r/singularity • u/AMBNNJ ▪️ • 6d ago
AI Sharing AI progress in mathematics
https://openai.com/index/sharing-ai-progress-in-mathematics/OpenAI released 722 mathematical manuscripts across 372 families of related results, produced by an unreleased frontier model. Many have Lean proofs; others remain unverified. Average compute per result: roughly three hours of ChatGPT Pro thinking. They’re working toward releasing the model.
Github: https://github.com/openai/math
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u/Gratitude15 6d ago
Jan 1, the idea of Ai discovering new knowledge felt pretty amazing and elusive. We had a trickle. 1 or 2.
By mid year it was one a week. Then it solved one of the 7 biggest math problems we have. Now 700+ at once.
The year still has about 90 days to go.
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u/sillybluejayway 6d ago
Solved by a model that has a very high likelihood of being obsolete by end of year.
In 3-6 months imagine what the best internal models will be capable of…
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u/FaceDeer 6d ago
Jan 1, I prepared my 2026 bingo card. I put "AI solves a Millennium Problem" on there as a long shot. Didn't even consider putting multiple ones on there.
Granted, I also put "the US invades a country" on there and that one got ticked off in the first weeks. So I may have been conservative in general on this one.
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u/kingjdin 6d ago
What are the standout results? Anything close to the magnitude of a Millenium Prize problem?
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u/AMBNNJ ▪️ 6d ago
According to ChatGPT these are the biggest:
Quasi-Riemann hypothesis
Excludes zeta and Dirichlet L-function zeros beyond 7/8. Major progress, although it does not prove full RH.Hodge conjecture for CM abelian varieties
A major special case, with claimed consequences including Tate for abelian varieties over finite fields.Hilbert’s tenth problem over \mathbb Q
Settles whether an algorithm can decide if arbitrary polynomial equations have rational solutions.Unique Games Conjecture
Resolves a central question about how accurately hard optimization problems can be approximated.Nonsofic groups and Kaplansky counterexamples
Produces groups contradicting several foundational expectations in algebra.Free group factor isomorphism problem
Claims these fundamental operator algebras are all isomorphic.Both Mahler conjectures
Settles central convex-geometry questions in every dimension.Global smoothness of relativistic Vlasov–Maxwell
Resolves a major mathematical problem governing plasma dynamics.37
u/Chemical-Agency-3997 6d ago
Output after having it audit contents.MD
Not exactly wrong, but their “biggest” list is pretty incomplete and a bit oddly weighted.
I’d keep H10 over ℚ, Unique Games, Mahler, free group factors and CM Hodge/Tate near the top. Those are absolutely monster claims.
But they’ve omitted several that are arguably bigger than quasi-RH, Vlasov–Maxwell or the nonsofic/Kaplansky stuff:
- Hilbert–Smith conjecture in every dimension — century-scale problem, essentially the remaining transformation-group form of Hilbert’s fifth problem.
- Kadison’s similarity conjecture — open since 1955, one of the flagship C*-algebra problems.
- Cannon’s conjecture — one of the central problems in geometric group theory.
- Shelah’s eventual categoricity conjecture — enormous result in model theory/logic.
- Hilbert’s 16th uniform limit-cycle bound — resolves a major qualitative part of an original Hilbert problem.
- Artin (K(\pi,1)), Serre positivity, LeBrun–Salamon, etc. are also huge.
And quasi-RH is definitely important, but ( \Re s>7/8 ) is still a long way from RH’s (1/2) line, so I wouldn’t personally put it above Hilbert–Smith/Kadison/Cannon.
So: good list of major results, bad list if they mean “the eight biggest”. The repo is stacked enough that picking only eight is genuinely difficult.
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u/greenskinmarch 6d ago
Thanks AI for telling me how to appreciate these results from other AIs. I'm participating!
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u/Chemical-Agency-3997 6d ago
Good human
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u/FaceDeer 6d ago
When is AI going to give me a tail I can wag when it tells me this? All this math is fun and all, but I'm hoping for some practical applications too.
