Posted by smilelamp 16 hours ago
Once again perpetuating the cardinal sin of lionizing mathematics heroes. Which to be fair is just THE culture of higher mathematics.
What good is a minuscule elite Cabal of savants? If these deep insights are inaccessible to 99.999% of the population, then they are no better than the manuscripts written by AI. We already have those.
among all the discourse, it seems mathematicians are vaguely converging on this higher layer of abstraction being where the human value in math is now. It seems across domains (such as in software too), people speak of “judgement”, “taste” and other fuzzy concepts around defining problems rather than solving them. The lowest level of abstraction where humans win is asking the questions, rather than merely answering them.
As math is so verifiable, the “transition” seems most poignant and quick there. Watching these big name mathematicians discuss this unfolding revolution in real time is fascinating.
Sure it can solve math problems by just following the implication arrows. But those are just low hanging fruits, i.e problems that humans were too lazy to deal with.
> AI is now undeniably capable of making groundbreaking contributions across many areas of mathematics.
These fall under the class of problems that have solutions which can be inferred more easily from applying massive computation, which is a subset of problems that human minds are trying to solve.
It's like being a CIA analyst, maybe. You have an overwhelming number of information sources of varying quality and non-obvious relationships. Applying massive computation will definitely allow you to draw new insights and identify trends that would have been difficult, or nearly impossible for unassisted human reasoning.
From what I understand, this is the sort of thing that the LLMs have been particularly effective at in mathematics, applying massive computation to the existing field and with a combination of impressive vector space search and runtime evaluation, deriving plausible solutions to certain narrowly defined problems.
Here's a harder one: you're in a bar, sitting having drinks with friends. There's an attractive girl sitting with some of her friends that has glanced at you a couple of times. What should you do?
Taking into account, of course, the entire human experience from marriage status, age, rejection likelihood, your friends opinions, her friends opinions, your family, your hormones, everyone's intoxication level, how well you slept, the noise level, how long her glance lingered, and the billions of other things that go into it - entire lifetimes of experience, genetic behavior predisposition, etc...
This is just a small example of a brief problem that a normal human has to solve hundreds or thousands of times per day that don't fit into the class of solutions that LLMs would be particularly adept at. It's easy to come up with a lot more.
So yes, I'd argue that those neatly formulated, clean problems with clearly provable solutions are low hanging fruit.
Some of these problems have had mathematicians dedicating their careers towards getting closer to a solution. Your comment reads like wishful thinking.
I won't even start on "AI is unconscious"...
Machine proofs are useful machine understanding. You don't read the proofs, that's holding it wrong. You point another agent at the proof and prompt "use these ideas to prove this lemma that's useful to me". And it works, agents are faster given access to the proofs than without.
This analogy is pants on head stupid. They're talking as though the only thing AI will ever solve is the Langlands program, not as though we have discovered a generic tool.
It's like saying "they drove the car one mile -- and every mile driven leads to more roads that we can trot along, why are you so worried about the future of horses?"
If we have a theorem proving machine, then we can use it to prove theorems. If we have a machine to solve the Langlands program in one day, then we'll think of more things to prove after that. There's a million unsolved questions in number theory unrelated to Langlands, and if we knew Langlands (and why it was true) we could make new conjectures that our theorem proving machine could solve, rather than having to speculate for 50 or 100 years like now.
The possibility he's not considering is that the machine might be better even at conjectures, and then there really is no role for humans once the machine already knows things our primitive meat brains are too small to understand. But what he's saying isn't "pants on head stupid".
If you've forgotten how to think for yourself, you can also ask an LLM.
The host of the blog, Tao, was an early booster. He didn't think through the implications, and seems to have expected it to remain unable to do interesting work. Today he's on a "war footing".
I don't think mathematics are uniquely skilled at predicting the future, and the impacts of AI on their profession.
I perfectly understand his point and it is not about being selfishly frustrated by a machine being better than him. Is that really your interpretation of the discourse?
Either way, either there's no future for AI in math, or there's no future for people in math. I think this is true for many professions.
https://fortune.com/article/ai-godfather-radiologists-obsole...
Ironic that you resort to “think for yourself” as your silly name calling go to btw
It took us a while to make the planets line up neatly in a heliocentric system. Just last month I read that a whale mother "might" grief while carrying her stillborn child.
The limiting factor is human imagination and comprehension. No offense, but see your comment.
I think AI has already invented new math, but the guys haven't looked for it because they didn't think it possible. And even under their noses, they wouldn't understand what they see.
> It's not what you look at that matters, it's what you see. —Thoreau
Could AI create a novel set of axioms (a new math) from which things like RH become a by product? I think that would be hard to miss.
They have been so far.
I know, unrelated truths and coincidental timelines, part of me giggles nonetheless since the whole belief system behind the market relies on infinite coincidences
Sums up the reaction from a lot of developers too.