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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

#771

Post by Certhas »

teiferer wrote: post #727
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…

> Every day, it grows harder and harder to contain a mental map of recent relevant progress by simple virtue of the amount being produced. And by opening the door to LLM-generated results, you'll see greater and greater amounts without any hope of ever navigating this field again without machine help. It's a little like a software project which more and more gets extended by a AI agents with less and less review by h…

The amount of papers produced passed the point of being digestible by humans a long time ago.

I do think we will need to find a way to get away from publishing papers. But I thought that before the AI came along and made mediocre papers something you can produce in a day. The academic system seems utterly incapable of self-correcting on this point though. We haven't even managed to get rid of for-profit publishers. So how this all will go down is anybodies guess right now.

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

#772

Post by geraneum »

varenc wrote: post #425
iLoveOncall wrote: post #347

Absolutely no proof that any LLM actually found the result, and just a mention of an "internal model". Served to you by one of the biggest liars in the world. Why would anyone believe this to be true even for a split second?

This has been an unsolved open problem for 80 years. What you're suggesting is that someone connected to Open AI solved this very hard math problem, but then rather than taking credit for it, falsely attributed it to AI? The point of having an AI solve an unsolved problem, is to make it very clear that the insight must have come from the AI and wasn't in the training data. Sure, it's possible OpenAI had access to som…

> but seems unlikely. That human would be turning down a potential Fields Medal for this discovery.

I also don’t like the tin foil hatty theories and don’t know what OpenAI actually did, but an NDA does wonders! Just pointing out that this line of operations is not really unlikely.

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

#773

Post by cleaning »

bigstrat2003 wrote: post #600
Supermancho wrote: post #572

Earlier quoted context omitted.

>That's literally my job... Since you’re not in a unique position, I can confidently state that your comparison of LLMs to jr developers seems unfounded. Today, LLMs produce code that is superior to junior developer code by an order of magnitude. Notably, they demonstrate consistent syntax, clear separation of concerns, strong test coverage, organizational rigor, idiomatic API usage, and the ability to generate and m…

LLMs absolutely do not exceed the abilities of junior devs. They don't even meet that bar, let alone exceed it. Junior devs are capable of getting syntax right without someone going "hey you messed that up". LLMs are not. Junior devs get basic logic right. LLMs do not. Comparing an LLM to a senior developer is an absolute joke.

What model are you using? Llama 3.1 8b? This has not been true for years.

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

#774

Post by perching_aix »

mathisfun123 wrote: post #611
staticman2 wrote: post #603

Earlier quoted context omitted.

What's laughable is an OpenAI employee invented the term "PHD level intelligence" and you think that " PHD Level intelligence" is a real term that describes a real thing and you are repeating it here.

[flagged]

Thinking you're magically smarter than others is indeed an essential part of the NPC trend, to the extent that it in itself becomes an NPC thing to say.

It's pretty much a 1:1 match to the "we're all unique snowflakes" meme, with an army of Buzz Lightyear toys repeating the same in the background.

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

#775

Post by ricardobayes »

bandrami wrote: post #693
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…

I am curious if LLMs are better at some kinds of problems than others. IIRC this and another big recent one were cases of the LLM producing a counterexample to a conjecture.

IMO, it's due to some problems being better documented, with more well-documented, previous research available. LLMs don't really create novel mathematics, they mostly "connect the dots". LLMs by design are not coming up with anything new, unless by statistical probability, aka "brute forcing". I don't want to minimize LLMs capabilities, it's pretty cool they are doing this, and it's useful from a research point of view. But it's important to set expectations.

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

#776

Post by wartywhoa23 »

diordiderot wrote: post #732
virgildotcodes wrote: post #698

Earlier quoted context omitted.

I’m not in academia myself, and I think AI solving all our problems ASAP is ideal, even if it means no humans get attribution. What I’m saying is that the ultimate goal of those in power are not these sorts of altruistic or even scientific pursuits, and that the massive labor disruption and hyper concentration of power in the hands of those who are proving time and again that advancement of science and benefiting the…

Oh good. But I think you're over estimating the 'concentration of power', and under estimating 'benefiting the whole of humanity' Most homeless people have smartphones, and consistent access to food and clean water. Your average 'poor person' in America has HVAC. An unimaginable luxury in the EU

Does your average poor person in America have happiness after 100s of years of relentless technological progress for the benefit of human advancement, and especially today, in the age of becoming spaghettied into the AI event horizon?

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

#777

Post by rightbyte »

jplusequalt wrote: post #573
amelius wrote: post #223

Earlier quoted context omitted.

This is like saying a sculpture always existed, the sculptor just had to remove the superfluous material. Or like a musical octave has only 12 semitones, so all music is just a selection from a finite set that already existed. Sure the insane computation we're throwing at this changes our perspective, but still there is an important distinction.

Michelangelo never used references, instead he simply "freed" the sculptures from within the marble.

Isn't that a way of saying working with the grain of the material?

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

#778

Post by ocimbote »

wartywhoa23 wrote: post #766
biztos wrote: post #731

Earlier quoted context omitted.

I'm no mathematician but it seems like if this happens, we get to a quite intriguing place as a species. Say we achieve interstellar travel, but nobody actually knows how it works. Or we cure cancer, but the "cure" requires a microrobotic implant, and it runs as a blackbox AI, and only the other AIs can make one, and there's no guarantee they will know how to make one tomorrow. Or we solve global warming but it requi…

Noble " save the humankind using the tech nobody fucking understands " textbook goals like curing cancer, solving global warming and achieving interstellar travel would always turn up when owners of trillions of dollars place orders on positive AI narratives, but in reality all of that will wither down to " It's what plants crave! It's got electrolytes. "

That is fascinating how the more knowledge and reasoning we can get our hands on and actually produce, the higher the risk of us, as a species, to become actually much dumber.

It's hard to describe the feeling of seeing intelligence being delegated increasingly to AI. If that's not a pivotal moment, a revolution, I don't know what is.

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

#779

Post by ivell »

biztos wrote: post #731
teiferer wrote: post #727

Earlier quoted context omitted.

> Every day, it grows harder and harder to contain a mental map of recent relevant progress by simple virtue of the amount being produced. And by opening the door to LLM-generated results, you'll see greater and greater amounts without any hope of ever navigating this field again without machine help. It's a little like a software project which more and more gets extended by a AI agents with less and less review by h…

I'm no mathematician but it seems like if this happens, we get to a quite intriguing place as a species. Say we achieve interstellar travel, but nobody actually knows how it works. Or we cure cancer, but the "cure" requires a microrobotic implant, and it runs as a blackbox AI, and only the other AIs can make one, and there's no guarantee they will know how to make one tomorrow. Or we solve global warming but it requi…

We don't know how many things in nature work. For example, we don't fully understand our own brain. As long as it can be replicated, we are fine.

In case of AI we have a better chance to understand what it is doing through chain of thought and explainability. Nature never gave us that..

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

#780

Post by wartywhoa23 »

seanmcdirmid wrote: post #613
mathgradthrow wrote: post #530

Earlier quoted context omitted.

I think when your work is no longer required, you will probably come to regret this sentiment, not that it matters.

Scientists think differently from craftspeople. They want to know the unknown, using any tool they can get their hands on.

> using any tool

This "any" shines like a thermonuclear fireball.

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