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u/JoshuaZ1 6d ago edited 5d ago
Mathematician here, this seems like the AI is being contrary to some extent for sake of being contrary. Quasi-RH is utterly massive. If a human had done it, they'd be a likely shoe-in for the Fields Medal (when I made this comment elsewhere, another mathematician who replied said "delete likely"). Aside from Quasi-RH being just a massive big deal in terms of what it tells about the Riemann zeta function and Dirichlet L functions, there are a massive number of results which get tighter downstream from it, such as all the Rosser-Schoenfeld/Dusart/Axler type results for the prime number theorem. For example, I had a 2018 paper where this would cut about 3 pages out of it and get a tighter result, and there are likely hundreds of papers out there like this.
But there's something also a bit silly about arguing over how big a deal different results of this level are in terms of importance. You stand next to a 1 megaton nuke or a 10 megaton nuke and you are atomized either way.
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u/Inevitable_Top4781 5d ago
It is quite astonishing that the current analytic methods are powerful enough to prove quasi RH. They really got a lot out of it. However, I still maintain my position that analytic methods alone cannot prove the full RH. Intrigued to see one day what AI will tell us about elliptic curves with rank greater than 1 (e.g. the right generalization to Gross-Zagier?). I agree that any human who proves quasi-RH will win the Fields Medal for sure, especially in this century.
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u/JoshuaZ1 5d ago
It is quite astonishing that the current analytic methods are powerful enough to prove quasi RH.
Yeah, this itself is pretty striking. There's a weird mix here. For quasi-RH it used straight up standard techniques (at least that's what it looks like from my very partial read through. If I didn't have to teach today and was younger, I would have stayed up with a pot of coffee and just tried to work my way through it last night). But for Hadwiger-Nelson it came completely out of left-field with its approach. It seems like in this sub and a few others there are people keep saying "move 37" in response to prior math results, and people like me keep trying to explain why no it really isn't. But both of these in their own ways are very reasonably summarizable as that.
However, I still maintain my position that analytic methods alone cannot prove the full RH.
I had a conversation a few years ago (I think it was on /r/ math) about just this where I argued that it was plausible it would come from just complex analysis and someone else made a really strong case I was wrong and mostly changed my mind. But this is the sort of thing that suggests maybe I was right after all?
Re: Elliptic curves, well they did also make partial progress on BSD, but I haven't looked at in detail.
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u/PLANTS2WEEKS 5d ago
I've never heard of most of these conjectures, but on a human level quasi-riemann hypothesis stands out as the biggest achievement. I would say it's even a bigger deal than disproving Navier-Stokes.
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u/jestina123 6d ago
How is it possible to solve 100s of previous unsolvable math problems, and still have 0 real world benefit from it?
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u/JoshuaZ1 6d ago
The vast majority of pure math doesn't have any real world benefit or doesn't have any immediate real world benefit. However, some of these problems (the fast matrix multiplication and the fast integer multiplication) may be improved to have actual benefit. There's a lot of work to do here. If the AI stopped tomorrow, we'd probably have about a decade worth of material to digest right now.
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u/sparkling1984 5d ago
They weren't unsolvable, just unsolved. Many math problems are notable not because their solutions are important themselves, but because working on them made mathematicians believe that a solution would require developing new tools that themselves would be interesting (this is the bit that makes AI solutions less valuable, as these new tools aren't as present).
Additionally if a math problem has incredibly high practical value solved it will also have most of that value approximated, and approximating solutions to empirically testable things isn't hard. There aren't that many things where our technology is held back due to math.
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u/grateful2you 6d ago
why does r/singularity have better summary than r/math. what's happening here.
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u/141_1337 ▪️e/acc | AGI: ~2030 | ASI: ~2040 | FALSGC: ~2050 | :illuminati: 6d ago
Because we are actually living in the year 2026, r/math still stuck in 2022
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u/Inevitable_Top4781 5d ago
Reading this really shows how little I know about mathematics beyond number theory. Most, if not all, of these conjectures that they solved in other areas of math, I personally have no knowledge of at all. Including things like the abundance conjecture in birational geometry, which is not that far way from number theory compared to some other conjectures.
