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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

#861

Post by bayindirh »

withinboredom wrote: post #844
bayindirh wrote: post #841

Earlier quoted context omitted.

However, you can assemble a team of humans who knows the whole pipeline. This trajectory lands us squarely in "The Machine Stops" of "Pump Six" territory, where assembling such a team or going back to a simpler system is impossible

Sorta. Take a look at a brick in a house. You'd need everyone from geologists to miners to kiln specialists to construction workers and engineers -- not to mention all the people required to make the tools required to make the tools. The team would likely involve well over 1000 people. So, "just assemble a team" is not quite as simple as you make it sound.

Doesn't matter. At the end of the day, the knowledge is embodied by humans, or can be learnt again. Let it be 100, 1000 or 10000 people. At the end of the day, they are made of meat.

When you let the machines do it, and don't care about moving it towards human domain (i.e. meatspace), you're done.

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

#862

Post by nicman23 »

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…

like the research team that rediscovered calculus for treating diabetics

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

#864

Post by fc417fc802 »

withinboredom wrote: post #844
bayindirh wrote: post #841

Earlier quoted context omitted.

However, you can assemble a team of humans who knows the whole pipeline. This trajectory lands us squarely in "The Machine Stops" of "Pump Six" territory, where assembling such a team or going back to a simpler system is impossible

Sorta. Take a look at a brick in a house. You'd need everyone from geologists to miners to kiln specialists to construction workers and engineers -- not to mention all the people required to make the tools required to make the tools. The team would likely involve well over 1000 people. So, "just assemble a team" is not quite as simple as you make it sound.

I don't think that's true in the sense meant. Sure, to reproduce a near replica of a specific brick from first principles. But not to produce something broadly functionally equivalent. You can (rather inefficiently) manufacture approximately equivalent bricks in your backyard on your own, possibly even from locally harvested material depending on where you live.

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

#865

Post by red75prime »

vatsachak wrote: post #529
red75prime wrote: post #368

Earlier quoted context omitted.

It has been tried. Lenat's Automated Mathematician, for example. The problem is that the system succumbs to combinatorial explosion, not knowing which directions are interesting/promising/productive. LLMs seem to pick up some kind of intuition from the data they are fed. The generated data might not have the needed "human touch" or whatever it is.

It might just be that we didn't have enough compute till now. StockFish definitely has superior intuition

StockFish amplifies weak "intuition" (heuristic and simple neural estimators) through extensive Alpha-Beta search made possible by the low(ish) branching factor of chess. It doesn't work for Go already (KataGo uses larger neural networks to guide search more efficiently). I doubt either will work for math where branching factor is even bigger and the success criteria (is the result interesting and so on) are not strictly defined.

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

#866

Post by rashar »

cm2012 wrote: post #455
missyougowers wrote: post #348

Earlier quoted context omitted.

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 seems like you have an axe to grind about AI capabilities that is making you think irrationally

It is very rational and standard journalistic practice to focus on academic funding provenance.

Gowers is funded by XTX markets:

https://www.renaissancephilanthropy.org/ai-for-math-fund

XTX markets heavily uses machine learning and disguises the influencer money as "philanthropy":

https://www.xtxmarkets.com/

But you would probably say that Magnus Carlsen's previous engagement with the Maltese gambling company Unibet and him releasing a couple of YouTube videos talking positively about poker and gambling have nothing to do with each other. Nothing at all.

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

#867

Post by rashar »

missyougowers wrote: post #480
cm2012 wrote: post #455

Earlier quoted context omitted.

If seems like you have an axe to grind about AI capabilities that is making you think irrationally

This is a popular HNism. Focusing solely on "capabilities" is the irrational thinking. Asbestos is the most "capable" material where extreme thermal, chemical and electrical resistance is required.

And academics have promoted all sorts of things, including cigarettes, with the proper funding.

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

#868

Post by Biganon »

jldugger wrote: post #430
edbaskerville wrote: post #92

Earlier quoted context omitted.

I just visited a McDonald's for the first time in a while. The self-order kiosk UI is quite bad. I think this is evidence in favor of the idea that an incompetent AI will soon be incompetently running a McDonald's.

>The self-order kiosk UI is quite bad. Most repeat customers use the app, which sports the digital equivalent of a loyalty program, and various coupons. And lets you save your 'usual' order with customizations etc. Plus the annoying push notifications for FreeFrydays or whatever. And upsells, new product launches, etc. My recollection is that the kiosk is just a weak facsimile of the app. And wasn't terrible, but eve…

The app doesn't work on GrapheneOS :(

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

#869

Post by dxroshan »

dhosek wrote: post #639
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…

One of the challenges I had in graduate mathematics was just trying to keep all the concepts in my brain. It doesn’t help that you end up with things like homomorphism and homeomorphism tangling one’s brain thanks to their superficial similarities. Heck, just keeping track of basic theorems and definitions is a challenge.

When I return to a subject after spending some time on other topics, I had the same issue with such definitions.

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

#870

Post by fc417fc802 »

marand23 wrote: post #860
pocksuppet wrote: post #845

Earlier quoted context omitted.

Billionaires are going to benefit from AI at the expense of everyone else. That's not leftist ideology, that's just a fact. That's happened with every technology that's ever been created. It happened with the industrial revolution. Why would it be different this time?

A few years ago i had laser eye surgery and now i can see well. Something that was not possible 50 years ago. Claiming that EVERY new technology comes at the expense of normal people is an absurd statement.

Coming at your expense and benefiting you in some way are not mutually exclusive. For that matter coming at the expense of the average joe and then many years later benefiting the average joe seems to be a common theme.
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