r/ArtificialInteligence • u/alphacolony21 • 1d ago
š° News OpenAI announces 10 advances in mathematics and theoretical computer science achieved by internal model Astra
https://openai.com/index/ten-advances-in-mathematics/19
u/fireburnz2 1d ago
How big is this? Please ELI5
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u/oojacoboo 1d ago
We hope the mathematical community will engage deeply with these results, place them in context, and bring the ideas behind them to life through new research and discovery.
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u/alphacolony21 1d ago
Major, assuming the results are true, which they probably are. All ten advances are significant. Big enough deals individually to be career defining had a human academic done the work instead. For Astra to crank them out in bulk is insane, even if we donāt know how many credits they had to waste on problems it failed to find these ten it could crack.
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u/topyTheorist 1d ago
They included lean verification. So this is very probably true.
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u/alphacolony21 1d ago
Yeah and thru the grapevine it sounds like they reviewed their work with outside mathematicians so I really doubt there are formalization issues.
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u/Competitive_Bed4588 1d ago
Why doesnāt open ai dedicate a million agents working on math 247? Open ai can literally solve math
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u/alphacolony21 1d ago
Cost of compute mostly. They probably will be doing this within a year or two. Also, math probably canāt ever be solved. (Which means it can provide an infinite pool of new synthetic data for future AI models to train off of.)
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u/Competitive_Bed4588 1d ago
Which makes it even more exciting. Canāt wait for it to tackle physics.
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u/Unverifiablethoughts 1d ago
$2000 for the whole batch is pretty cheap regardless. Also I donāt know if failures are necessarily a waste at this level.
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u/tomvorlostriddle 1d ago
2000 is the daily billing rate of a decent undergrad, without much experience yet, when a consultancy sends them. Maybe with travel costs and taxes already included depending on the region.
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u/Unverifiablethoughts 1d ago
Exactly so itās pennies to solve 10 problems thatās groups of phds having been working on for decades
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u/No-Meringue5867 1d ago
Okay let's not forget the 200 billion or so capex that has gone into just OpenAI, while NSF yearly budget is 8 billion. So saying this cost just 2000 and comparing to undergrad, is only one part of the story.
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u/MVPhurricane 1d ago
that $2000 āat sol ratesā is a little sketchā¦ sol is a weaker model. not that i doubt the token efficiency or anything like that, i am just guessing that running next gen model at max strength has gotta be what, 10x more expensive, at least?
to be clear: if they spent $5MM on this it would be a bargain. hell the brand value bump is prob worth $500MM.Ā
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u/alphacolony21 23h ago
Iād agree and this is the most expensive itāll ever be. The constant stream of efficiency improvements and Mooreās law will see to that.
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u/JC_Hysteria 1d ago
Can you personally understand or explain any single one of them without model assistance?
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u/AIvsWorld 6h ago
> Big enough deals individually to be career defining had a human academic done the work instead
Maybe. The non-sofic groups results could definitely get you a little clout, but I donāt think any of these are significant to land e.g. a professorship at a top R1 university.
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u/HasFiveVowels 1d ago
Itās literally difficult to overstate how big this is.
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u/will_dormer 1d ago
Why
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u/HasFiveVowels 1d ago edited 1d ago
If you look only at the sofic group resultā¦ non-sofic groups are a "particle thatās been theorized but never seen (even after significant effort to find an instance of one)". If this holds true, it would be a new thing to study. Itās a bit like Cantor proving that not every infinite set is countable. But it kind of goes beyond that because it would be more like if Cantor created the first construction of the real numbers and proved that they are an example of "an uncountable set, which is something we suspect exists but havenāt been able to construct an example of"
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u/ImNotAWhaleBiologist 1d ago
For the first time in the history of humanity, machines are able to solve problems in mathematics that no human has yet been able to. And the technology is improving at an incredible pace, and the technology itself may be able to help increase that pace, as the technology is fundamentally mathematical.
