[isotypic]

I cannot quite share your enthusiasm. The clearest analogy that I can think of to try to explain why I feel this way is that it seems there will eventually be a phantom textbook of all of mathematics contained in the weights of an LLM; every definition, every proof, etc; and the role of a mathematician is going to be reduced towards reading certain parts of this phantom textbook (read: prompting an LLM to generate a proof or explore some problem) and sharing the resulting text with others, which of course anybody else could have found if they simply also knew the right point of the textbook.

To be blunt, this seems incredibly uninteresting to me. I enjoy learning mathematics, sure, but I just don't find much inherent meaning in reading a textbook or a paper. The meaning comes from the taking those ideas and applying them to my own problems, be it a direct proof of a conjecture or coming up with the right framework or tools for those conjectures. But, of course, in this future, those proofs and frameworks are already in the textbook. So what's the point? If someone cared about these answers in the first place, they probably could have found the right prompt to extract it from this phantom textbook anyways.

You could argue for there being work still like marginal improvements and applying the returned proof to other scenarios as happened in this case, but as above, what is really there to do if this is already in the phantom textbook somewhere and you just need to prompt better? The mathematicians in this case added to the exposition of the proof, but why wouldn't the phantom textbook already have good enough exposition in the first place?

I think my complete dismissal of the value of things like extending the proofs from an LLM or improving exposition is too strong -- there is value in both of them, and likely will always be -- but it would still represent a sharp change in what a mathematician does that I don't think I am excited for. I also don't think this phantom textbook is contained even in the weights of whatever internal model was used here just yet (especially since as some of the mathematicians in the article pointed out, a disproof here did not need to build any new grand theories), but it really does seem to me it eventually will be, and I can't help but find the crawl towards that point somewhat discouraging.

[ted_dunning]

In Erdös idiosyncratic nomenclature, all the best proofs are "in the book" and it was always a joyful thing to not only find a proof, but to find the proof that is in the book.

Who cares if it is God's book or the machine's Xeroxed copy?

[xamuel]

Long before Erdös, we had Plato and Socrates develop the theory of anamnesis, that there is no such thing as learning, but rather, whatever we supposedly learn, we actually remember (we knew it already and had forgotten it). Presumably this should be understood only of universal facts (like mathematics), not contingent facts (like who was the president of the U.S. in 1950).

[teiferer]

Remember from ...when?

[xamuel]

Before birth. ...Hey, don't point that pitchfork at me, point it at Socrates. In his defense, that kind of does describe when LLMs acquired their knowledge (if we consider "birth" to be the moment when the already-trained weights are sent to the GPU) https://en.wikipedia.org/wiki/Anamnesis_(philosophy)

[teiferer]

> Before birth

Any scientific basis for this claim?

Pre-conception is unlikely to be really possible outside some esoteric circles. While in the womb there could be some limited experiences that get ingrained in the mind as memories, but I don't think that's the topic here.

[isotypic]

I mean, my reaction to God coming down and saying they were bored of being God and instead they would just sit around and answer all of the mathematician's questions would largely be the same, so yes, who cares if its God's book or the machines Xeroxed copy?

"The Book" is more interesting to me if I am the one coming up with the ideas to fill it in. Maybe this is a bit egotistical, but I'd like to think it is allowed to have a desire that you, personally, are contributing to something in a meaningful way. Like, if you are on a sports team, it'd be more fun to win a game if you were on the field than if you were benched, and I think that's okay. And ultimately I don't find dredging for proofs from an LLM particularly meaningful, nor do I see it as a particularly personal contribution, as anybody else could have done the exact same thing with the same prompt.

This isn't to say I wouldn't love to read the proofs in "The Book" for problems I care about, I just think I'd eventually get bored of only reading. And so its hard to be enthusiastic when this book is being built through an LLM.

[energy123]

If ASI does create an abundant future I think many are going to have that familiar listless feeling of enabling cheats on a computer game and all the mystery and fun is gone.

Technology in general (smartphones, social media, search) even without AI is creating this feeling, as it shrinks the world and makes it less mysterious.

It's worse than boredom it's more like nihilism.

Then when you strip purpose and meaning from a human you get something very bad, despondency being the best case outcome.

[Windchaser]

Aye, but it’s also possible for people to find their own purpose and meaning. Some find it in religion, some in art, some in love or nature.

It will be a transition, for sure - there would no longer be meaning in “winning the game” in a capitalistic or scientific sense. Anything you want to produce or learn, the AI could already produce or has already learned. Now you have to do it just for the love of the process.

I have a musician friend who likes to say that good artists overwhelmingly make art for their own benefit. Not to advance the world or blow people’s minds, but because something inside of them needs to come out, and art is how they express it. And that part of us isn’t going to go away.

[energy123]

Basically that's Viktor Frankl's insight and it's more important than ever. Combined with the Buddhist precept of non-attachment.

[qnleigh]

> it'd be more fun to win a game if you were on the field than if you were benched

This is a good analogy for AI work displacement. Probably would resonate with some of the college students who boo'ed Eric Schmidt.

[k_roy]

And you just expressed the thoughts of every engineer that writes code for a living who is either left behind, or embracing the technology to hit KPIs and QVRs.

[qnleigh]

I want to push back against the notion that the math already exists in the weights, both in the practical and the philosophical sense. The LLM had to do an enormous amount of computation to find the counterexample. We know it wasn't looking up the answer from its internal representation, because the conjecture was unproven. The proof came into being when the model output it, and if they'd run it for less time or asked it something else then the conjecture would still be unsolved.

I'm also afraid of a world where AI completely replaces human mathematicians, but if we remain collaborators, then that's a world I can still feel excited about.

[BobbyTables2]

It’s funny because the shift from handmade goods to automated factories didn’t seem so bad. Same for mechanized farming instead of mules and people.

Shifting from “human calculators” to machines for arithmetic is also hard to argue against.

I think what makes the AI transition difficult is it impacts a wide range of high-value activities that would have been implicitly assumed to always remain human.

I do have great trouble seeing how a pile of matrices is ever going to be capable of innovation. Maybe with sufficient entropy and scale, it will… The day that becomes practical will be a turning point in history.

Economically, goods and services are often priced based on labor/“value added” aspects. Lawyers’ fees aren’t driven by paper costs! If AI takes a huge bite out of intellectual labor, the future could become very different…

BTW, your book description reminds me of the 2025 movie “A.I”. I thought it was quite good.

[kaashif]

There isn't anything functionally special about the human brain - why is there some reason to expect the human brain is capable of innovation but no program, even one far more powerful than the brain, is not?

You admit this possibility so I'm not arguing with you, but it seems far more plausible to me that we can build something better than the brain.

In the limit we can just grow brains and put them in computers anyway, then the debate is moot. That's a really hard problem but of course not physically impossible.

[naasking]

The cool thing about LLMs is not only might they be a database of all mathematical theorems, but they can also apply those ideas to the problems you're trying to solve, which is exactly what you said you're interested in. Not sure why you lack enthusiasm.

[isotypic]

LLMs applying the ideas to problems I'm trying to solve is exactly what I said I wasn't interested in, actually. Because the LLM doing this for me reduces back to me simply reading from the textbook, only now I have no problems I'd be interested in applying things to since, again, they're already in the textbook.