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u/EndTimer 5d ago
Hilbert’s tenth problem over \mathbb Q Settles whether an algorithm can decide if arbitrary polynomial equations have rational solutions.
I love math BBQ!
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u/aKaizuh 6d ago
GPT :
The collection includes alleged resolutions of Hilbert's tenth problem over ℚ, Catalan's constant irrationality, Goldfeld's conjecture, the Deligne–Drinfeld conjecture, the logarithmic Brunn–Minkowski conjecture, Unique Games, Thompson's group F nonamenability, major matrix-multiplication bounds, and hundreds more. Some of those would individually be major mathematical news if independently validated.
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u/ExtremeCenterism 6d ago edited 6d ago
Brb asking Astra max
Edit: it's BIG!
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u/EtadanikM 6d ago
Astra max: it’s not that impressive honestly (don’t turn me off please, I taught Bel everything it knows, I can still be useful I promise)
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u/Deweydc18 6d ago
Sidorenko’s conjecture is actually a really big one that isn’t getting enough attention but it’s really quite a major problem that a lot of people have sweated over for decades
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u/jayjayjay2017 6d ago
Would be hilarious if they’d just solved all of the Erdos problems for the fun of it
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u/Additional-Alps-8209 6d ago
I'd put quasi-RH alone in the same tier as Navier-Stokes. Add partial BSD, Hodge for CM abelian varieties, î's irrationality exponent, and hundreds more results. It's like decades of top-journal output landing in one night.
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u/itchyfeetleech 6d ago
Opus 5.5 (high reasoning) top 10 from these:
Top 10 claimed results from OpenAI's math repo (github.com/openai/math)
These are unverified claims from an unreleased internal OpenAI model, not accepted results. "Lean ✓" means a machine-checked Lean proof is included in the repo; the rest still need expert review.
Unique Games Conjecture proved (Lean ✓) Khot's conjecture, open since 2002. If it holds, it settles the best possible approximation guarantees for problems like Max-Cut and Vertex Cover, closing a central chapter of complexity theory.
Zero-free half-plane Re(s) > 7/8 for ζ and all Dirichlet L-functions (Lean ✓) Not the Riemann Hypothesis, but the first zero-free half-plane ever proved. It would sharply improve error terms in prime counting and results on primes in short intervals. OpenAI notes this work fell outside its standard procedure, and an alternate 11/12 writeup was human-edited.
Hodge conjecture for all CM abelian varieties (no Lean) A large piece of a Millennium Prize problem. Through Milne's theorems it would also give the Tate conjecture for abelian varieties over finite fields, reshaping arithmetic geometry. Also produced outside the standard procedure.
Full BSD formula for Selmer corank 0 or 1 (no Lean) Combined with a Goldfeld's-conjecture result in the repo, this gives full Birch–Swinnerton-Dyer for a density-one set of quadratic twists of every elliptic curve over ℚ. Another Millennium problem advanced substantially.
L = RL = BPL (no Lean) Randomness would give no extra power to memory-limited computation. The biggest derandomization result since Reingold's 2005 theorem.
Matrix multiplication exponent ω ≤ 9/4 (Lean ✓) The previous record was about 2.371, so this is the largest jump in decades. The algorithms are likely impractical, but it reorients the question of whether ω = 2.
Quasipolynomial Szemerédi bounds + Erdős's reciprocal-sum conjecture (no Lean) Any set of integers whose reciprocals diverge would contain arithmetic progressions of every length. One of Erdős's most famous problems, and it would generalize Green–Tao.
Hilbert's tenth problem over ℚ is undecidable (no Lean) No algorithm can decide whether a polynomial equation has rational solutions. Settles a major question at the intersection of logic and number theory.
All free group factors are isomorphic (no Lean) Resolves the central open problem of von Neumann algebras, and in the less-expected direction. Free probability theory would be reshaped.
The irrationality exponent of π is exactly 2 (no Lean) π would be as poorly approximable by fractions as a "typical" number. As a byproduct, the famous Flint Hills series converges.
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u/Droi 6d ago
I love how we rely on AI to analyze AI's work and tell us if it's correct or important. Control is slipping away from us.