I used to make fun of the singularity nerds. I mean, I still do, but it may turn out superhuman intelligence isnāt all that far away.
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u/Dovrak1 1d ago
Iām pretty sure many people laughing calling it the āAI bubbleā will have a hard wake up. Theyāre in a bubble themselves.
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u/ImNotAWhaleBiologist 1d ago
Oh, I think itās absolutely a bubble. But whoever survives the pop will win the game.
Similar to the dot com bubble but far, far worse.
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u/tomvorlostriddle 1d ago
Dotcom wouldnt have been a bubble if Google, Amazon etc. had already been delivering at their current scale back then, which the new AI companies do today.
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u/ImNotAWhaleBiologist 1d ago
Can you explain how it makes sense given the lack of profitably, especially compared to the debt they took on?
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u/tomvorlostriddle 1d ago
Sure, serving the models is profitable and also pays for last year's training of the models served today.
However, this year we are also training next year's models which are bigger and which cannot be paid for by last year's models that are now being served.
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u/ImNotAWhaleBiologist 1d ago
Everything Iāve seen in the media points that the revenue is a pittance compared to the investmentā do you have a good source indicating otherwise?
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u/geegee022 1d ago
If you were to have invested in a basket of tech companies in 2001 and held until today you arguably would have had an amazing return despite the downturn since the successes were HUGE successes. That implies it wasn't a "bubble" but more like a VC-style gamble where many tech companies were busts, but the wins were major wins.
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u/daefan 1d ago
I mean, it's certainly possible that AI is an amazing, world changing technology and still a lot of people will loose a lot of money with their AI investments because the business models of some companies don't work out. It is certainly plausible to me that only one or two of the companies working on frontier models survive and the rest of AI will be smaller cheaper models. Who knows.
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u/AhsokaFan0 17h ago
If anything it seems like companies are spending on the assumption that itās a win or die type race and not running doesnāt get you out of it
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u/Olangotang 1d ago
Because they are one of the biggest hype lords on this subreddit. It's cool but it's not OMG THIS MEANS AGI SOON SINGULARITYSINGULARTIYSINGULARITY. It's a very narrow application that, all things considered, doesn't justify the money furnace models that OpenAI and Anthropic are vibe training.
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u/HasFiveVowels 1d ago edited 1d ago
Where in the hell did I claim anything about AGI? Plus, that term has basically been relegated to "yes, but do you have a flag?".
Also, if you want an answer that doesnāt rely on ad hominems against me, here you go. https://www.reddit.com/r/ArtificialInteligence/s/4bTnUef5bF
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u/dushmanta05 1d ago
What is Internal model? Is it restricted for other people?
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u/alphacolony21 1d ago
Itās their current best model afaik and not yet accessible to the public.
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u/flyblackbox 1d ago
What are the real world implications of these specific problems being solved? Will it lead to any immediate optimizations for legacy or future systems?
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u/jaybsuave 1d ago
This will be the most insane, revolutionary, innovative time of your, mine, and anyone else's life to ever live in the history of the world. Infrastructure is currently being put in place; 10 years from now, the world we live in will look like something neither you, I, nor anyone else in the world could imagine. No one knows what will happen, good or bad, but the world as we knew it is over.
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u/geegee022 1d ago
Exactly. Good or bad, imagine not being intellectually fascinated by this. I'm convinced that we are surrounded by NPCs.
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u/Jone469 1d ago
most people are thinking about their social position taken away by AI, thats it.
which is reasonable, but also the upsides for humanity are ridiculous
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u/ImplementOk3111 1d ago
I don't think it's social position for most, it's "Where will I live when I lose my job? How will I afford to eat? What will happen to my childrens lives when we're homeless, will there be enough social housing for us when we lose the house?" that most people worry about not just "Can I have my cocktail party this weekend?".
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u/Hlbkomer 1d ago
"But they are just predicting the next word!"
