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- Hacker News
- Other than the undeniable breakthrough in math, the important point is the ability to orchestrate 10k agents to productively work on a single problem, which creates options:
> OpenAI, meanwhile, says its experience with Navier-Stokes could open the door to solving puzzles with more practical relevance. “We are now able to spend millions of dollars on a problem that we really care about and that really matters: developing new materials, finding cures to diseases,” Bubeck said. “All of those things that we have been talking about for a long time—now they seem to be at our fingertips.”
by pama - My impression: the re-aristocratization of scientific research seems inevitable.by rrhjm53270
- Your local trailer park was never going to be able to afford sponsoring high energy particle physics experiments projects that hollow out a mountain and use up a ton of xenon to try to detect a stray particle. High end science has required deep pockets for a long time.
But given the cost of a college textbook this is a pretty silly complaint to lobby against a subscription that's $200 a month, in the context of the cost of a variety of other materials and tools out there. (If you think that's expensive you've clearly been lucky enough to never have to deal with commercial software costs) Also not sure how quickly this stuff uses up limits; $100 or even $20 subs might be enough for students. And if a student is scrappy and figures out that Luna can meet their needs then I'd imagine Luna is effectively unlimited on some of these subs. Luna Max scores pretty high.
by mrngld - What do you mean?
In any case mathematics is humanity's oldest open source project going on for millenia, it never belonged to a single country, institution or class.
by epolanski - Even in the past a lot of “aristocrats” had to earn a living. Among scholars, many worked as teachers or had sinecures that paid the bills, or held clergy posts with minimal responsibilities.
Aristocrats were a dime a dozen.
by analog31 - OpenAI apparently used Buckmaster and Alpöge‘s work w/ Codex to bootstrap “their” dis-proof. https://cims.nyu.edu/~tristanb/statement.pdfby snsr
- And according to that team OpenAI only started asking their own model these questions after those submissions had occurred. So OpenAI had these critical clues and info before they started. If OpenAI did or did not use that to produce their own “proof” is an open question, but OpenAI hasn’t definitely denied it.by cmiles8
- FYI: The problem at hand is an existence problem. No real construction of any real formula for the solution is provided, only a singular perturbation expansion.
In short: The problem is about whether a solution (of the NS Equations with external driving force) can be found that blows up in finite time. i.e. exhibits infinite velocity at a point even for a viscous flow.
The solution: Take a circular curl ansatz which shrinks in xy-direction and elongates in z-direction and see whether you can find linearized waves so that these waves show a blow up when propagated on the curl. Then prove that the higher orders of the perturbation are regular before the T0 singularity time and you have solved the problem. The external force is just the remainder of the NS-Equation right hand side.
It is a lot of tedious formula juggling of all the higher orders and some singular perturbation expansions. Perfectly suited for algebra systems. OpenAI was using probably python sympy for the formula work and the researchers had to guide the LLM what to do in higher mathematical language.
Here is the paper:
https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8...
when you upload it to chatgpt astra can explain what they do and why it works, have fun.
by fxj - > Navier-Stokes is one of six “Millennium Problems” on a list compiled by the Clay Mathematics Institute in 2000.
Seven, not six. One is solved already, but is still a millennium problem.
by paxys - Yes, that's a strange mistake to make.by JohnKemeny
- Interestingly of the two solved, both have rejected the prize money.by cma
- I see the six seven reference there mateby ltononro
- Regardless of the end result, OpenAI's behavior would be a career-ending ethics scandal for a human mathematician. This bit alone would be a career-ender.
> According to Buckmaster, OpenAI offered to give him sole authorship on the Navier-Stokes solution—but only if Alpöge’s name was removed from the work and if the write-up would acknowledge the problem had been resolved by an internal OpenAI model.
I wonder if an appropriate response from the mathematical community would be a good old-fashioned shunning. Mathematicians are allowed to use OpenAI's tools as much as they want, but no one with any current or prior OpenAI affiliation gets published in a reputable journal, ever.
- Many mathematicians would be willing to end their careers for $1m. What makes this so sad is that OpenAI spent more than that for this empty PR stunt.by zarzavat
- Extensive discussion on OpenAI's blog post on Navier-Stokes: https://news.ycombinator.com/item?id=49613262 .
