Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

After Math

terrytao.wordpress.com

Post reply on HN
Print view View original

81–90 of 171 posts

Re: After Math

#81

Post by alansaber »

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…

Exactly, people are jumping at the shadow on the wall- LLMs have achieved remarkable things regarding their limitations, but those limitations show no signs of yielding

Re: After Math

#82

Post by reisse »

The elephant in the room no one talks about yet, imo, is "should public funding of math studies be adjusted due to AI breakthroughs?"

The sports comparison is wrong here because general public never paid for the specific match results. The value was always in the show, the advertising and betting around it, the health and educational value of doing sports, etc. And the sport mostly lives on what it earns, not on public funding.

Math, on the other hand, was paid for because people and states believed progress in math might lead to meaningful improvements in other branches of science, and, in turn, in our lives. If this is better served by AI, should we keep paying for the same number of tenure positions? Should we increase their number to handle the speedup brought by AI? Or decrease because they're being replaced? Should we pay more to those using AI to do their research, or to those explaining and exploring the AI-generated results?

Re: After Math

#83

Post by dash2 »

What I don’t see much of in the article - and still less in the comments that seem to see AI-led progress in mathematics as nothing but a disaster, because mathematics exists only to provide employment to mathematicians - is a sense that mathematics has a social purpose, or duties beyond the community of mathematicians.

I thought the reason we were encouraging people to go into STEM, and providing clever people with large salaries, was that mathematical results were of practical value to the wider human race. In which case, it’s surely very good news that AI can get those results.

Isn’t all this handwringing just the equivalent of Hackney cab drivers bemoaning the advent of the motor car? Phrased in much fancier language, of course, because the people involved are cleverer and more articulate.

Re: After Math

#84

Post by justinparus »

"It is not the destination, but the journey that matters"

For now, AI will be another tool in the toolbox of mathematicians. With humans driving the conversation to help understand the world better. If/when AGI is reached maybe we won’t be in the driver seat as much. I don’t think that matters. The goal of math is to achieve greater understanding of the world, regardless if humans are driving or if an AI is.

Re: After Math

#85

Post by QuesnayJr »

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.

I think it's possible that it will play out that way, and that it's just too soon to see it. Tao was very optimistic about AI up until a few months ago, and I think what's changed is that an AI generated proof isn't that informative unless it is understandable by humans. So far experts are finding the solution to Navier-Stokes incomprehensible, so we only learn one thing (it's false), instead of the hundreds of things we learn from reading a proof we can understand.

Maybe this is a one-off, or maybe in a few weeks we'll figure out how to get AI to explain the proof in terms we can understand. Then math research will accelerate. But maybe it's not a one-off, and by this time next year we will have an oracle that just answers all of our questions, but in such a way that we don't even know what questions to ask anymore. Then AI will just mop up the existing and the subject will end.

Re: After Math

#86

Post by peacefullmind »

zkmon wrote: post #51

It shows that the human quest has been in wrong direction since the industrial age began. Domains like math and other inter-connected or inter-dependent domains - all exist in modern times only to keep people employed outside of basic work such as farming and survival. All of these domains can be removed and humans can still continue with their lives taking care of what really is needed for their survival and sprawl.…

You can remove pretty much everything in the modern world, from cars to computers etc.. and humans would still continue with their lives. Such and argument is only anti-progress.

Re: After Math

#87

Post by justinparus »

dash2 wrote: post #83

What I don’t see much of in the article - and still less in the comments that seem to see AI-led progress in mathematics as nothing but a disaster, because mathematics exists only to provide employment to mathematicians - is a sense that mathematics has a social purpose, or duties beyond the community of mathematicians. I thought the reason we were encouraging people to go into STEM, and providing clever people with…

I agree at the high level. STEM bringing general benefit and greater understanding of the world is the main reason. This is true whether or not humans or an AGI is driving the progress.

Re: After Math

#88

Post by anonymouz »

charcircuit wrote: post #72
anonymouz wrote: post #71

Earlier quoted context omitted.

The authors discuss the dual roles of proofs, and the new need to differentiate them better, clearly in the article.

I disagree with the idea that they require serving both roles in order to be considered a proof.

You can, mathematicians generally don't. That's what the article is partially about - a purely formal proof doesn't get us much.

Re: After Math

#89

Post by pylua »

rdedev wrote: post #75
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…

> AI will run and trample anything that stays in front of it. Right now that entirely depends on the whims of a few people. We can try to make it not be that but I don't have much hope in that area. See climate change > As a software engineer, I myself have only recently recovered from it Can I ask you how you came here? Right now I am getting closer to "purpose death" as you call it. Software engineering is one of t…

It’s not the execs, it’s the economic pressures. If they don’t cut cost someone else will.

For the record I feel like I dm in your position also.

Re: After Math

#90

Post by moralestapia »

justinparus wrote: post #84

"It is not the destination, but the journey that matters" For now, AI will be another tool in the toolbox of mathematicians. With humans driving the conversation to help understand the world better. If/when AGI is reached maybe we won’t be in the driver seat as much. I don’t think that matters. The goal of math is to achieve greater understanding of the world, regardless if humans are driving or if an AI is.

Why would my tax dollars go to fund someone's journey on what's essentially a hobby at this point?
Post reply on HN