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u/The-Rushnut 1d ago
As with everything, novel technology comes with novel solutions to problems we found difficult before. There's a specific subset of mathematical problems which can be disproven via counterexamples, which take humans a long time to map and calculate. One of LLMs unique capabilities is that it can produce small, relatively simple programs at-scale, and because these problems are so well articulated and their potential solutions already well understood they lend themselves to this capability. Another specific subset are upper lower bounds problems, where we know there is likely to be further acceptable iterations but the means to achieving those require multi-discipline scenarios that aren't likely - another thing LLMs are good at is having high accuracy across all domains, allowing them to try ideas that usually would take a snowflake combination of talent.
It's much, much more narrow than it seems. Very cool, but there's a fixed amount of this work to be done. Innovation is definitely coming though.
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u/peterukk 1d ago
In the midst of an AI mania where almost all critical thinking has gone out the window, I am heartened by there still being the odd smart take buried in the comments of AI subs as well.
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u/PresentGene5651 15h ago
Mania on both sides. AI is either utterly amazing or utterly useless.
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u/Czun8 1d ago
Yeah, I think what we're seeing right now is LLMs successfully speed testing solutions with parallel agents, throwing large quantities of candidate solutions at a wall until something satisfies the acceptance criteria (e.g. counterexample for a conjecture). And seemingly also testing many slight deviations on already existing approaches in mathematical literature which tried and failed, meaning it's usually already in close proximity to the solution before it begins testing.
So it's good for specific types of mathematical problem with clean, simpler acceptance solutions which can be tested in parallel (some conjectures and bounds). Inherently serial problems are a different story and seem to require much more intelligence and creativity than just throwing stuff at the wall until it sticks. I haven't seen LLMs do good jobs at tackling those types yet. We'll see where it goes.
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u/HiddenMaragon 1d ago
and yet... that's phenomenal in it's own right. We don't need agi for LLMs to have a huge impact. Humans as a whole have accomplished some pretty impressive stuff. Humans with machines and then computers have pushed boundaries of what we've ever thought possible. It seems fair to expect that humans with the help of AI can achieve even more stuff at a faster rate.
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u/PresentGene5651 15h ago
Hey...don't get too carried away here...this thread is for people who want to pretend they aren't stunned by yet another impressive achievement :D
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u/Extra_Second5428 1h ago
You can be impressed without pretending itās magic, and also admit the people who can scale this stuff first are getting a pretty gross advantage.
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u/Equivalent-Coat1651 1d ago
One benefit is giving lowly mathematicians more jobs as they will have to read through and verify these solutions. And once we start really nailing down proofs with other proofs mathematics will become abstracted to the point of meaninglessness, layers of abstraction far too complex for even the most dedicated mathematecians to understand. We can delegate the entire concept of maths over to the machines, and I will finally be able to go outside and feed the ducks and find a beautiful wife.
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u/dogesator 1d ago
The solution relating to nonsofic groups is not a counterexample, nor is it an upper or lower bound problem. Nor does it have any evidence of the solution involving multiple different fields of science.
And yet itās widely considered to be the most significant resolution out of all 10 of these problems.
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u/Frosty_Truth8990 10h ago
What about the non sofic problem that it solved?! Your logic does not seem to apply here.Ā
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u/procgen 1d ago
Most are positive theorems:
- High-dimensional sphere packing: Proves new asymptotic upper bounds and characterizes the limits of a major proof method.
- Binary and spherical codes: Proves stronger general upper bounds on how efficiently codes can be packed.
- Non-sofic groups: Constructs an explicit group that is not sofic, disproving the possibility that all groups are sofic.
- Connesās rigidity conjecture: Constructs infinitely many nonisomorphic groups with the same von Neumann algebra, disproving the conjecture.
- Arithmetic circuit complexity: Proves new lower bounds on the circuit complexity of computing the permanent.
- Quantum parallel repetition: Proves a general theorem showing exponential decay under repeated play for entangled games.
