101–110 of 366 posts
> AI-generated papers could overwhelm peer-review systems with low-quality work That's not a problem unique to math, or even to academia. It's a problem in every context in human life where people communicate via written documents.
It is potentially worse with math because accuracy is much more important and there are fewer reviewers compared to other fields.
Earlier quoted context omitted.
To further this assertion, there is almost no value to deeply esoteric math that is technically correct, but completely inapplicable to any scientific reality, and completely unintelligible to humans. Consider these findings deep, dark corners in the unfathomably large hyperspace of mathematics. My guess is AI will be incredibly adept at identifying these types of findings, and it will be exceedingly difficult for hu…
Sorry but I couldn't agree less. Deep esoteric research and trivial looking boring research can be as useful as state of the art trending areas. "Jobs for nerds" as has been stated, has given surprising and unexpected advances, or leveraged incredible advancements. An standard and boring bacteria in a specific Spanish biome, gave us CRISPR-Cas. There ar hundreds of examples. True knowledge is, and will be, a human en…
> …
> True knowledge is, and will be, a human endeavor, deiven by human curiosity. Promoting curiosity is the sign of a developed society.
Unless I misunderstand, it sounds like you do agree? My point is that without human mathematicians LLM output is meaningless, and without human mathematicians holding the reins, LLMs would probably quickly devolve into “proving” things that are not only completely unintelligible by humans, but have no utility.
Your examples of esoteric mathematical concepts are anecdata. The vast majority of esoteric mathematics does not have utility. Mathematics is an incredibly large space of concepts. Consider the number of provable theorems in number theory alone, perhaps even related to specific subsets and sequences of numbers. The vast majority of the findings in that domain will not be isomorphic to some real world problem, they will be trivia.
We will need mathematicians to separate the signal from the noise.
I'm curious about whether we will start discovering new maths in the next few years that provide insight into unsolved CS or Physics problems!
This is all contingent on AI forays into mathematics being slop and low quality. However it's clear that recent AI models are capable of genuine mathematical achievements which surpass the frontier of what humans are able to accomplish (wrt the unit distance Erdos problem). The issue is, how is a group of intellectuals, whose identity derives from their ability to do something rare, useful, and requires many years to…
It's literally a set of recommendations for researchers on how to use AI to advance the field and prevent slop from overwhelming the people who might do anything with the research produced.
For people who are so eager to declare that everyone else is just having an existential crisis because "your culture is commodified", AI people are getting awfully defensive about this document.
Another mathematician already predicted this, but you didn't listen. His name was Theodore Kaczynski. It's time to reap what you've sown.
I think plenty of people "listened." But what was his plan and how would you have proposed implementing it?
> However, the declaration argues math is more than a machine for producing correct answers. There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.
The most important part of math is advancing human understanding. A correct answer by itself is not as important as understanding why it is correct.
Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field. Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI gene…
The future may not have access unless we fight to ensure they do. This is how I read the article.
Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public. Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question. The annoying thing about recent AI advances is that they target questio…
That's an interesting perspective and I wholly disagree with the conclusion You are saying that tough problems with no applicability are useful because people that you happen to respect got good by their curiosity and pursuit of trying to solve these kinds of problems and failing, but branching off into other cognitive areas as mathematicians Now if I know anything about math for the sake of math, and academics, thes…
Earlier quoted context omitted.
The most important part of math is advancing human understanding. A correct answer by itself is not as important as understanding why it is correct.
To further this assertion, there is almost no value to deeply esoteric math that is technically correct, but completely inapplicable to any scientific reality, and completely unintelligible to humans. Consider these findings deep, dark corners in the unfathomably large hyperspace of mathematics. My guess is AI will be incredibly adept at identifying these types of findings, and it will be exceedingly difficult for hu…
Earlier quoted context omitted.
Like other commenters, I think you’re also underestimating the complexity of esoteric higher level math. Consider the “Magnus Carlsen” of mathematics, who is more capable of understanding mathematics than any other human. But then also realize that that individual has probably devoted their entire career into a specific subdomain of mathematics. Within other deep recesses of mathematics, this Magnus equivalent will b…
I don't get it. LLMs don't have ego, they don't have the ability to say "no, this should be obvious, I'm not going to explain further", they are just token predictors, and given context, they can generate more tokens. If you don't understand how the answer was derived? You just ask more questions and it isn't going to get bored or annoyed, it will just try to answer the questions. Is that what is offending you so muc…
Of course it'd be super helpful to have, say, a teacher who could tailor explanations to anyone's precise background (e.g. where possible, using examples that come from the student's field of study when explaining some abstract concept). Or, if some definition comes with some precondition that has no obvious purpose, perhaps an omniscient teacher could explain why it's there with concrete counterexamples.[0] But even granting all this, I think that mathematical intuition is necessarily based on a lot of hard work actually exploring definitions on one's own, with pencil-and-paper and a lot of thought. That is to say, even though the process could probably be sped up a lot with a nigh-omniscient teacher[1], I doubt that a student wouldn't still need years of training to even have a clue what's going on.
(I'm saying all this, by the way, as someone who is terrible at all this and has very little mathematical maturity[2]—I'm speaking from my own frustrating experience....)
[0] c.f. Lakatos' excellent book Proofs and Refutations
[1] without the "curse of knowledge," or else we're back to square one of "answers that are correct but useless"
[2] e.g. the "post-rigorous stage" described in https://terrytao.wordpress.com/career-advice/theres-more-to-...