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After Math

terrytao.wordpress.com

41–50 of 170 posts

Re: After Math

#41

I appreciate the wordplay in the title.

It's a clever pun, but it implies maths is ended, which is the exact opposite of what the article says. Given how many people responded to strawman misinterpretations of the Fields medallists' statement yesterday I don't expect that to have a positive effect on the discussion.

Re: After Math

#42

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 read

> The important question is, therefore, not whether AI will defeat mathematicians, but which mathematical ends we want AI to serve.

and had the opposite interpretation as I see you having. To me, it reads as the authors [1] acknowledging, as you put it, that

> AI will run and trample anything that stays in front of it.

and that mathematicians need to find out where they want to go:

> Rather, it is an opportunity to clarify what mathematics is all about. We should ask again what we are after when we do mathematics.

This surely does involve purpose death, but also purpose rebirth.

[1]: Silvia De Toffoli and Eamon Duede, instead of Terence Tao, although I imagine Terence endorses the message.

Re: After Math

#43

Earlier quoted context omitted.

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'…

You might have delivered 10x more code, but did you deliver 10x more value?

Or put another way, are you making 10x more money?

It's easy to spend excess productivity effectively wasting time. Most companies did it before AI, and will continue doing it after.

It's easy to believe you are not wasting time because you have more bugs fixed or more features delivered, but if it doesn't move the bottom line, what is the point?

Re: After Math

#44

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.

Most mathematicians do compete for funding, based essentially on how many articles they can publish and where. Publication strongly favors problem solving. Universities are ranked on the same criteria.

What we see is a panic reaction to the fact that problem solving is "easy", which affects the future of the management of mathematics, not of mathematics itself.

Mathematicians are not luddites afraid of AI, is the academic publishing industry mixed with management interests speaking here.

If you look at the Leiden Declaration https://leidendeclaration.ai/ then you notice two weird IMO facts:

- that it was stirred by the International Mathematical Union Committee on Publishing

- that is a mixture of the older San Francisco Declaration on Research Assessment DORA https://sfdora.org/read/ and recent fear of commercial AI competition

Re: After Math

#45
post #25
post #21

Earlier quoted context omitted.

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 nov…

This is tricky, because we really want language-independent training of skills. We know that self-play type of reinforcement learning is incredibly effective when possible. But at the same time, they are our tools - so we need supervised language training for this reason? It's possible that training just needs to be rebalanced so that RL with rewards is balanced with rounds of language adjustment. And to really make that happen, benchmarks need to score the models on that.

Re: After Math

#46
post #26

Earlier quoted context omitted.

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.

So you decide that the reality is another view and that's settled?

Re: After Math

#47

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…

Tha Jacobian conjecture is (was?) notorious for publication of false proofs. There have been many, not all by those who shouldn't have known better.

Re: After Math

#48

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…

Most people don’t reach self-actualization and never have. This has nothing to do with AI.

With regards to technology specifically, new tech has been making high-investment skills useless for the last 500+ years. The printing press, the loom, etc. This is not anything new.

Some of these AI doomers really need to read more than AI Substacks and Twitter feeds. I suggest a book about the history of technology.

It is perfectly reasonable to suggest that we make an effort to direct a technology in certain directions. It is not reasonable to throw all rational thought out the window and operate as if real world AI is synonymous with science fiction.

Re: After Math

#49

I feel like, to different degrees, we’re witnessing the same effect seen in image generation or text generation. People who don’t know better about art or writing would be impressed by what gen AI can produce and will find it indistinguishable from a human-produced equivalent. This admittedly is good enough for most business endeavors that cared only about the process, and would gladly avoid the cumbersome (to them)…

business endeavors that cared only about the process, and would gladly avoid the [...] process

you mean they care about the product...

Re: After Math

#50
post #24

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…

> Any interruption or automation to what Im currently doing will just open the door to exploring new and different things.

But that's the rub: At some point, possibly sooner than most people think, there won't be anything left that isn't automated. Any human trying to do something new will then be worse at achieving it, and likely even detrimental. Just like the monetary value of horse labor today isn't just small, it's actually negative.

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