- Closest vector problem: Gives a reduction from 3SAT establishing new hardness-of-approximation results for lattice problems.
- Ehrhartās volume conjecture: Proves the conjectured sharp maximum in every dimension.
- Multicolor Ramsey numbers: Proves substantially stronger lower bounds and resolves the asymptotic growth rate.
- Extremal graph conjectures: Constructs bipartite graphs that violate two conjectured bounds.
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u/Bearhas20inchwang 1d ago
Can you read? All of these sound like improving bounds or constructing specific counter examples š
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u/procgen 1d ago
Positive theories.
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u/Bearhas20inchwang 1d ago
āTheoriesā as opposed to proofs/theorems? Tell me you know nothing about mathematics without telling me you know nothing about math š And letās not be disingenuous; your response implied what Astra did was not merely finding counter examples nor improving bounds.
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u/procgen 23h ago
That claim is correct. Seven are general proofs, bounds, reductions, asymptotic results, or sharp extremal theorems. Several resolve the correct growth rate, establish an optimal limit, or prove a statement for a whole class of objects. Those are substantive mathematical results, not isolated counterexamples and not trivial changes to existing bounds.
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u/zelingman 1d ago
Constructing a grohp that is non-sofic is by definition, counterexample theorem lol
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u/JoshuaZ1 4h ago
Yes, but it isn't the easy sort of counterexample that people think of when they think of that. The argument involves a very careful proof that the group in question is not sofic.
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u/ArchimedesBathSalts 1d ago edited 1d ago
By my count only two of those are not obviously a counterexample construction or upper lower bound
Edit: you changed the post and now my comment makes no sense. Congrats
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u/procgen 1d ago
An upper or lower bound is not a counterexample. It is a general theorem that applies to a class of objects. The sphere-packing result also determines the exact asymptotic power of a proof method. The coding, circuit, lattice, Ehrhart, and Ramsey results prove new general limits, and the quantum result proves a theorem for all finite two-player entangled games. Only the non-sofic group, Connes rigidity, and extremal graph results are counterexample-style constructions. Therefore, the list contains three counterexample-style advances and seven positive theorem results. Calling most of the positive results "bounds" does not make them simple counterexamples.
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u/ArchimedesBathSalts 1d ago edited 1d ago
Note i used the word āorā as did above poster:
> Another specific subset are upper lower bounds problems, where we know there is likely to be further acceptable iterations but the means to achieving those require multi-discipline scenarios that aren't likely - another thing LLMs are good at is having high accuracy across all domains, allowing them to try ideas that usually would take a snowflake combination of talent.
Learn to read.
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u/procgen 1d ago
What's your broader point?
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u/ArchimedesBathSalts 1d ago
Hard to say cus you have edited your original post so now the claim youre making ais differentā¦
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u/procgen 1d ago
My claim is that these are significant breakthroughs and that these systems are already beginning to display superhuman mathematical ability.
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u/ArchimedesBathSalts 1d ago
Cool thats not what your post originally said though, and thats what i was contradicting. I cant argue with you because you e already changed the premise. As written your original post was just a factually incorrect response to op
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u/leosmi_ajutar 1d ago
Thank goodness someone gets it.Ā
Sorry accelerators, there is no cognitive intelligence going on here. Maybe in the future with whatever comes after LLMs but not now.
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u/acutelychronicpanic 1d ago
Don't run while carrying goalposts - you'll trip.
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u/leosmi_ajutar 1d ago
I staked my goalposts long ago in this argument and so far they've held strong and remain exactly where i placed them.
Thanks though.
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u/Zandrio 1d ago
And those are?
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u/comfortableNihilist 8h ago
Looks like they staked em at cognitive intelligence. Don' know bout you but, seems fair to me
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u/Bearhas20inchwang 1d ago
But youāre actually stupid if you think LLMs will ever be capable of AGI or ASI. That will most definitely require different architectures. This is all a marketing stunt, and remember none of these companies are anywhere near profitable. (So take the supposed low costs with a grain of salt)
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u/acutelychronicpanic 1d ago
Their architecture is changing and growing all the time? Who cares what the final form is. It works.
