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After Math

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Re: After Math

#31

Post by charcircuit »

>The first assumption is wrong because to really solve a mathematical problem, providing a mere answer (even if formally certified) is not sufficient. What is missing is an intelligible proof that human mathematicians can understand and use to advance the aims of mathematics.

This makes a bad assumption that humans need to be the one to advance the aims of mathematics. LLMs could be what advances the aims of mathematics and we just have to worry on making it so LLMs can digest these proofs.

>Nevertheless, if it turns out that what OpenAI has provided is a mere answer

It has a proof attached. Saying that it "doesn't provide understanding" does not invalidate that there is a formal proof. It fundamentally is trying to expand the requirements of proof to be something more than is required.

Re: After Math

#32

Post by robotpepi »

yazaddaruvala wrote: post #12

I think as a civilization we need to postulate a new term: “purpose death” Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence. I truly think because of the pace of innovation this will be a universal feeling for every hu…

> I’d say Terrance has recently left the denial phase, the anger phase

What are these comments? Tao, in particular, has been pro AI since years ago...

Re: After Math

#33

Post by robotpepi »

charcircuit wrote: post #31

>The first assumption is wrong because to really solve a mathematical problem, providing a mere answer (even if formally certified) is not sufficient. What is missing is an intelligible proof that human mathematicians can understand and use to advance the aims of mathematics. This makes a bad assumption that humans need to be the one to advance the aims of mathematics. LLMs could be what advances the aims of mathemat…

For the moment, AI is not capable of advancing mathematics _in the sense_ you're describing. AI is very bad at designing stuff, asking questions, etc. Maybe in the future you'll be able to ask the AI "cure cancer" and it'll do it, but for now we're very far away from that (this doesn't mean the current achievements aren't impressive).

Re: After Math

#34

Post by brador »

Math needs its own unique type of prompt engineers who can understand the output quickly.

That’s where the future of mathematicians lies.

Re: After Math

#35

Post by charcircuit »

robotpepi wrote: post #33
charcircuit wrote: post #31

>The first assumption is wrong because to really solve a mathematical problem, providing a mere answer (even if formally certified) is not sufficient. What is missing is an intelligible proof that human mathematicians can understand and use to advance the aims of mathematics. This makes a bad assumption that humans need to be the one to advance the aims of mathematics. LLMs could be what advances the aims of mathemat…

For the moment, AI is not capable of advancing mathematics _in the sense_ you're describing. AI is very bad at designing stuff, asking questions, etc. Maybe in the future you'll be able to ask the AI "cure cancer" and it'll do it, but for now we're very far away from that (this doesn't mean the current achievements aren't impressive).

This is why we may see the role of people wanting to advance mathematics instead of trying to do proofs themselves to push the frontier instead focus on improving these models to be capable of advancing mathematics.

Re: After Math

#36

Post by robotpepi »

octoberfranklin wrote: post #3

The first assumption [1. AI really did solve a problem in mathematics] is wrong because to really solve a mathematical problem, providing a mere answer (even if formally certified) is not sufficient. This subjective attitude turns mathematics into nothing more than number-poetry. That would reduce mathematics to something very pathetic. Focus instead on attribution. Yes, OpenAI took the last tiny step in the process…

> This subjective attitude turns mathematics into nothing more than number-poetry.

I don't think you understood the point. The point applies to all of basic science. You of course want some explanation supporting the raw answer, so you can use that insight in other contexts.

Re: After Math

#37

Post by skissane »

yazaddaruvala wrote: post #12

I think as a civilization we need to postulate a new term: “purpose death” Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence. I truly think because of the pace of innovation this will be a universal feeling for every hu…

> I truly think because of the pace of innovation this will be a universal feeling for every human for the rest of existence.

Why would it be? Imagine a man who is a student in a kollel in Kiryas Joel. He spends his day studying the Torah, Tanach, Mishnah, Talmud, the Mishneh Torah, the Shulchan Aruch, the Zohar, etc. Then at night he goes home to his wife and 12 kids.

Do you think he experiences "purpose death"? Do you think his wife does? Do you think his children will? Do you think AI is going to make them start?

If anything, AI might make his lifestyle more economically sustainable than it was before – if nobody works because AI has taken all the jobs, and everyone gets paid universal basic income, he is no longer faced with the arduous struggle of supporting a large family as a full-time student.

And there's nothing specific to Judaism about this – I'm sure in some seminary in Qom, you'll find the Usuli Twelver Shi'a analogue.

Re: After Math

#38

Post by robotpepi »

charcircuit wrote: post #35
robotpepi wrote: post #33

Earlier quoted context omitted.

For the moment, AI is not capable of advancing mathematics _in the sense_ you're describing. AI is very bad at designing stuff, asking questions, etc. Maybe in the future you'll be able to ask the AI "cure cancer" and it'll do it, but for now we're very far away from that (this doesn't mean the current achievements aren't impressive).

This is why we may see the role of people wanting to advance mathematics instead of trying to do proofs themselves to push the frontier instead focus on improving these models to be capable of advancing mathematics.

I don't think the essay was proposing that mathematicians should continue to focus on proving everything by themselves forever. It's mostly a critic of how the discussion is focusing too much on that mere "yes/no" answers is the same as makign mathematics advance.

Re: After Math

#39

Post by coderenegade »

The problem with the article's line of thought is that mathematicians can't control what others do with models that are capable of generating proofs for hard problems. Sure, maybe there's a career in taking known proofs spat out by the oracle, and translating them for mortal digestion, but I'm not sure that's what most mathematicians signed up for.

Re: After Math

#40

Post by robotpepi »

zarzavat wrote: post #28

The hand wringing is premature. Thus far AI has only shown a superhuman aptitude for brute forcing proof of existence: - Disproof of the Jacobian conjecture by example - Construction of a non-sofic group - Existence of singularity in Navier-Stokes Mathematical conjectures tend to be universally quantified, especially those conjectures that are used as building blocks (e.g. RH). If anything, AI models are currently pe…

> Disproof of the Jacobian conjecture by example

It should be noted that there was a manuscript, available online since the beginning of 2025, with a solution to the Jacobian conjecture:

"Adrian Vasiu claims that the 7 page AI paper on the 3D Jacobian conjecture counterexample used notation and concepts from a draft of a paper jointly written with Alexander Borisov and Ofer Gabber, dated to January 14, 2025 and made publicly available on January 16, 2025."

The extract is from wikipedia, where the sources are given.

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