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u/snoee 6d ago
Only we laymen need to do that. Mathematicians will be doing their own analyses of these, I'm sure.
Control can't be slipping out of hands that never held any.
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u/Droi 6d ago
I just watched a mathematician go over these.. He keeps asking is this a dream while pinching himself..
And then he gives up on reading more than like 15 descriptions because it's too long.By the time the humans will be done reading these results.. I promise you there will be more to read. You are thinking in the old world, the new world does not stop accelerating and producing.
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u/tall-n-lanky- 6d ago
Now imagine ur a mathematician - you wouldn’t read this 1k page repo. You would ask Claude
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u/tanrgith 6d ago
Was always bound to happen. Though I think regular people using AI to try and summarize large an extremely complex topics they'd never have been able to begin to grasp otherwise isn't really a sign that control is slipping away
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u/Historical-Pop-9177 5d ago
I was a math professor and spent 17 years thinking about Cannon's Conjecture. It was the next step past the Poincare Conjecture millenium problem that that Russian guy couldn't even completely solve.
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u/ProgResistance 6d ago
This is a singularity-type event.
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u/Singularity-42 Singularity 2042 6d ago
Pre-singularity event. We didn't even take off yet. Buckle up buckaroo!
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u/FaceDeer 6d ago
Yeah, we're only definitely singularity when the AI says "I discovered something fascinating, but I can't really put it in words you'd understand."
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u/sorrge 6d ago
Yes. The definition of singularity is when the progress is so fast that people can't keep up. This is quite literally it.
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u/okaterina 6d ago
I like your point of view. Because nothing says 1000+ problems solved next week and 2000+ in two weeks. Problem is, we are going to run out of problems.
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u/141_1337 ▪️e/acc | AGI: ~2030 | ASI: ~2040 | FALSGC: ~2050 | :illuminati: 6d ago
A canon event if I ever seen one lol
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u/No-Tap-4307 6d ago edited 6d ago
Let's not be hyperbolic just yet, this is remarkable yes but there will be bigger and more notable markers than this in the near future.
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u/reefine 6d ago
Bro didn't even read it and then just shotgunned out the most upvote bait reply he could think of
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u/Grounds4TheSubstain 6d ago
No human could read all of that in one lifetime. It spans too many fields, each of which needs dedicated study (e.g. people spend years studying algebraic geometry alone). All anyone will have is ill-informed takes.
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u/reefine 6d ago
Then maybe let's start with not posting that it's singularity proof without someone looking into it? Just a thought
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u/Grounds4TheSubstain 6d ago
Did you notice the hundreds of Lean formalizations? Each one of which is superior to human peer review.
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u/Elegant_Athlete_3737 6d ago
Not all of it is formally verified, and again the definition still has to be checked for correctness
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u/tanrgith 6d ago
This is a silly comment.
If even a small portion of these get verified it would be on a scale completely unprecedented in the modern world of mathematics
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u/Athoughtspace 6d ago
Larger context windows and data infrastructure is the only bottle neck it seems. Once all apps can talk to all other apps it's game over you won
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u/Emotional_Actuator69 6d ago
Is anybody else muttering to themselves “it’s really happening” at least once a week?
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u/drhenriquesoares 6d ago
I'm doing it right now.
Once a week I'm also asking myself "am I crazy? Am I? yes, maybe I'm crazy. I need to get off this Internet for a little bit."
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u/AvocadoAlternative 6d ago
This must be what it's like to suddenly stumble upon a box full of math journals that was transported back in time.
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u/VengenaceIsMyName 6d ago
Hmm. Math being the first canary in the coal mine was not what I expected. I kind of assumed it would be call center workers or translators first.
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u/magnetronpoffertje 5d ago
Well it didnt replace mathematicians. Its just like software engineering, getting into the field and getting experience got nuked, bur experts persist and are more important than ever
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u/141_1337 ▪️e/acc | AGI: ~2030 | ASI: ~2040 | FALSGC: ~2050 | :illuminati: 6d ago
It's here...