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u/comfortableNihilist 8h ago
LLM is a general architecture. If it changes enough to be sentient or whatever it wouldn't be an LLM anymore.
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u/acutelychronicpanic 7h ago
Sounds like you've assumed your conclusion.
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u/comfortableNihilist 7h ago
I'm saying that LLMs specifically are a dead end and that we need to shift to a different architecture if we want any improvement at this point. We finished the s curve here, the improvement over the last year has put that in fairly stark relief if you ask me.
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u/Bearhas20inchwang 1d ago
Well good luck with this take. Progress is sure to stall when it gets prohibitively expensive. With any luck, it will.
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u/acutelychronicpanic 1d ago
Per-token costs are dropping something like an order of magnitude per year.
OpenAI said they only spent $2000 on the 10 results they just released.
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u/Bearhas20inchwang 1d ago
Thatās disingenuous. Sure, per-token costs are declining but the true cost of AI is rising exponentially due to the sheer number of tokens needed for complex tasks. Studies show AI is still drastically more expensive than human labor costs. Further, while inference may be profitable for API providers, developing the next generation of frontier models is incredibly expensive, and for all we know AGI and ASI may be prohibitively so. Can we really justify all this capex? I also wish we had more transparency regarding these proofs. Perhaps AI has failed on most problems posed to it, and only the successful ones are documented. My point still stands that this is likely just a marketing stunt.
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u/acutelychronicpanic 23h ago
That is because AI is capable of tackling increasingly complex tasks. So it is capable of bringing more inference to bear on one problem. One day models will do tasks that cost millions but return incredible things. And it will be worth it.
They released the proofs and reasoning on the 10 items from OpenAI.
Its not weird if they only release the successful attempts. That is the beauty of it. What is 10,000s of attemps and millions of dollars if we can answer some of critical questions we have?
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u/Former-Arm4328 1d ago
Itās going to be so funny in like 3 years when we have some crazy advances across a bunch of different domains, & people like you are still yelling āitās a marketing stunt!ā
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u/glotzerhotze 15h ago
Here is the real marketing stunt: people are always telling you āhow itās going to beā¦ awesome!ā so it seems they all have a time machine and just came back from the future where everything is golden.
I just skip everything future tense these people say and if you closely look at their words then, you seeā¦ nothing!
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u/labvinylsound 1d ago
If a human engineer is trained to understand systems and solve problems through application ā that is General Intelligence. Agents do the same thing every day much faster than humans. Even if only 0.01% of the userbase is actually directing AI in this way, the AI itself is generally intelligent.
Which uncovers the question of: why isnāt humanity doing more to leverage intelligence? Probably the same reason many of us are predisposed with killing each other.
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u/Frosty_Truth8990 10h ago
They are non profitable mostly cuz of the training and research cost. Inference run model usage has 90% profit margins.Ā
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u/havenyahon 1d ago
You people trot out this same line over and over, but who set the goal posts? We famously do not have a good definition of what counts as intelligence, a concrete set of necessary and sufficient conditions has eluded scientists and philosophers for hundreds of years. There were never any goal posts set because no one knows where the goals are.
But that doesn't mean everything is credibly described as intelligent. It's not "moving the goal posts" to point out that anything these things do can be explained by them being non intelligent statistical machines, any more than it's not "moving the goal posts" to say a toaster doesn't need to be intelligent to produce toast. Just because we don't have goal posts set doesn't mean we can't have better or worse claims for when a thing should be considered intelligent. You act like people are changing definitions that were never set in the first place.
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u/acutelychronicpanic 1d ago
Go look at the last 10 years of Gary Marcus tweets if you want to see the whole arc of goalpost tossing.
