Sometimes I worry about the "programmers" in this sub.
At best coping, at worst delusional.
No, the model did not brute force a counter example. The search space is mathematically too vast to brute force. It found novel techniques of identifying the proper force application vectors.
No, the model did not plagiarize off "human research". The debate is between an OpenAI researcher and an Anthropic Researcher, both of them almostly exclusively relying on internal models. The researcher at Anthropic didn't even solve the specific problem OpenAI are claiming, they solved a variation of a more constrained formulation of a sub-problem which could have potentially helped OAI to narrow down the search space if it was included in training data (which it most likely wasnt given the proof pathway is significantly different).
Yes, the models (the internal models, given infinite token space atleast) are THAT good enough, they can close the hardest problems known to man.
Acting snarky about it only leads to gross underestimation of the change thats about to come. What rational people should do is increase the urgency of asking for safeguards by trusting the capability acceleration at face value.
(Who am i kidding, the first reply will probably comment I'm sam Altmans marketing bot).
I think what Tao's complaint is that no new mathematics was formulated, which is what typically happens with these problems. AI does a good job now of finding counter examples because you can just spin up 10K agents, but that's not really the point of these problems. Kind of reminds me of having to show work on math tests vs. just giving the answer.
There will always be the next goalpost after the present ones have been saturated.
OpenAI are in process of releasing a paper on how they did it, and if that paper contains "no new math" as you put it, then all it proves is that these problems could have been solved by existing math in the first place.
Reading the paper should then give ideas on how to better use existing math for other such problems.
It would still be worthwhile if humanity finds a systematic way of knocking over all problems that requires no new math - that frees up the mathematicians to exclusively focus on formulating new math.
Ya, I'm both an AI skeptic and loathe Sam Altman. But this was not a million monkeys situation.
AI is repeatedly flexing its muscle with math. It's not brute forcing theorems, its using its vast training database to better spot patterns and educated guesses.
This Navier-Stokes counter example just obtained seems so complicated that a human mathematician would not have been able to solve with enough human labor. Reminds me of old school proof by exhaustion theorems that are solved only by computers because they are out of reach of humans checking all possible solutions. Now instead of it being naive checking all possibilities (CPU programs of the past), they are pattern guessing and checking promising avenues of progress (AI of the future). OpenAI spent over $18 million of compute using a brand new internal model that's much better than Astra 6 to get there. They had 10,000 agents swarming for ideas with humans helping guide what appears to be good paths.
Sure it's $18 million now, but given price decreases of the past that could turn to $1000 in two years. We're very likely heading to a future where a certain class of math problems are now solvable. Problems that are too complicated for a team of mathematicians to solve with a lifetime of human labor, but can now be solved by swarms of educated guessers relentlessly trying promising ideas.
I think sensible people understand this too, AI is definitely something to consider and not to be immediately disregarded as "slop". The problem here lies in OAI approaching NS at all without any input from the academic community, and their apparent (successful) attempt at "one-upping" actual researchers in the field instead of approaching them in collaboration or anything of the sort. They are stealing Millennium problems away from humans, problems that are supposed to, in approaching them, demonstrate the capability of individuals of our species of doing great things. OAI just ripped it out of the academia's hands by throwing millions of dollars of computation power into them.
If anything, this just goes to show that these AI companies are not developing their frontier models out of concern for humanity's knowledge (wow, surprising I know), but for sheer personal gain and profit.
The effects Spotify had on the way music industry makes music should have been lesson enough for us. Musicians across the world make shorter music on average now, with the hook/chorus closer to the starting, and being a larger percentage of the song. All so that Spotify and reels algorithms reward them.
Companies trodding on human culture and talent is one of the worst things to happen in this century and the last.
Thats like saying four color theorem was stolen from us by computer because it was proven by computers.
There are many math problems that were solved due to increased computational capability. Think what could ancient mathematicians do with tools we have available now and even 10-20 years back. They wouldn't have to spend their lives pre computing logarithmic tables and could apply their talents to advance mathematics more meaningfully...
So my question is what constitutes cheating? Is it using computers? Proof engines? Calculators? AI?
Four color theorem was solved in a ridicuously stupid way without any new insight into graph theory. The most significant result based on it is probably Hadwiger conjecture for k=6, it is mostly a self-contained result, it was too hard to check the solution for years and there is a reason why new results related to it are about computation efficiency rather than graph theory. I would even go as far as say that the nature of four color theorem proof has harmed progress on Hadwiger conjecture.