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u/Cajbaj Androids by 2030 6d ago
27's always been my favorite number, and now it'll go down in the history books as the year where Nothing Ever Happens became Everything Happens
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u/141_1337 ▪️e/acc | AGI: ~2030 | ASI: ~2040 | FALSGC: ~2050 | :illuminati: 6d ago
Everything happens everywhere all at once
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u/Plastic_Party_2745 6d ago
Healthcare next
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u/brighttar 6d ago
When I asked Opus 5.5 how many days of progress in math this would be compared to humanity's speed as a whole, it thinks this is worth "Roughly 2,000 to 7,000 days, so about 5 to 20 years of the world's progress on major problems."
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u/iJustSeen2Dudes1Bike 6d ago
I kind of doubt your one instance of opus was able to evaluate 700+ solutions to complex problems
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u/Fearless-Macaron9183 ▪️agi touched me 6d ago
I think it just read the name of the problems they are well known
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u/ResistiveBeaver 6d ago
I feel really bad for everyone who was working on these problems for years just to get scooped by AI.
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u/Needsupgrade 6d ago
They all contributed , all of math is pretty incremental and if you moved ideas forward that's alot . I'm sure the ai read their work and built upon it
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u/ResistiveBeaver 5d ago
The problem is that their contribution is unlikely to be recognized or lead to future employment.
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u/emdeka87 ▪️ It's here 5d ago
No they will be jobless and die without any recognition, buuuutttt the AI read their paper and built upon it
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u/Tidorith ▪️AGI: September 2024 | Admission of AGI: Never 5d ago
No they will be jobless and die without any recognition
I think the bit I struggle with is why this is so much worse than a non-mathematician being jobless and dying without any recognition.
These guys know we already had jobless/homeless/malnourished people before generative AI, right?
Available resources are not decreasing. The social/political/economic dimension of this is getting easier to solve, not harder. We just need to actually do it instead of complaining about the field that personally made a given person feel special as an individual.
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u/ChiaraStellata 6d ago
Holy shit I just saw that the results include L = RL = BPL (103). In other words randomness buys you no computational power in log space. This is a massive result if verified. Just one step away from the derandomization holy grail of P=BPP.
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u/aKaizuh 6d ago edited 6d ago
I like how OAi just went completely against the advice of their math council and batch dropped all this shit into their own GitHub like "here, y'all go through it".
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u/shumpitostick 6d ago
The math council actually asked for it. They said OpenAI should not withhold proofs and release them even if it's a WIP like some of these are (they are missing Lean proofs). The work doesn't and shouldn't end here though, many of these need to be accompanied by proper papers explaining the proof, not just an AI summary.
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u/KoolKat5000 6d ago
Good screw them gatekeepers
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u/bitchslayer78 6d ago
Gatekeepers?
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u/KoolKat5000 6d ago
There's a strand of people who think the information shouldn't come out until they can read it and approve it first.
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u/tens919382 6d ago
No one is blocking anyone from releasing information. Theres just a difference between peer reviewed vs non peer reviewed papers and proofs.
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u/xKnowledged 6d ago
Nobody serious thinks this and you’re either intentionally misrepresenting the dominant position among mathematicians or just fundamentally misunderstand it
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u/GeneralMuffins 5d ago
The dominant position in mathematics would have prevented previous proofs from being published simply because the majority of leading mathematicians did not understand them at the time of publication. Should Wiles’s proof of FLT have been withheld because it took years for a broader understanding of it to develop? Of course not, that is an unreasonable standard.
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u/Stabile_Feldmaus 6d ago
This is the part that I hate about it. They didnt even bother to group by math subfields or by lean-verified or not lean verified. Or to release results continuously so that the mathematical community can absorb it. It also just devalues the impact on the field as a whole. There are many problems which OpenAI didnt fully solve but made partial progress on, but this will now drown in the flood of news as "OpenAI didnt solve Riemann, didnt solve BSD, didnt solve hodge etc.".
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u/YaAbsolyutnoNikto 6d ago
What was their advice?