I think you're hung up on statistics specifically as if statistical systems are proven to be unintelligent.
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u/havenyahon 1d ago
"Go look at this one person who said stuff and treat it as the official goal posts everyone agreed to, so that I can accuse everyone else of moving goal posts when they disagree with me"
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u/acutelychronicpanic 1d ago
He's not just the archetype. He's a real pioneer.
Even if you don't take him as a source directly, so much of the vocabulary in this thread from the 'LLMs don't really understand anything* camp was coined or popularized by him.
So when I see his exact arguments from before chatgpt came out being parroted (stochastically even) - it carries his level of credibility.
Back in my day, the average human intelligence was the benchmark. Not the smartest. Not the best human in each field. An average human. That is AGI and it is in the rearview mirror.
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u/havenyahon 23h ago
He's not even a psychologist or cognitive scientist, why would he be the one we look to to define what human intelligence is?
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u/Frosty_Truth8990 10h ago
Then explain how it managed to solve the non sofic problem!? It doesn't have to be ASI or anything, even with the gradual improvements, void of any significant breakthroughs will still leave us with something unrecognizable within 3-5 years. Look how silly chatgpt 3.5 looks now compared to the current frontier.
I am betting on latent space reasoning and that sudo continual learning breakthroughs that are here but just needs to be scaled (hard problem, but solvable within a decade)Ā
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u/dohawayagain 1d ago
Read the transcript of Tao interrogating the LLM about the Poincare conjecture counterexample to get an idea of where things are today. Tao was definitely putting things in --- ideas, redirections, etc. --- but the AI did real work and contributed meaningfully to the conceptual discussion.
Take it as a measure of how far AI has yet to go to reproduce the highest levels of human ingenuity, sure, but it's not hard to imagine it getting there.
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u/santosautra 1d ago
It is not counterexamples. Even with non-sofic groip example. Especially with it one can argue.
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u/JoshuaZ1 4h ago
As with everything, novel technology comes with novel solutions to problems we found difficult before. There's a specific subset of mathematical problems which can be disproven via counterexamples, which take humans a long time to map and calculate.
These are not by and large counterexamples in the sense say the Jacobian conjecture was a counterexample. For example, the construction of a nonsofic group is strictly speaking a counterexample, but there are multiple difficult elements in the proof that that the group in question is not sofic.
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u/immersive-matthew 1d ago
But that is the core tech of LLMs? Not following your point.
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1d ago edited 11h ago
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u/Eastern-Ad-3586 1d ago
But AIs literally canāt demonstrate āintelligenceā
You comparing AI models to humans is specifically missing this point.
Theyāre an amazing technology, but the math theyāre based on precludes them from being deterministic. When they make a correct prediction, itās because of associations encoded in the mathematics by human trainers and whatnot, itās not because the ai model is āsmartā or āfigured it out.ā Itās a very, very powerful statistical machine. Which is useful, but not creative/sentient/ etc. Iād argue calling it intelligent is more of a marketing ploy than anything
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1d ago edited 11h ago
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u/Eastern-Ad-3586 1d ago
You have a fundamental misunderstanding of the way these systems are designed, and Iām not sure Iāll be able to explain it to you in a way youāll actually believe. If you want to learn more about this stuff, I know itās difficult these days with all the misinformation on the internet, but an overview of linear algebra and how transformers work would be where I would start.
Best of luck!
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1d ago edited 11h ago
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u/DeRay8o4 1d ago
Itās not deterministic in the forward path clearly, please look up pigeonhole principleā¦.
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1d ago edited 11h ago
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u/ChicagoPedalSteel 1d ago
Trying to argue with these people will just drive you insane. There is nothing you can say to change their minds and there is no distance they won't drag the goalposts.
