Yet another Hacker News

29 points throwaway81523 3 hours ago 13 comments

sp-ti-en-ma-in 1 hour ago | parent

I feel like things have changed dramatically overnight. The field of mathematics seems to be moving at an extraordinary pace, especially following the recent developments around the Navier-Stokes problem.

25 Field Medalist and 5000+ mathematicians from leading institutions around the world endorsed an open letter expressing concerns about the impact of AI on mathematics:

https://www.mathandai.org/

More than 1,900+ mathematicians have also shown concern over the Caltech Mathathon:

https://docs.google.com/document/d/1IL0b2oG2KvvSnxn_DuXsNxuH...

James Maynard, a Fields Medalist, has also publicly expressed concerns about the implications of AI for mathematics:

https://www.youtube.com/shorts/R9VQnNv5SoI

octoberfranklin 58 minutes ago | parent

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 of solving this problem (= proving it). But it cannot attribute credit to all the mathematicians whose chat logs from the past few months were fed into its training data. Unlike a human, it can't even remember where it learned things from! For many theorems, I can still recall which exposition was the one that "sank in" for me (often not the first one!) a decade after grad school.

In my mind, this makes current LLMs unfit to deserve any credit at all -- they cannot give credit to others, so they and their owners deserve no credit themselves. OpenAI's LLM took the last tiny step, but not any of the important ones.

traject_ 53 minutes ago | parent

I don't think that's particularly true. The whole point of the Millennium Prize problems as the article states was not on absolute difficulty of the problems but on the high chance of a proof producing fruitful results leading to new concepts and theories. Any pursuit of capital T truth will of course aim for better and more clarifying abstractions and is not a subjective turn by any means.

octoberfranklin 51 minutes ago | parent

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.

traject_ 40 minutes ago | parent

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 a more readable first few pages in the proof. If it wasn't a Lean compiled proof and presented as a human artifact, it would be hard to assess if the deviser of the solution had any actual understanding of the solution.

Pulcinella 49 minutes ago | parent

Focus instead on attribution. Yes, OpenAI took the last tiny step in the process of solving this problem (= proving it). But it cannot attribute credit to all the mathematicians whose chat logs from the past few months were fed into its training data. Unlike a human, it can't even remember where it learned things from! In my mind, this makes it unfit to deserve any credit at all -- it cannot give credit to others, so it deserves no credit itself. It took the last tiny step, but certainly not any of the important ones.

Yes I fear a lot of doom and gloom around AI is unearned and only really serves to prop up the valuation of AI companies. It's still very much unclear how much work OpenAI actually did versus just copying the nearly complete homework of someone 5 minutes earlier.

stabbles 50 minutes ago | parent

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.

matherial 25 minutes ago | parent

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 "wow, they couldn't have pulled that off before". All the vibecoded "Show HN" projects seem to be half-broken and then abandoned before being finished.

It feels like we've gotten less ambitious, not more. Because yes, you can prototype more easily, but this means less commitment to what we create.

Mathematics is probably the same way. There's a short-term rush when you pull the lever, but there's less desire to get invested in what comes out.

yazaddaruvala 17 minutes ago | parent

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 human for the rest of existence.

As a software engineer, I myself have only recently recovered from it. So, it’s really interesting to watch a prominent figure in their industry publicly go through “purpose death” and the related grief. It’ll be a useful case study to re-read his written meditations through this cycle.

I’d say Terrance has recently left the denial phase, the anger phase I’m sure he wisely kept off the Internet, and is currently in the bargaining phase - ie scrambling to change the goal posts. I wonder if he will wisely keep the depression / burnout phases also off the internet.

However, soon as the goalposts keep falling, I think like most humans he will accept, retool, and come out of this grief with renewed purpose with larger expectations of himself and mathematics. This recent post even starts towards some of that - but sadly is slightly off the mark.

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

He still thinks there is controlling AI. AI will run and trample anything that stays in front of it. He needs to one day find acceptance in letting AI run while he learns how to suggest it minor course corrections which it may or may not accept, and when it doesn’t accept quickly learn from the AI why he was right or wrong.

I maybe wrong, but I think this is the cycle of “purpose death” we will all have to contend with in our own time.

camillomiller 6 minutes ago | parent

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

jacobolus 4 minutes ago | parent

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.

niemandhier 16 minutes ago | parent

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.

camillomiller 8 minutes ago | parent

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) process that leads there. But art or writing is not just about the product as much as it is about the human process itself. That is true for all creative forms, even the ones that are normalized in business. Now with the advancements of the frontier models, we’re seeing this in growingly complex fields like mathematics. It does seem to produce results, but the process is equally important. Yet we pretend to measure its ability only based on the result. It’s as if these tools grow to become better at pretending to be top of the crop in increasingly complex fields, which makes it harder and harder for people that actually have a deep grasp of those fields to explain why that’s not exactly what’s going on.