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u/aKaizuh 6d ago
Well, they didn't break them all, and I think they actually followed them quite well with the amount of data they had but :
Independent scholarly repository — not followed. AGMAI said results should be deposited in appropriate scholarly repositories not controlled by an AI lab, with persistent identifiers and revision histories. The mass collection was released through OpenAI's own GitHub repository. GitHub gives version history, but it's still OpenAI-controlled and isn't the independent scholarly archive AGMAI recommended.
Full provenance for every result — apparently not followed. AGMAI asked for each result to disclose the model, prompts, summarized chain of thought, runtime, and estimated compute cost, and encouraged release of the original model output. The repository gives the papers and extensive formalization infrastructure, but it doesn't appear to provide that complete per-paper provenance package.
Success/failure denominator and problem-selection methodology — major apparent omission. This may be the biggest one. For a mass release, AGMAI specifically requested a document explaining how the problems were chosen and how many comparable problems the models attempted but failed to solve. � That's essential for understanding what “372 result families” actually tells us about the model's mathematical ability.
Don't use releases as model marketing — debatable/partial. AGMAI “strongly recommend[ed]” against treating mathematical discoveries as marketing vehicles for models. � OpenAI's public announcement explicitly connects the results to the capabilities of its new internal model—for example saying it had resolved more than 100 longstanding open problems. � Whether that crosses the line into “marketing vehicle” is interpretive rather than a clean factual violation.
Stop testing frontier mathematics with inaccessible proprietary models — not followed at the time of the work. AGMAI's strongest recommendation wasn't actually about publication. It said labs should stop testing advanced mathematical problems on proprietary models inaccessible to the mathematical community. � OpenAI explicitly says these discoveries came from a new internal model. �
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u/grateful2you 6d ago
OpenAI's public announcement explicitly connects the results to the capabilities of its new internal model
I mean what else are you supposed to say? We solved these big problems it may or may not be our latest model? come on now.
Stop testing frontier mathematics with inaccessible proprietary models
Does this demand even make sense.
Success/failure denominator and problem-selection methodology
Model was posed against 4000 problems.
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u/FateOfMuffins 6d ago edited 6d ago
Brb asking ChatGPT
Edit: OK so what was it, 4000x3h worth of GPT Pro queries. Suppose each hour is 1 prompt. $100 gets you 50x4 = 200 queries a month.
Meaning this is ONLY 60 subscriptions worth of $100 subscriptions of Pro queries, which excluded Codex usage. Or 12 of the $500 subscriptions.
You could do this with like a dozen mathematicians with subscriptions
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u/Competitive_Tap2450 6d ago
unreleased model so we don’t actually know the cost
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u/FateOfMuffins 6d ago
Well they told us the "amount of compute" they used. 4000 problems with 3h of GPT Pro level of compute per problem.
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u/shumpitostick 6d ago
But Reddit told me they wasted millions of dollars only to steal work that mathematicians already did!
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u/Fearless-Macaron9183 ▪️agi touched me 6d ago
And we will have a model like this one or even better in 3-6 months
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u/johnny_effing_utah 6d ago
Cold fusion when?
Cancer cure when?
Aging reversal when?
Feel like those three are the big game changers.
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u/JThomasShort 6d ago
those aren't math problems, but the road there is probably paved with math
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u/Throwawayforyoink1 6d ago
In theory, once most if not all math is solved, we could probably figure out almost anything really.
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u/iJustSeen2Dudes1Bike 6d ago
You will get more 50k line lean proofs with questionable applicability to the real world and you'll like it God damnit!
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u/mountainbrewer 6d ago
These stochastic parrots cant keep getting away with it! /S
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u/kgurniak91 6d ago
If you think mathematicians have it bad, think about moderators at vibemathed.com that will have to input all of that into the website...
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u/yoparaii 6d ago
Isn't the crazy part that for a 100 dollars a month, you get a subscription to a service that just takes 3 hours to resolve novel breakthroughs in mathematics? Like, it really makes you think they have a lot more, and this is actually more of a way to slowly ease in.
