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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

#991

Post by orsenthil »

missyougowers wrote: post #348
ks2048 wrote: post #133

Timothy Gowers' tweet about this: "If you are a mathematician, then you may want to make sure you are sitting down before reading futher.". woah.

Unfortunately Gowers has taken Tao's lead on this one. Gowers has one of my favourite video series about how he approaches a problem he is unfamiliar with: https://www.youtube.com/watch?v=byjhpzEoXFs It is disheartening to see him jump into this GenAI puffery. I hope these GenAI labs are paying Tao handsomely for legitimizing their slop, but more likely he's feeling pressure from his University to promote and work wi…

If you and I can understand this paper, or use the process to achieve something similar for the ends we care about, wouldn't that be enough? Why do you care who it is coming from and what their motivations are?

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

#992

Post by cold_harbor »

0x5FC3 wrote: post #30

Is there a reason why we only hear of Erdos problems being solved? I would imagine there are a myriad of other unsolved problems in math, but every single ChatGPT "breakthrough in math" I come across on r/singularity and r/accelerate are Erdos problems.

Erdos problems are well-posed for AI — elementary statements, exact counterexample targets, extensively catalogued. selection bias: these are exactly the problems AI can actually search

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

#993

Post by YeGoblynQueenne »

cma wrote: post #984
YeGoblynQueenne wrote: post #955

Earlier quoted context omitted.

Yeah, maybe it's just the Texas Sharpshooter Fallacy basically, but with AI. And if it isn't, we should find out very soon. If AI has got so good as OpenAI's post implies, then we should soon see a veritable blooming in the production of mathematical results, by lay people no less. No mathematicians needed! OpenAI say that their secret LLM solved the planar unit distance problem "autonomously" and the companion remar…

#326 solved https://github.com/teorth/erdosproblems/wiki/AI-contribution...

Is that 326 solved? As per my comment above?

>> If that's true, if we're really at that level of autonomous mathematical reasoning ability, then we should see hundreds, even thousands, of open problems suddenly solved in a matter of years if not months.

Stressing "hundreds, even thousands".

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

#995

Post by turzmo »

cma wrote: post #984
YeGoblynQueenne wrote: post #955

Earlier quoted context omitted.

Yeah, maybe it's just the Texas Sharpshooter Fallacy basically, but with AI. And if it isn't, we should find out very soon. If AI has got so good as OpenAI's post implies, then we should soon see a veritable blooming in the production of mathematical results, by lay people no less. No mathematicians needed! OpenAI say that their secret LLM solved the planar unit distance problem "autonomously" and the companion remar…

#326 solved https://github.com/teorth/erdosproblems/wiki/AI-contribution...

Yes, as some of these are being solved by the same person, I think my point is even more relevant: you try 1000 problems and solve a few, and only report the few, and it just seems like a matter of time until the rest are solved. But if you report that it didn’t work on the others, your conclusion is different.

I think it is important to temper expectations in light of the fact that these announcements are coming from a startup company with shady values looking to imminently IPO, and thus represent the most biased and misleading take of the situation possible.

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

#996

Post by ric2b »

CSMastermind wrote: post #145
0x5FC3 wrote: post #45

Earlier quoted context omitted.

Interesting. OpenAI could also be trying to solve other problems, but Erdos problems maybe falling first?

No, Erdos problems were accepted as sort of a benchmark. There's a bunch of reasons they're favorable for this task: 1. They have a wide range of difficulties. 2. They were curated (Erdos didn't know at first glance how to solve them). 3. Humans already took the time to organize, formally state, add metadata to them. 4. There's a lot of them. If you go around looking for a mathematics benchmark it's hard to do better…

I'm curious how the relative difficulty between the problems can be assessed when no one knows how to solve any of them.

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

#997

Post by JacobAsmuth »

xigoi wrote: post #987
JacobAsmuth wrote: post #531

Earlier quoted context omitted.

Exactly. Maybe OpenAI paid mathematicians to keep this discovery quiet, then added their proof to the training data, then manipulated a second team into prompting for this question such that the model could regurgitate the solution. This would plausibly explain why the model seems so capable at doing things like refuting fundamental theorems of mathematics while in things like competitive programming, biology, and ph…

Being in the top 99.9% is not a big achievement.

I know - it's pathetic and embarrassing. If there's billions of people on this planet then being in the top 99.9% means that you're just as unique as a person who decides to move to New York City. Who cares?

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

#998

Post by darkwater »

fragmede wrote: post #945
darkwater wrote: post #756

Earlier quoted context omitted.

> as well as microprocessors I mean, microprocessors have been on the "impossible to bootstrap from scratch in a short period of time" for 20 years already.

More like 50. The Intel 4004 came out in 1971, and there's no way to bootstrap even that level of technology after some sort of doomsday scenario.

But I would say that processor like the Z80 are so simple and well-known and documented in the wild that they would have some chance to be bootstrapped again with what would realistically survive, one way or another, in a doomsday scenario. But yeah 20 year is too short, it's more like 40 years.

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

#999

Post by Yizahi »

lgas wrote: post #956
Yizahi wrote: post #414

Earlier quoted context omitted.

Because it is, for now. For a while at least. You can prove that LLM doesn't understand what it does and it is surprisingly simple. Request it to add two integers and then ask it to explain how it arrived at that result. The answer will be completely unrelated to the actual process LLM used because both results were generated independently and without understanding their meaning and connection.

This is likely true for the majority of humans too.

Objectively untrue. Any human who can add two integers or use a knife to cut food or write a word with a pen can afterwards describe what he did at least in some way. Unless he is lying which is a separate topic, we assume an honest attempt. If I wrote a word with a pen via execution motions with my hand, I wouldn't describe it as "I levitated the pen by manipulating gravity with my mind". Or if I added two integers, I wouldn't say that "I created a a lookup table of a many loosely adjacent numbers (different from the numbers in a task) and run statistical analysis on them and did a few more things like that a in a loop". No, I would say that I either calculated sums of decimals, or I I did a school technique with rounding up and then subtracted that adjustment later, or anything which actually happened. If I used a Python sum() in a CLI I would also say that I used exactly that not the other method. LLM can't do it.

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

#1000

Post by aspenmartin »

pojzon wrote: post #971
xbmcuser wrote: post #625

Earlier quoted context omitted.

This is the main thing that I keep harping about that human knowledge is too vast today for a person or even a group of people and llm will change that many discoveries that require serendipity in the past will be more likely than ever

There is one issue with this. When noone can prove or disprove what AI came up with. Currently we can live with it because someone can review that work. Soon we wont be able.

We can use things like Lean for math proofs, verification is tractable.
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