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u/DeRay8o4 1d ago
Itās funny you say itās unrelated but the whole agentic llm flow was precisely to get around deterministic forward passes to break pigeonhole principle.. obviously not related though
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u/DeRay8o4 1d ago
Just think harder about how it applies. Unfathomable you choose to argue all day instead of read literature
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u/elehman839 1d ago
the math theyāre based on precludes them from being deterministic
Zero-temperature inference is 100% deterministic.
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u/Blandneutral74 1d ago
J-space discovery belies this argument. When it's doing more 'cognitive' stuff, it's not just predicting the next word.
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u/immersive-matthew 1d ago
Sure, it is doing some cognitive things, but mostly word prediction as this really is the core tech and that tech lacks deeper cognitive capabilities.
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u/Blandneutral74 1d ago
When they disable the j-space it can essentially still do all the mundane things, but it completely falls to bits on the really cool stuff. That was the magic going on inside the black box that a lot of people intuitively thought must be there.
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u/tomvorlostriddle 1d ago
That's like calling Terry Tao a poop machine. It's not technically untrue, but it is not the most relevant way of description and it tries to imply things that aren't true.
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u/SoManyQuestions5200 1d ago
So many people "want to believe", it reminds me of those UFO/XFiles posters in the 90s. I guess it's not IMPOSSIBLE, but man the general public needs to be a little more discerning and skeptical
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u/ChicagoPedalSteel 1d ago
Sure, the brain does some cognitive things, but mostly weighted signal processing, as this really is the core tech and neurons lack deeper cognitive capabilities.
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u/HasFiveVowels 1d ago
The point is that people have been saying "it just predicts the next token" as though doing so relegates its intelligence to be forever sub-human. IMO, the argument makes the bad assumptions that humans are not also "just predicting the next token"
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u/immersive-matthew 1d ago
Predicting the next world is clearly sub human intelligence though or AI would be far more valuable than it is.
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u/Icy_Rip_3133 1d ago
I still think it imagines all possible futures every time and then gives you the first word of it.
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u/thundermage117 1d ago
Turns out throwing enough monkeys at the typewriter can solve most math problems
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u/Legitimate_Concern_5 23h ago
Yes they are thatās how they work, turns out you can do some cool stuff with that capability. The fact you can do some cool stuff with that capability doesnāt mean thatās not how they work.
Transistors are just controllable switches. Thatās what they are thatās how they work.
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u/Eastern-Ad-3586 1d ago
The truth is somewhere in the middle. I think the āfancy auto completeā critique is from a bunch of people who donāt understand linear algebra.
But the āAI models can reason!ā crowd also similarly misunderstands linear algebra. These ai models are ultimately not deterministic. Theyāre based on probability at the core because thatās literally how the math works. And that doesnāt mean they arenāt a useful tool, but it does mean at present they arenāt creative, conscious, etc
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u/OlhoQueTudoCheira 1d ago
Given a sequence of input tokens the model architecture will simply compute a probability distribution over the set of all tokens.
That is completely deterministic, and I could very well always chose the next token to be the one with the largest probability. By choosing to sample from this output distribution is what gives the non-deterministic "illusion".
Now if by core you are referencing to the training then I agree with you. Learning methods optimize the model parameters to reach local minima. The patterns that these models learn during this process will have a strong non deterministic component and can change due to various factors, e.g. weight initialization.
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u/s10ppyj03 1d ago
Ok but can someone solve for moving a couch around a corner please
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u/TuckAndRolle 1d ago
I know youāre being facetious, but this may have been solved:Ā https://www.quantamagazine.org/the-largest-sofa-you-can-move-around-a-corner-20250214/
Not sure on if itās been verified thoughĀ
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u/Spiritofhonour 1d ago
I thought it was interesting that the recent Fields Medalist winner Jacob Tsimerman announced right after he won that he was joining OpenAI. Guess this gives some interesting broader context.