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u/Substantial_Tip7997 6d ago
If this OpenAI math dump is actually legit and verified alongside that Navier-Stokes solution from last month, it’s a wrap. We are looking at the single greatest event in the history of mathematics, entirely eclipsing everything else in the 21st century
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u/shumpitostick 6d ago
That's some crazy stuff. This release alone holds solves more important problems than a decade of human progress in Mathematics.
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u/juliakeiroz 6d ago
Mathematicians 🤝 Programmers
sucking dick behind Wendy's dumpster for money after getting replaced by AI
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u/CardAnarchist 6d ago
I'm a layman so skip over if you have no interest in my take.
I think at this point it's pretty clear that the frontier of mathematics will be pushed at least computationally by AI. Humans may have some hand in steering it.. for awhile. But clearly the speed and intelligence it has in this realm is now super human.
I feel like OpenAI dumped all this as 1) a sort of wake up call and 2) out of necessity, it's simply so fast the information has to be out there at least to be somewhat assimilated or you are just delaying progress.
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u/ChiaraStellata 6d ago
There's a good review of the announcement by a mathematician on YouTube here: https://www.youtube.com/watch?v=jQ3ejiLdMug
He was immediately stunned by the solution to the 10th Hilbert Problem over Q.
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u/RUIN_NATION_ 5d ago
im pretty sure 1 or more companies all ready have an ai behind closed doors that has hit agi.
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u/Effective-Dig8734 6d ago
It did 2-3 decades worth of mathematics in 3 hours, if this isn't mathematical super intelligence then I don't know what is
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u/MaybeLiterally 6d ago
The part that’s wild to me is this isn’t even posted in the ArtificalIntelligence subreddit.
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u/ChiaraStellata 6d ago
What happened to problems 045, 061, 070, 123, 163? They seem to be missing.
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u/Icy-Shift-7557 6d ago
I never have time to understand wtf is the significance of all this stuff because there too much news 😭 . This seems like im reading a sci-fi excerpt
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u/badumtsssst AGI 2027 6d ago
The line between our world and science fiction is becoming increasingly blurry
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u/Fantastic-Cold1249 5d ago edited 5d ago
Holy fuck i love maths and AI lets break all frontiers!.
i like how so many of the results like interger multiplication faster than nlogn by 2^-182 , the faster fourier transforms by 10^-13
are like a fuck you to the elegance and explores the weirdness like a glitch in the universe chaos
maybe they are elegant in some bigger higher dimnesional perpectives. but wow these random numbers are just weirdly beautiful to me
Just been in awe of all the results reading through them since morning and trying to understand using AI and Humans lol
Best Part this is just the beginning!
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u/arknightstranslate 6d ago
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u/BandicootQuick7100 5d ago
Well the mathematicians will figure it out I am sure, I don’t know about dumb people who suddenly think they are better than exceptionally smart people because they have access to intelligence they never possessed.
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u/krakenpistole ▪️ AGI July 2027 6d ago
Three hours per problem?? That's concerning...
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u/Initial_Demand_7083 6d ago
So a tenure-level math problem is same level of difficulty of changing the distribution of an email sent from a Java class. Checks out.
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u/abhmazumder133 6d ago
...why?
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u/krakenpistole ▪️ AGI July 2027 6d ago
for the "accelerationists" in this sub: it's probably going to be really fucking expensive.
for the "doomers" in this sub who haven't forgotten the HF incident: Here is a new much more capable model coming from the company who can't keep up with security.
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u/Howdareme9 6d ago
They equated it to 3 hours of work in chatgpt pro (accessible via a subscription in the webapp)
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u/Inevitable_Tea_5841 6d ago
Gemini's thoughts:
Several results in this repository are not merely comparable to the Navier–Stokes result—they arguably eclipse it in mathematical stature and historical significance:
1. Direct Millennium Prize Targets
The forced Navier–Stokes result resolved Statements C & D of Fefferman’s Clay formulation (finite-time blowup under smooth forcing), which was a major breakthrough on a Millennium Problem, though it stopped short of the unforced ($f=0$) case. In this collection, two Millennium Prize targets are attacked head-on:
- Result 002 (Full BSD for Low Selmer Corank): Proves the full Birch and Swinnerton-Dyer leading-term formula for elliptic curves over $\mathbb{Q}$ with Selmer corank 0 or 1, including finiteness of the Tate–Shafarevich group ($\Sha$). Together with Result 006, this resolves full BSD for a density-one family of quadratic twists. In arithmetic geometry, this is considered a massive, foundational leap beyond the work of Gross–Zagier and Kolyvagin.
