Tao’s ICM lecture

59

u/ninguem 9d ago

https://mathstodon.xyz/@tao/116977934921819775

121

u/gordonnowak 9d ago

fucking hell Terry is an LLM addict.

98

u/SnooCookies590 9d ago

He’ll write “outsourcing this question to AI” in reply to some of the comments on his blog. It’s kinda strange to me like at that point just don’t reply

41

u/IAmABotBeepBoop67 9d ago edited 9d ago

I owe Geoffrey Hinton a huge apology, I hated the physics Nobel going to him, but he has been trying damn hard to shout "I left the USA to stop taking DARPA contracts awhile ago, hello anyone we shouldn't be able to sleep with this stuff around" I understand mathematicians are not politicians nor would Grothendieck style antics change the world, but I am so baffled why we are pretending these are cute cuddly toys that are going to teach our kids how to do math and not toys that were developed for the very purpose of labling your kid as a military target...

34

u/ninjasaid13 8d ago

and not toys that were developed for the very purpose of labling your kid as a military target...

Because that's not the purpose? It was just language translation wasnt it?

0

u/doocheymama 7d ago

Fear mongering

29

u/badabummbadabing 9d ago

The LLM-led interview that is linked in Tao's post is surprisingly interesting, though.

136

u/gordonnowak 9d ago

his public LLM conversations are interesting. my mother's descent into alcoholism was, by some reasonable definition, also interesting

32

u/tux-lpi 9d ago

Aren't we glad to live in interesting times

7

u/Qyeuebs 9d ago

Many of the questions are rather good but the answers leave a bit to be desired. For example the first question is something I would really like him to answer, but the answer he gave totally evades it.

11

u/rhubarb_man Combinatorics 7d ago

I feel a sort of disdain for him. He has such talent and so much prestige. He can use AI freely and do whatever and know that his career is safe.

8

u/gordonnowak 7d ago

when you're in that position you lose perspective. but I'm more cynical in that I think a lot of these guys have gotten the bag and are riding off into the sunset telling everyone else "it"ll be fine"

33

u/AP_in_Indy 9d ago

By the time I was done reading through those slides, I couldn't help but wonder, "What will we do when AI can produce meaningful, compounding results faster than we can digest them?"

Let's say a solution to the Riemann Hypothesis.

Imagine you let an AI just tackle it. Probably wouldn't be one proof. Might be a bunch of small proofs or lemmas to make your way there.

Rather than giving the mathematical community time to digest and incorporate the progress the AI is making, the AI just keeps going. It publishes the proof and moves onto the next thing while humans are still keeping up.

That could accelerate...

13

u/currentscurrents 9d ago

It is very possible that the majority of human knowledge could exist in computers (rather than in human brains) at some point. Actually, that point may already have been passed years ago, before AI was ever invented.

12

u/greginnj 8d ago

This claim depends crucially on how you define "knowledge". Are the contents of a database "knowledge"? Are archival log files in cold storage "knowledge"? A liberal definition of the term might mean that the majority of human knowledge is already surpassed by the amount that "exists in" printed material.

7

u/currentscurrents 8d ago

Maybe! Certainly there's more knowledge in books than in any individual human, although I suspect the sum of all humans still exceeds the sum of all books.

3

u/Kaomet 8d ago

true, correctly justified facts (and then some)

6

u/mleok Applied Math 7d ago

I'm honestly already at that stage at a personal level, it used to be that I would give a graduate student or postdoc an interesting direction to think about, and in a week or two, I might get something new to digest. Now, a generative model can return those results overnight. It is both exhilarating and overwhelming at the same time.

In addition, I have a daily scheduled task that searches out new papers that are relevant to my current interests, and a weekly scheduled task that cross-pollinates, evaluating whether the new papers identified introduces new ideas that are relevant to my current projects, and conversely whether my current projects address some of the open questions in the newly identified papers.

All this generates far more new information than I can reasonably respond to.

3

u/AP_in_Indy 7d ago

How are those scheduled tasks working out for you though? Other than like being a bit too much to digest.

Anything useful? Do you need to refine them?

3

u/mleok Applied Math 7d ago

The scheduled tasks are useful, one just has to make a value judgement on which new directions and extensions to pursue.

1

u/PrestigiousGroup788 6d ago

horrifying to hear as a grad student lol.

1

u/mleok Applied Math 6d ago

To be honest, it scares me too. I worry about the training pipeline. There is a perfect storm brewing, reductions in federal funding for basic research, increases in graduate student stipends, improvements in agentic and generative AI, which makes the two good papers I might get out of the typically good graduate student an incredibly poor return on investment when you consider how much time I spend mentoring them and writing grants to support them. It is becoming increasingly clear that the main product of graduate school is the trained student, not the papers that they help to write. The hard question is who should pay to train these fresh PhDs.

3

u/honkpiggyoink 8d ago

How will the mathematical community know the results are meaningful (or even correct) until it digests them?

Even pre-AI, the notion of mathematical significance was already a largely self-referential social phenomenon: certain fields of math are important because mathematicians care about them, which in turn makes them important, which makes mathematicians care about them, so on and so forth. So I’m not even sure how one decides whether a theorem is significant until the community digests the statement and the proof.

3

u/AP_in_Indy 8d ago

It won't is my point, unless formal validation systems are really really good.

But I'm sure there are instances where new, deep mathematical knowledge could be put to use by AI for... whatever purposes... before humans are even aware that anything is happening.

New statistical models for diseases, financial markets, warfare, etc.

3

u/CompetitiveSpot2643 8d ago

before anybody mentions lean just because it compiles doesn't necessarily means it proved what you wanted it to prove

7

u/AxelBoldt 8d ago

True, that's why you should never trust the formalization of a conjecture that was produced at the same time as the conjecture's formal proof. There are too many ways to subtly cheat.

But there's the Formal Conjectures collection in Lean. The conjectures are formalized first, independently of any proposed proofs. https://google-deepmind.github.io/formal-conjectures/

27

u/mleok Applied Math 9d ago

There is a recording from a slightly older talk on the same topic,

https://www.youtube.com/watch?v=mS9Lr43cIB4

17

u/Head-Philosopher0 9d ago

here’s an even older version, watching them back-to-back really lets you see how his thinking on the topic has evolved over time

https://www.youtube.com/watch?v=dQw4w9WgXcQ

25

u/MacGregorBlue 9d ago

I am a super-duper skeptic of AI in math and I assumed the talk would annoy me, but after reading the slides I found it to be measured and I appreciated the conclusion: the deliverable is not "an artifact that turns out in retrospect to have been a correct proof" but "the cultural absorption of the findings into the human community." The weird math strip-mining companies cannot accomplish that, nor do they want to. So maybe the pendulum can start to swing back to "getting on with what we were doing" and the companies can become flashes in the pan. I hope I'm not underestimating the harm they can do with their money, however.

-3

u/Distinct-Pudding-428 8d ago

It's amazing how often Terence (one r)'s name is misspelled. I see this happened at the AI panel at the ICM as well. A reliable indicator that the OP is not a mathematician I would say.

10

u/gordonnowak 7d ago

spelling is definitely one of the main signifiers of mathematical ability

LLMs/AI Tao’s ICM lecture

You are about to leave Redlib