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An OpenAI model has disproved a central conjecture in discrete geometry

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Re: An OpenAI model has disproved a central conjecture in discrete geometry

#511

Post by dyauspitr »

ori_b wrote: post #205
vatsachak wrote: post #11

As I have stated before, AI will win a fields medal before it can manage a McDonald's A difficult part was constructing a chess board on which to play math (Lean). Now it's just pattern recognition and computation. LLMs are just the beginning, we'll see more specialized math AI resembling StockFish soon.

We're automating art and science so that we can flip burgers. This future sucks.

No, we’re not going to be flipping burgers either, they will have physical robots for that. 20 years down the line I wonder what work all of us will be doing.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#514

Post by davebren »

ex-aws-dude wrote: post #503
davebren wrote: post #323

Earlier quoted context omitted.

> I think that's just a matter of having them able to work on longer and longer time horizons. No this will never do the kind of math that humans did when coming up with complex numbers, or hell just regular numbers ex nihilo. No matter how long it's given to combine things in its training data.

You're just stating the opposite of the commenter with no additional discussion Its like just commenting "I disagree" its totally pointless for discussion. That's why you're getting downvoted if you're wondering.

What did you say that added to the discussion? I wasn't wondering at all. More compute time won't create new mathematics. To believe otherwise is to misunderstand the technology and there is no amount of hackernews votes that will change that.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#515

Post by davebren »

virgildotcodes wrote: post #502
davebren wrote: post #398

Earlier quoted context omitted.

Well yeah there is likely an equivalence between computability and epistemology, but I'm not sure it matters when comparing LLM intelligence to human intelligence. There is clearly a missing link that prevents the LLM from reaching beyond its training data the way humans do.

If you look at the life efforts and accomplishments of the ~100 billion humans who have ever lived, how many lifetimes would you discount as having "non-human intelligence" based on the lack of "novel" contributions to frontier of our species' scientific understanding according to the same high bar you apply to LLMs? Do you pass that bar yourself?

Ordinary humans do novel things all the time. Where do you think LLMs got all the training data that their responses come from?

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#516

Post by xgulfie »

raincole wrote: post #280

I like how everyone laughed when OpenAI said their models will have "PhD-Level Intelligence" and now the goalpost has been moved to if AI can create new math (i.e., not PhD-Level, but Leibniz/Euler/Galois level.)

large language models do not have pigeon-level intelligence. They can't even feed themselves.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#517

Post by dawnerd »

dilap wrote: post #306
dawnerd wrote: post #299

Earlier quoted context omitted.

Yet it still codes like a junior developer that memorized all of stack overflow.

Personally I don't find this to be true anymore! It's not always great and does still will often tend towards unneeded complexity (especially if not pushed a bit), but I often find GPT 5.5 writing code I would have written myself. This was very much not true with earlier models (who make something that worked, but I'd always have to rewrite to make it "good code").

Personally I found 5.5 a massive step back from 5.4. Both of them still use way too many fallbacks and unnecessary checks, especially if you're having it output php. It's fine if you're just one person and checking everything and able to catch and correct. But it's really bad when you have a team all using it, not checking the output and trusting it's output leading to spaghetti code. Technically works, but very messy and will no doubt lead to buggy code.

It still writes like a junior dev, in that despite AI being able to get a picture of an entire repo, it's changes are typically confined to the task it's working on and will opt to duplicate logic to keep changes contained. Again, technically works, not ideal.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#518

Post by trostaft »

School-Cotton wrote: post #361
trostaft wrote: post #232

Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…

Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.

I spent years grinding to learn mathematics because it was the language I needed to solve problems that excite me. If the tools I need to do so change, I can change too. Research training is not so rigid that it can only applied to the single set of skills I developed it in the context of. I can learn this too.

Moreover, truth be told, I don't really see myself doing any less math and requiring less from my skills. At least from the moment I've begun incorporating LLMs into my research workflow to now, the demand I've had from my own skills has only grown. At least in an era prior to Lean formalization.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#519

Post by libraryofbabel »

jryan49 wrote: post #457
libraryofbabel wrote: post #448

This HN thread depressed me. I’m still thinking about why. Look past the press-releasey gushing from OpenAI and there are all sorts of interesting and subtle questions here about the role for LLMs in mathematical research. I urge folks to click through to the accompanying comments from mathematicians published alongside the result. There is a really interesting discussion going on. I particularly recommend Tim Gowers…

People are afraid for their livelihood. What do you expect?

Well yes, but there is a choice being made here and I would love to believe we can do better. The rational response to being afraid about your livelihood isn’t to spend time filling every HN thread on LLMs with embittered negativity. Not to mention all the flat denials that LLMs can do mathematics and write decent code, which is almost a self-contradictory position if you are worried they are going to replace you.

There are a lot of big issues at stake here and just because a person is interested in what AI can do and curious to discuss it does not make them uncritically positive about it’s effects on society, the economy, and the world. Yet that is often the assumption and it leads to battle lines being drawn, on every AI discussion, over and over again. It means the serious discussion gets swamped and that makes me sad.

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