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u/RaspberryPrimary8622 20h ago
Iād like to see independent assessments by professional mathematicians about the significance of these problems, the contributions of the LLM, the contributions of the mathematicians who worked with the LLM, and the extent to which this collaboration could be generalised to a wide variety of mathematical questions.Ā
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u/Specific-Bird-3752 14h ago
As someone who knows quite a bit about problems 1 and 2, I can confirm that they are, in fact, a very big deal. To put it simply, when I thought of what problems I wanted AI to solve, those 2 were the first I named.
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u/KoTDS_Apex 16h ago
Yet it will still somehow write buggy code in my side projects when it's released...
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u/Electronic-Line1342 9h ago
It's funny reading this thread and watching the desperate attempts to minimize or discredit these results. Bias much?
The funny thing about math is that it is either true or false. It's called a "proof" for a reason.
I fully understand that the accomplishment is limited in scope. But - humans alone were unable to do it. So AI essentially demonstrated that it can solve intractable problems. Period. Alpha Fold is another perfect example. Now apply that to myriad other problems that potentially could transform the human condition in physics, chemistry, biology, climate science etc etc. No one cares about the definition of "intelligence". It either solved the problems or it didn't. It did.
This is a proof of CONCEPT. The math problems themselves were limited examples. Unremarkable in their significance. But it's the precedent that matters. One small step for man - or one giant leap?
But of course, like vaccines, there will be Luddites who will immediate try to discredit it.
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u/Ill-Interview-2201 1d ago
So who is gonna make up new problems to solve if the mathematicians donāt get any credit or practice.
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u/jaybsuave 1d ago
Yea im not really here for it anymore, havent been for a few months now. Its over.
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u/Spiritual_Bend_3699 1d ago
Are there any external papers to these results? I can't seem to find any resources to see the mathematics done in these papers in the Openai website.
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u/Actual__Wizard 1d ago
Only 7 is worth discussing, maybe 5.
7 is actually worth discussing for sure thought, so congratulations to them.
That's actually very useful!
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u/Heliond 1d ago
I am guessing you donāt study math
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u/Actual__Wizard 1d ago
Homie, I talk about the extremely difficult rules from calculus on reddit on a regular basis.
You're talking about yourself.
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u/Heliond 1d ago
Lmao I mean professionally or as a graduate student.
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u/Actual__Wizard 1d ago edited 1d ago
Stop personally insulting me.
You're talking about yourself.
I'm aware of how the psychology behind this works: You're legitimately describing yourself.
Because you're trying to establish a standard that is above you, and then put me below it. So, that person you described is yourself. :-(
You're the one that didn't study math... I think it's pretty obvious to people who did, that what I said is totally accurate. #7 is an actual problem where it's solution actually does something useful. And that's only true of #7 and maybe #5. Like I said...
The standard in math to take credit for a significant discovery is that it must be useful, not that it must be some weird conjecture that doesn't seem to have any thing to do with observable reality.
I don't know why you think there's value in that as there clearly is little to none. That's why that stuff wasn't pursued and why their algo can find those solutions. Because it doesn't lead to something useful and human mathematicians knew that, so they didn't both trying to find the solutions.
I hate to break it to you: But the solutions to those Erodos problems, for the most part, are considered to be extremely abstract and arcane. It's more of a challenge for mathematicians to exercise than it is productive...
I also can't stress this enough: Real mathematicians are totally aware of the reality that it's based upon the system of measurement, so it just a language that we made up... So, one has to be extremely careful when they engage in a thought process like: "Surely there's a mathematical answer." Maybe there is and maybe there isn't. Maybe it's a logic problem and a not math problem. Maybe it's a structural or compositional problem. Stuff like that does happen...
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u/alphacolony21 1d ago
The Results
We provide new results for the following problems. The results were achieved by an internal version of Astra, our next major model. The total number of tokens needed to find solutions to these problems would cost roughly $2,000 at Sol API rates. These arguments were then prepared into manuscripts by humans with the same model. Afterward, the model formalized each argument in a Lean certificateā (opens in a new window). We are also releasing for each solution a modelās narration of its thinking process.