Do you "know", in any meaningful sense, any of OpenAI's recently publicized proofs? Do you suppose that there is any large community of non-academics that does?
One of the points the parent makes, along with the TFA, is that academia -- or more specifically, the "mathematical community"-- is a setting primarily for creating and ingesting mathematical knowledge, and disseminating it to the next generation and to other fields. Humans absorb this material slowly, through lots of discussion and collaboration -- it is necessarily a slow process. Facilitating this is one of the important functions of academia. Your usage of academic as a slur here is a bit silly for this exact reason.
I don't claim it is perfect, and we can argue about pedagogy in elementary courses till the cows come home. That's not really material. But this is one of the only settings in which such knowledge is broadly valued for its own sake, and in which there is a semblance of incentive to help others "know" this stuff as well, be they future generations of mathematicians, science and math educators and communicators, practitioners in other fields, or genuinely curious amateurs.
Your point is largely addressed in the article, did you try reading it? "In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align."
The point is that these proofs are largely useless without the insights. The value of a proof is largely in the travel, not so much in the destination.
Different person here, I read the article and they are all wrong. Hope that helps.
Okay, to elaborate, substantively, their point is that the people using these AI models are not doing it for the love of the game, but for marketing. And instead of them - and nobody - spending millions of dollars to solve the problem, successfully, they want every problem of their academic industry to persist because even though they never solve the problem, they synthesize and solve lots of other problems nobody asked for. And get to boost their egos?
Yeah, stop that. Actual alignment is on the humans themselves, if they want to remain relevant as academics and mathematicians, they need to learn how to replicate the proofs and the steps that alluded humans for decades and don't worry about the narcissistic elements that slow their industry down.
Mathematical breakthroughs with commercial relevance are few and far between, and often depend on dusting off old results which were, at the time of discovery, "solutions nobody asked for."
The NS counterxample is actually, by any market measure, a "problem nobody asked for" in the sense that its existence doesn't have any commercial relevance (beyond juicing OpenAI's IPO). So the only long-term value solving it could have is by virtue of whatever reusable theory/insights were generated along the way to the counterexample itself. The letter is absolutely right on that point.
It's not actually clear that those insights will come faster from reverse engineering this LLM proof vs. humans building theory to solve the problem themselves. So what you're saying may or may not even be an efficient way of operating. Also, it implicitly depends on mathematicians to do the hard work of creating problems and then deciphering LLM hieroglyphics for essentially free while the only immediately profitable component gets outsourced to a frontier lab. In what world is that model going to work?
Reading between the lines, it seems like maybe you have a personal grudge for some reason and simply think the technology will advance enough to where we won't need academics at all. But you should say that in the first place.
Their claim is only indirectly related to the motivations of the people using their models. What they're saying is that doing math in this way does not produce the same value as traditional mathematical research, and the people using these AI models aren't concerned about that because their marketing objectives don't depend on whether their results produce mathematical value. If people doing valuable work are made irrelevant by people doing a larger volume of non-valuable work, that's not a positive outcome.
Do you "know", in any meaningful sense, any of OpenAI's recently publicized proofs? Do you suppose that there is any large community of non-academics that does?
One of the points the parent makes, along with the TFA, is that academia -- or more specifically, the "mathematical community"-- is a setting primarily for creating and ingesting mathematical knowledge, and disseminating it to the next generation and to other fields. Humans absorb this material slowly, through lots of discussion and collaboration -- it is necessarily a slow process. Facilitating this is one of the important functions of academia. Your usage of academic as a slur here is a bit silly for this exact reason.
I don't claim it is perfect, and we can argue about pedagogy in elementary courses till the cows come home. That's not really material. But this is one of the only settings in which such knowledge is broadly valued for its own sake, and in which there is a semblance of incentive to help others "know" this stuff as well, be they future generations of mathematicians, science and math educators and communicators, practitioners in other fields, or genuinely curious amateurs.
Your point is largely addressed in the article, did you try reading it? "In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align."
The point is that these proofs are largely useless without the insights. The value of a proof is largely in the travel, not so much in the destination.
Different person here, I read the article and they are all wrong. Hope that helps.
Okay, to elaborate, substantively, their point is that the people using these AI models are not doing it for the love of the game, but for marketing. And instead of them - and nobody - spending millions of dollars to solve the problem, successfully, they want every problem of their academic industry to persist because even though they never solve the problem, they synthesize and solve lots of other problems nobody asked for. And get to boost their egos?
Yeah, stop that. Actual alignment is on the humans themselves, if they want to remain relevant as academics and mathematicians, they need to learn how to replicate the proofs and the steps that alluded humans for decades and don't worry about the narcissistic elements that slow their industry down.
Mathematical breakthroughs with commercial relevance are few and far between, and often depend on dusting off old results which were, at the time of discovery, "solutions nobody asked for."
The NS counterxample is actually, by any market measure, a "problem nobody asked for" in the sense that its existence doesn't have any commercial relevance (beyond juicing OpenAI's IPO). So the only long-term value solving it could have is by virtue of whatever reusable theory/insights were generated along the way to the counterexample itself. The letter is absolutely right on that point.
It's not actually clear that those insights will come faster from reverse engineering this LLM proof vs. humans building theory to solve the problem themselves. So what you're saying may or may not even be an efficient way of operating. Also, it implicitly depends on mathematicians to do the hard work of creating problems and then deciphering LLM hieroglyphics for essentially free while the only immediately profitable component gets outsourced to a frontier lab. In what world is that model going to work?
Reading between the lines, it seems like maybe you have a personal grudge for some reason and simply think the technology will advance enough to where we won't need academics at all. But you should say that in the first place.
1 reply →
Their claim is only indirectly related to the motivations of the people using their models. What they're saying is that doing math in this way does not produce the same value as traditional mathematical research, and the people using these AI models aren't concerned about that because their marketing objectives don't depend on whether their results produce mathematical value. If people doing valuable work are made irrelevant by people doing a larger volume of non-valuable work, that's not a positive outcome.
10 replies →