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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

#591

Post by windexh8er »

aroman wrote: post #410
rogerrogerr wrote: post #389

Earlier quoted context omitted.

People who enjoy thinking. Ya know, the "intellectual" part.

This is the beginning of thinking, not the end...

It depends. If you are in a disadvantaged class it is very likely going to err towards a dismal result long term. However if you are a privileged intellectual these models can accelerate and expand your horizon. It isn't the end, surely. It is, however, both impressive and depressive simultaneously and that perspective only depends on your point of view.

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

#592

Post by ninjagoo »

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.

> the closer the expertise you spent your whole life building is to being worthless.

Perhaps it is time for life to be considered intrinsically valuable, instead of being "worthy" only based on output or capability. Disability, animal and environmental advocates have been fighting for this for a long time. Not too long ago women and minorities were in the same boat. Even now, there are many advocating and fighting for a return to the dark old days.

> Along with all the rest of what humans find meaningful and fulfilling.

Some humans. Many are content to enjoy simply existing, and the beauty of life and the universe around us. Just like many non-scientists today enjoy and benefit from the work of scientists, tomorrow too many will enjoy learning from, and applying the coming advancements and leaps in many fields.

And those of a scientist or other research-type mindset? No doubt they will contribute meaningfully by studying the frontier, noting what remains unanswered, and then advancing the frontier, just like researchers do today; just because scientists in the past solved many questions doesn't mean that there aren't any questions to answer today.

IMHO, AI means that the frontier expands faster, not that it is obliterated. Even AI cannot overcome the laws and limitations of physics/universe: even Dyson spheres only capture the energy of one star, thus setting a limit on the amount of compute, and thereby a limit on intelligence. And we are a loooong way from a Dyson sphere.

PS: I think you're being unfairly downvoted. Your question is not invalid and deserves responses, not downvotes.

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

#593

Post by davebren »

pickleRick243 wrote: post #192
blueone wrote: post #132

Earlier quoted context omitted.

> what basis do you have for assuming an LLM is fundamentally incapable of doing this? because I have no basis for assuming an LLM is fundamentally capable of doing this.

Except this has been said since the 2010's and has been proven wrong again and again. Clearly the theory that LLM's can't "extrapolate" is woefully incomplete at best (and most likely simply incorrect). Before the rise of ChatGPT, the onus was on the labs to show it was plausible. At this point, I think the more epistemologically honest position is to put the burden back on the naysayers. At the least, they need to a…

> Clearly the theory that LLM's can't "extrapolate" is woefully incomplete at best (and most likely simply incorrect).

What example is there where an LLM has extrapolated? All I've seen is a data set so large and an extra decomposition process making it so interpolation feels like extrapolation if you don't look close enough.

> but a theory of why further advancements can't solve the deficiencies

How about LeCun's?

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

#594

Post by isotypic »

naasking wrote: post #521
isotypic wrote: post #463

Earlier quoted context omitted.

I cannot quite share your enthusiasm. The clearest analogy that I can think of to try to explain why I feel this way is that it seems there will eventually be a phantom textbook of all of mathematics contained in the weights of an LLM; every definition, every proof, etc; and the role of a mathematician is going to be reduced towards reading certain parts of this phantom textbook (read: prompting an LLM to generate a…

The cool thing about LLMs is not only might they be a database of all mathematical theorems, but they can also apply those ideas to the problems you're trying to solve, which is exactly what you said you're interested in. Not sure why you lack enthusiasm.

LLMs applying the ideas to problems I'm trying to solve is exactly what I said I wasn't interested in, actually. Because the LLM doing this for me reduces back to me simply reading from the textbook, only now I have no problems I'd be interested in applying things to since, again, they're already in the textbook.

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

#595

Post by ninjagoo »

mathgradthrow wrote: post #530
cman1444 wrote: post #488

Earlier quoted context omitted.

Because for many people who pursue these fundamental truths, the reward is not necessarily personal fame, fortune, or even personal understanding. Advancing humanity's total knowledge (even if that knowledge is by proxy through AI) is reward enough.

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

> I think when your work is no longer required

i wonder if this is physically/mathematically impossible: the mere act of living involves processing energy, and therefore doing work :)

And there is a lot of energy to be processed in this Universe before the heat death...

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

#596

Post by rjzzleep »

cpard wrote: post #224

The proof brings unexpected, sophisticated ideas from algebraic number theory to bear on an elementary geometric question. The more I read about these achievements the more I get a feeling that a lot of the power of these models comes from having prior knowledge on every possible field and having zero problems transferring to new domains. To me the potential beauty of this is that these tools might help us break thro…

What you describe here has always been true in all sciences, but also in medicine. But both modern engineering and education runs completely counter to this. You are encouraged to stay in your niche and never look out. People with vast interested are filtered out by hiring managers.

So the crossdomain pollination that used to exist in scientists is not only not encouraged. It's also actively punished by society.

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

#597

Post by brikym »

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.

Hey ChatGPT, if a person spills hot McCoffee on themselves who is at fault?

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

#598

Post by brookst »

cpard wrote: post #301
doubledamio wrote: post #238

Earlier quoted context omitted.

I’ve always been skeptical about the role of LLMs in mathematics, but this is the first time I’ve seen this argument, and I actually find it very compelling. Maybe LLMs will help us develop more horizontal understanding of the field.

It's up to us I think. We can use LLMs to generate web pages in candy crash style and end up dumper by outsourcing thinking to the machines or we can use it to expand our cognitive capabilities. What makes me more of an optimist in this case is that people who today decide to go into these sciences are mostly people who are driven by intellectual activity so I feel they are the right ones to figure this out, probably…

The “we’s” are different. Some of us will use AI to replace human relationships and our own decision making, others of us will use it to make amazing art and invent new things.

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

#599

Post by Enginerrrd »

fartfeatures wrote: post #555
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.

I think by that point humanity will having some pretty fundamental discussions about the nature of work and money.

Go ahead and have that conversation with the billionaires running a worldwide satellite grid of data centers to power their AI surveillance dragnet and autonomous robot soldiers. See how far it’ll get you.

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

#600

Post by bigstrat2003 »

Supermancho wrote: post #572
dawnerd wrote: post #512

Earlier quoted context omitted.

That's literally my job...

>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.

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