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After Math

terrytao.wordpress.com

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Re: After Math

#21

Post by kzrdude »

magimas wrote: post #18
niemandhier wrote: post #13

The proof OpenAi presented allegedly reads like written by someone in acid. It will take probably a while before we will get a translation into something that than will actually have a positive impact. That could be either a second proof or a streamlined version of the AI one.

You even notice that with the recent opus and fable models by Anthropic. If you give them a wide open problem statement, they'll start talking a lot of semi intelligible gibberish. My guess is that this happens because that's not what they are evaluated on anymore for these kinds of tasks. The generated code is evaluated (in this case the lean code). So talking a bit of gibberish in the language part so you have more…

We need to recognize this as a failure in training. It did some useful stuff but it can be much better. A training signal is likely missing.

Re: After Math

#22

Post by doctor_phil »

matherial wrote: post #11
stabbles wrote: post #7

Wouldn't AI make the field of mathematics more ambitious? In software development it feels that way: there are often tasks I can take on that would have been too risky in 2025, because it was unclear if they were worth it. Now you generate a prototype and can make much better judgement calls what is possible and what is worth pursuing.

It might feel that way, but I'll ask again: where's the payoff? Where's all the amazing software that everyone is now supposedly shipping 10x faster than before? If I look at the software I'm actually using day-to-day, or that my friends are using, all this stuff looks exactly the same as it did in 2021. Not a single product release from Google, Microsoft, or more scrappy companies in the past 6 months made me go "wo…

From personal experience in a small (total <10 people) company, we have definitely 10x our product in the last two years. What 4 devs did in 4 years have been dwarfed by what 2 devs were able to do in 1 year with AI. I'm not so familiar with the giant companies, but from afar it seems like they already have practically all the code-writing capacity they wanted anyway. Google could say "let's build a browser" or "let's build a mobile phone OS" or "lets build an experimental Fuschia" and throw all the people they needed on it already.

Re: After Math

#23

Post by grey-area »

traject_ wrote: post #10
octoberfranklin wrote: post #6

Earlier quoted context omitted.

What you describe is Tao's rebuttal of #2. I fully agree with him there. It's his rejection of #1 that makes me sad.

If you mean > What is missing is an intelligible proof that human mathematicians can understand and use to advance the aims of mathematics. Then that is not necessarily subjective either if an AI can produce an actually intelligible proof. The problem is that as mathematicians with PDE expertise have mentioned on Twitter the actual solution seems to devolve into an unreadable mess focusing on irrelevant details after…

Well perhaps we should use occam’s razor here.

If it doesn’t seem like the lllm understands the proof, it probably doesn’t.

Just because it generated something that works doesn’t mean it understands it, and the evidence from its proof is that it does not, which is not very surprising given the technology we’re talking about, which generates likely phrases based on a corpus and training.

Re: After Math

#24

Post by malux85 »

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 would argue that purpose death is a normal step towards enlightenment and it was only the fierce, unrelenting, all consuming drive of capitalism in the western world over the last 4 or 5 generations that have pushed everyone to define themselves (nearly) solely in terms of their work.

I do not at all feel purpose death from AI (been a software developer professionally for 20 years, now a founder), but I consider myself a lifelong learner, with infinite curiosity, in a universe with infinite challenges. Any interruption or automation to what Im currently doing will just open the door to exploring new and different things. This doesnt come from an immediate desire to do anything different, but having the confidence that whatever comes along, I will figure it out and have a lot of fun doing so.

Re: After Math

#25

Post by NiloCK »

kzrdude wrote: post #21
magimas wrote: post #18

Earlier quoted context omitted.

You even notice that with the recent opus and fable models by Anthropic. If you give them a wide open problem statement, they'll start talking a lot of semi intelligible gibberish. My guess is that this happens because that's not what they are evaluated on anymore for these kinds of tasks. The generated code is evaluated (in this case the lean code). So talking a bit of gibberish in the language part so you have more…

We need to recognize this as a failure in training. It did some useful stuff but it can be much better. A training signal is likely missing.

As I understand it, the rough guess as to what's happening here is that most recent capabilities progress comes from specific verifiable-rewards reinforcement training (RL). The RL pressures are all about task performance, but (surprise surprise) highly human-legible English language usage isn't very important to the models abilities to address the tasks.

Weirdly enough, the pressures are having them drift toward novel dialects of English that work well for their own chains of thought. Open question about whether they'd drift all the way to a new language given enough time.

Re: After Math

#26

Post by rnewme »

camillomiller wrote: post #15
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 invite you to consider that your doomer views on AI trampling everything in front of it humanize the technology and give it an agency that is in fact in the hands of its creators. It’s very convenient for them to make people think they have no control over their creation. It’s like Facebook claiming they’re not a publisher but on steroids

Except that your view doesn't change the reality, and both views are true at the same time.

Re: After Math

#27

Post by gwt4life »

jacobolus wrote: post #16
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…

The authors of this piece are Silvia De Toffoli and Eamon Duede. It is hosted at Terence Tao's blog, but he did not write it.

AI could have told him this

Re: After Math

#28

Post by zarzavat »

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 performing a useful service by disproving false conjectures, a kind of mathematical weeding.

The good news from the last couple of years of coding agents is that while models have become more persistent and knowledgable, their creativity (defined as being able to escape their training distribution and synthesize completely novel ideas) is improving at a much slower rate.

AI will only become a threat to mathematics if/when it develops the capability for creative big-picture problem solving. If that happens, the impact on mathematics will be a footnote compared to the impacts on society at large, since creativity unlocks a host of new economic capabilities.

Re: After Math

#29

Post by fwlr »

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…

Conversely, I think mathematics should retain this aspect of “number-poetry”. Consider a mathematical pursuit that lacks number-poetry but retains other features such as attribution, calculation, and puzzle-solving: I think of competitions like the largest prime number or the furthest digit of pi. Do these not feel in some sense trivial, more suited to IFLS Facebook posts than arxiv preprints?

Re: After Math

#30

Post by alansaber »

malux85 wrote: post #24
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 would argue that purpose death is a normal step towards enlightenment and it was only the fierce, unrelenting, all consuming drive of capitalism in the western world over the last 4 or 5 generations that have pushed everyone to define themselves (nearly) solely in terms of their work. I do not at all feel purpose death from AI (been a software developer professionally for 20 years, now a founder), but I consider my…

I agree with this. The substansive counterarguments all revolve around the short-term economic and emotional instability this causes
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