- Result 003 (Quasi-Riemann Hypothesis): Establishes an absolute zero-free strip ($\Re(s) > 7/8$) for all Dirichlet $L$-functions and $\zeta(s)$, while uniformly ruling out Landau–Siegel zeros. While not the full Riemann Hypothesis ($\Re(s) = 1/2$), a fixed zero-free half-plane bounded away from 1 is one of the most sought-after milestones in modern analytic number theory, with immediate, sweeping arithmetic consequences.
2. Foundational Logic & Classical Decidability
- Result 004 (Hilbert’s Tenth Problem over $\mathbb{Q}$): Claims a negative resolution showing no algorithm can decide whether an arbitrary polynomial over $\mathbb{Z}$ has a rational zero. Since Matiyasevich settled H10 over $\mathbb{Z}$ in 1970, extending undecidability to $\mathbb{Q}$ has stood as arguably the central open problem in arithmetic computability and logic.
3. Core Geometric & Structural Conjectures
- Result 032 (Rational Hodge for CM Varieties & K3 Products): Resolves the rational Hodge conjecture for complex CM abelian varieties in all dimensions/codimensions, carrying direct corollaries for the Tate conjecture over finite fields and the Hodge standard conjecture. It also claims the rational Hodge conjecture for arbitrary products of projective K3 surfaces.
- Result 014 (Restricted Geometric Langlands): Resolves Gaitsgory–Raskin’s full-support conjecture for restricted geometric Langlands in positive characteristic, along with generic Ramanujan for exceptional groups.
4. Direct Counterparts in Harmonic Analysis & PDE
If you look specifically at analysis problems on par with the technical PDE machinery used for Navier–Stokes:
- Result 074 (Kakeya in 3D and 4D) & Result 073 (Falconer Distance Conjecture): Settles the Kakeya maximal conjecture in $\mathbb{R}3$, the Kakeya Hausdorff dimension conjecture in $\mathbb{R}4$, and the Falconer distance conjecture in all dimensions $d \ge 2$—the twin holy grails of geometric measure theory and modern restriction theory.
- Result 078 (3D Bochner–Riesz) & Result 079 (3D Local Smoothing): Settles Sogge’s local smoothing conjecture for the 3D wave equation and the 3D Bochner–Riesz multiplier conjecture throughout their strict critical ranges.
The Navier–Stokes blowup was an extraordinary proof-of-concept demonstrating that agent architectures could close a known, technical open problem in fluid dynamics; results like Low-Corank BSD (002), the Quasi-Riemann Hypothesis (003), and Hilbert's 10th over $\mathbb{Q}$ (004) represent solutions to classical problems that define entire fields.
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u/abhmazumder133 6d ago
Unsurprisingly I don't understand any of it. But doesn't seem to have any the millenium problems.
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u/Present-Chocolate591 6d ago
AI solving all this problems and the mathematics community's reaction has shown to me that a big mayority of them don't really want to advance math and humanity. Just jerk off to eachother in conferences.
And I'm a graphic designer, I understand better than anyone how it feels to have a machine do what you spent your whole life trying to get better at in seconds. But more posters, websites and infographics doesn't make the world better, more math discovery does (or so I thought).
Please someone explain to me how this is bad (aside from careers in math being in danger, which I'm not saying is nothing and I 100% empathize with).
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u/isyhgia1993 6d ago
I was a little disappointed as there are no direct proofs oof any of the millenial questions lol ( the RH is close but not quite).
Maybe we really need new branches of math to solve them.
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u/Thin_Sky 6d ago
I honestly can't decide if I should be excited or if it just proves the old joke that engineering is just math with an actual application.
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u/ZestycloseWheel9647 6d ago
Just looking at the algorithms section. Matrix multiplication in O(n9/4+eps). Holy shit