Quanta Magazine article that also discusses some of the controversy: https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-...
by pseudolus - And yet you still posted this dupe. That quanta piece more duplication. Everything already well discussed in the OpenAI and the Tristan Buckmaster threads! Do better.
- > “I certainly don't expect the industry to continue to spend millions of dollars to solve problems in mathematics, because there is no profit in it,” Columbia University mathematician Michael Harris wrote in an email to Science. But he worries the highly publicized achievement will be “extremely damaging to mathematics; it convinces decision makers that human mathematicians are obsolete, and it convinces young people that their passion for mathematics has no future.”
LLMs seem particularly suited toward these existence-proof problems. Working mathematicians seem absolutely essential for universally quantified results, still. I strongly doubt, for example, that if Fermat's Last Theorem hadn't been proven three decades ago, that an LLM would be able to do work equivalent to inventing the mathematics as Andrew Wiles did to solve the problem. I have similar doubts about P vs NP, the twin prime conjecture, even the Riemann Hypothesis (unless the latter has at least one counterexample).
And I want to be clear: I'm not downplaying the achievements of these models. This is remarkable! I simply think that the pattern of success is in existence proofs or finding counterexamples, which makes sense based on how LLMs function and are trained.
by elgertam - P=NP is for when both AI shops decide they want to go bankrupt LOLby y-curious
- > it convinces decision makers that human mathematicians are obsolete, and it convinces young people that their passion for mathematics has no future
Maybe those things are true, so maybe they should be convinced?
by kurtis_reed - It would be good if someone made a list of allresults obtained with AI so far just to see what kinds of problems AI excels at. Are there any that aren't of the existence-proof type?
Reductively, math can be said to be either problem solving or theory building - it seems the latter is a much harder thing to do right now.
by lhd1 - I only have an undergrad in math, so very little understanding, but I'd be pretty surprised if it couldn't do forall just as well. Like, say it found this counterexample which relies on axial stretching or whatever approach. Then it already knows how that made the proof work, and can use it to try to prove NS has smooth solutions modulo this particular kind of defect (so it could make some statement about cohomology, or some additional constraining equation). Or if that doesn't work, then it can find a counterexample, which we've established it's good at. Then repeat until you've characterized what does work. The various defects, along with being defect free, become definitions. Now you have a theory.by ndriscoll
- The whole thing reeks of the desperation of an unprofitable venture-backed startup looking for its next PR win to keep the wind in the sails.
But I think what’s being overlooked in the race to claim absolute credit is that both sides ultimately relied on a LLM (and one of OpenAI’s at that). Either a human researcher made a breakthrough discovery with the help of Codex, or the latest GPT model made a breakthrough with the help of human training data, or a little of both… either way it is undeniable that LLMs have quickly become an integral part of R&D workflows and are accelerating research.
This would be a major win for any normal company. You could even build a bigger collaboration with this guy, give him a big budget and push for extensions to this preliminary result, and in return do a write up on how he uses your model in his workflow. Huge PR win. What this says to me is that their valuation is so astronomical that they feel the only way to justify it is to demonstrate a fully autonomous discovery bot… which it simply is not.
by plaidfuji - A company that can solve Millenium problems is somehow still can’t ever make profits. How did you come to that conclusionby simianwords
- I think it was a pretty questionable thing to do by trying to front-run these researchers even if they didn’t make use of their techniques. The fact that they may have inadvertently “borrowed” their work via training data makes it much worse.
OpenAI’s behavior here — even if you only consider [their] side of the story — was (at best) in bad taste.
by timmg - Isn’t that how research works? You build on what others have done. I don’t understand the big deal. I’d rather have the result available sooner than later just to assuage some egos
- Yea, strongly agree. I think this is going to back-fire spectacularly. They better start preparing an apology...by lolakutty
- This is the take I agree.
It is mean spirited but nevertheless sold their model
by karmasimida - Strongly agree. And as one of the major AI companies, this is extremely tone deaf. If they saw a human (even if assisted) was making great progress on a major problem then you give them space. You don’t swoop in with millions in token spend to scoop them. There are tons of important problems where humans aren’t making traction - please go solve those.by kenjackson
- That’s the definition of current LLMs. They have trained “borrowed” on whatever humans have documented digitally and physically (books).by Oras
- Borrowing the work of others to replace them without crediting is the model of current AI companies.
They just used that occurrence as a PR stunt but it isn't worse than the others done at scale every second.
by cryptonym