but I should have seen it coming given your initial behavior toward the other person whom you disagreed with anyways.
You're also failing to comprehend my passing comment about professors as a minimum criterion for the diversity of what reasonable opinions on the issue ought to like. I said it order to increase an open minded discussion, whereas you then used your familiarity with academics to validate your specific views. There's a world of difference there already, and metacognitively yours is the problematic one.
The answer to that depends on exactly how one defines writing. If by writing we mean full alphabets, etc., then no, but that is not the critical function that the word played in what I wrote. If by writing we mean encoding structured mathematical information physically (which today consists not just of written words/sentences, but also non-linguistic equations and computer programs) so that it can be accurately and unambiguously digested (and modified or corrected by) others, then yes: as far as we know there was no mathematical knowledge outside of spoken and bodily counting or the most basic visual symmetries of objects like stones or sticks.
I was replying to your original post, which said nothing about mathematics. Rather it was about knowledge: "There is no such thing as knowledge that has never even been written down a single time by anyone or anything." And there's no evidence one way or the other about pre-writing math knowledge.
And of course Chinese is not written alphabetically, although I'm not clear what your point is about "full alphabets." (Technically, Arabic is not written with an alphabet either, but rather with an abjad--and the Arabs invented algebra. Similarly for most other languages written with Arabic script. But I won't argue that point, which I admit is rather esoteric.)