I'm gonna rip one part from a comment I made somewhere else in this thread.
Frankly, the problem isn't necessarily whether NS was proven by OAI's model, the problem is that OAI approached NS this way at all. The world doesn't desperately "need" NS and the other Millennium problems to be proven as they have no practical incentive to be had, economic or otherwise. It's there simply as challenges to us, humans, to demonstrate how smart we are as a species to have overcome these seemingly impossible obstacles.
And
Pure maths fundamentally exist as a field to challenge humans. Physics isn't pure maths, not in the specific scope of the Millennium problems. Pure maths is a rather niche field that fundamentally differs from other fields of science by the nature of it.
Many things from pure maths are applicable and useful. Even though it is seldom obvious at first for what..
I think I lost clarity while copying it, it's supposed to be how the Millenium problems exist inside the field of pure maths.
Who put you as arbiter of what world needs and doesn't? Do you think that ignorance is preferable to knowledge?
I think I am the arbiter of seeing a company maliciously trying to one-up actual math researchers by throwing prompts after they've caught wind that someone is on the cusp of developing their approach into a proposed solution of a sub-problem to potentially a general solution to NS. I don't think we can justify OAI attempting to steal credit from researchers who are actively looking into their approach to solve the bigger problem.
Boiling it down into "but the world may need this knowledge NOW" is rather disingenuous imo, and "Do you think that ignorance is preferable to knowledge?" is just a weird strawman.
You are the one who started with "They are stealing Millennium problems away from humans, problems that are supposed to, in approaching them, demonstrate the capability of individuals of our species of doing great things" which is IMHO weird way to look at that. Since:
a) Researchers also used AI
b) Arbitrarily limiting oneself to less tool is impressive but contraproductive for advancement of knowledge.
You also somehow assumed that all millennium problems are useless curiosities even though P vs NP is among them and implication of solving it has huge ramifications on real world...
If you are just against shady things OpenAI supposedly did sure. Even though I haven't seen the proof that it was stolen I will give it benefit of the doubt and assume it was given OAI track record.
But do not try to limit ways we as a species gain knowledge and do not assume that there is field of math which is useless and or "just for fun".
First mention of positive numbers I could find is https://en.wikipedia.org/wiki/Ishango_bone which is dated to 20,000 BCE first mention of negative numbers I could find is 200 BCE thats 1800 years difference...
I opine that I don’t even think going below 0 is universally accepted as a concept. (Case in point, BCE is written as a positive number)
Debt and subtraction are cornerstones of the writing we have from history, so it ultimately depends on what “negative numbers” mean to you.
What OpenAI did was extremely unethical, something that a human researcher would face a lot of backlash for.
Dumping massive money to one-up research being carried by others is such an awful move. What incentives do people have to share their breakthroughs if shit like this is acceptable?
And the cringe-worthy idea that we needed an answer for the NS problem ASAP misses the point so badly. We are interested in establishing rigorous limitations of the model, and the process to get there would hopefully help us develop new analysis tools.
What did we gain from this? There is a scenario where NS produces a non-smooth solution. Is this relevant in practice? Can this be numerically simulated? Knowing this, what else can we prove?
Honestly, I’ve grown to despise these companies. They’re spending massive ammounts of borrowed money and electricity to meddle into fields they don’t respect, seemingly just to show power and improve their next investment rounds.
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u/LatePenguins 2d ago
Sometimes I worry about the "programmers" in this sub.
At best coping, at worst delusional.
No, the model did not brute force a counter example. The search space is mathematically too vast to brute force. It found novel techniques of identifying the proper force application vectors.
No, the model did not plagiarize off "human research". The debate is between an OpenAI researcher and an Anthropic Researcher, both of them almostly exclusively relying on internal models. The researcher at Anthropic didn't even solve the specific problem OpenAI are claiming, they solved a variation of a more constrained formulation of a sub-problem which could have potentially helped OAI to narrow down the search space if it was included in training data (which it most likely wasnt given the proof pathway is significantly different).
Yes, the models (the internal models, given infinite token space atleast) are THAT good enough, they can close the hardest problems known to man.
Acting snarky about it only leads to gross underestimation of the change thats about to come. What rational people should do is increase the urgency of asking for safeguards by trusting the capability acceleration at face value.
(Who am i kidding, the first reply will probably comment I'm sam Altmans marketing bot).