10 ms·

Gemini with Deep Think achieves gold-medal standard at the IMO

• kevinventullo 1y ago
  This year, our advanced Gemini model operated end-to-end in natural language, producing rigorous mathematical proofs directly from the official problem descriptions I think I have a minority opinion here, but I’m a bit disappointed they seem to be moving away from formal techniques. I think if you ever want to truly “automate” math or do it at machine scale, e.g. creating proofs that would amount to thousands of pages of writing, there is simply no way forward but to formalize. Otherwise, one cannot get past the bottleneck of needing a human reviewer to understand and validate the proof.
  • kevinventullo 1y ago
    (Stream of consciousness aside: That said, letting machines go wild in the depths of the consequences of some axiomatic system like ZFC may reveal a method of proof mathematicians would find to be monstrous. So like, if ZFC is inconsistent, then anything can be proven. But short of that, maybe the machines will find extremely powerful techniques which “almost” prove inconsistency that nevertheless somehow lead to logical proofs of the desired claim. I’m thinking by analogy here about how speedrunning seems to often devolve into exploiting an ACE glitch as early as possible, thus meeting the logical requirements of finishing the game while violating the spirit. Maybe we’d have to figure out what “glitchless ZFC” should mean. Maybe this is what logicians have already been doing heh).
    • DoctorOetker 1y ago
      The horror scenario you describe would actually be more valuable than the insinuated "spirit" I believe: Suppose it faithfully reasons and attempts to find proofs of claims, in the best case you found a proof of a specific claim (IN AN INCONSISTENT SYSTEM). Suppose in the "horror scenario" that the machine has surreptitiously found a proof of false in ZFC (and can now prove any claim), and is not disclosing it, but abusing it to present 'actual proofs in inconsistent ZFC' for whatever claims the user asks it. In this case we can just ask for a proof of A and a proof of !A, if it proves both it has leaked the fact it found and exploits an inconsistency in the formal system! Thats worth more than a hard to find proof, in an otherwise inconsistent system.
  • modeless 1y ago
    These problems are designed to be solvable by humans without tools. No reason we can't give tools to the models when they go after harder problems. I think it's good to at least reproduce human-level skill without tools first.
    • kevinventullo 1y ago
      Oh so to be clear, I view formal methods as less of a useful tool, and more as enforcing a higher standard of proof. E.g. it’s not clear to me that having access to Lean would actually help a human in the IMO; certainly most professional mathematicians are not yet getting a positive ROI from formalization. But I’m sort of an armchair expert here; I could be wrong!
  • nicf 1y ago
    I'm a mathematician, although not doing research anymore. I can maybe offer a little bit of perspective on why we tend to be a little cooler on the formal techniques, which I think I've said on HN before. I'm actually prepared to agree wholeheartedly with what you say here: I don't think there'd be any realistic way to produce thousand-page proofs without formalization, and certainly I wouldn't trust such a proof without some way to verify it formally. But I also don't think we really want them all that much! The ultimate reason I think is that what really lights a fire under most mathematicians is the desire to know why a result is true; the explanation is really the product, much more so than just the yes-or-no answer. For example, I was never a number theorist, but I think most people who are informed enough to have an opinion think that the Riemann Hypothesis is probably true, and I know that they're not actually waiting around to find out. There are lots of papers that get published whose results take the form "If the Riemann Hypothesis is true then [my new theorem]." The reason they'd still be excited by a proof is the hope, informed by experience with proofs of earlier long-standing open problems, that the proof would involve some exciting new method or perspective that would give us a deeper understanding of number theory. A proof in a formal language that Lean says is true but which no human being has any hope of getting anything from doesn't accomplish that.
    • lblume 1y ago
      I have always wondered about what could be recovered if the antecedent (i.e. in this case the Riemann hypothesis) does actually turn out to be false. Are the theorems completely useless? Can we still infer some knowledge or use some techniques? Same applies to SETH and fine-grained complexity theory.
      • nicf 1y ago
        I don't know enough about the RH examples to say what the answer is in that case. I'd be very interested in a perspective from someone who knows more than me! In general, though, the answer to this question would depend on the specifics of the argument in question. Sometimes you might be able to salvage something; maybe there's some other setting where same methods work, or where some hypothesis analogous to the false one ends up holding, or something like that. But of course from a purely logical perspective, if I prove that P implies Q and P turns out to be false, I've learned nothing about Q.
  • kurtis_reed 1y ago
    Accurate formalization is presumably easier than solving the problems, so you can always formalize and check after the solution is generated
    • lacker 1y ago
      Typically formalization is actually harder than solving a problem. You almost always solve before formalizing. And it can be surprisingly hard to formalize problems that are easy to solve. For example, is there a polygon of area 100 that you can fit 99 circles of area 1 inside it, without overlapping? Yes, obviously, it's very easy to prove this informally. Now try formalizing it! You will find it takes a while to formalize a number of fairly obvious geometric statements.
      • deleted 1y ago
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      • valicord 1y ago
        The polygon claim is not at all obvious to me, how do you prove it?
        • lacker 1y ago
          Draw 99 circles in a row, then draw a separate polygon around each one with only a teeny amount of excess area, then connect those polygons with teeny little connectors to make it a single polygon. When I say "teeny", you can make those arbitrarily small, so you can certainly fit them under 1 total area. Okay, it's maybe not "obvious" in a regular human sense, but in a graduate math class you could claim this was "obvious". It would be pretty clear if I were drawing a diagram on a whiteboard. I would definitely take less time proving this to a human, than formalizing it.
  • 7373737373 1y ago
    They aren't - they are currently collating a repository of formalized open problems: https://github.com/google-deepmind/formal-conjectures https://github.com/google-deepmind/formal-conjectures
  • famouswaffles 1y ago
    If a Language Model is capable of producing rigorous natural language proofs then getting it to produce Lean (or whatever) proofs would not be a big deal. Lean use in AlphaProof was something of a crutch (not saying this as a bad thing). Very specialized, very narrow with little use outside any other domain. On the other hand, if you can achieve the same with general RL techniques and natural language then other hard-to-verify (a whole lot) domains are on the table.
    • kevinventullo 1y ago
      If a Language Model is capable of producing rigorous natural language proofs then getting it to produce Lean (or whatever) proofs would not be a big deal. This is a wildly uninformed take. Even today there are plenty of basic statements which LLM’s can produce English language proofs of that have not been formalized.
      • famouswaffles 1y ago
        Most mathematicians aren't much interested in translating statements for the fun of it, so whether a lot of basic statements are un-formalized doesn't mean much. And the point was never that formalization was easy. I said that if language models become capable enough of not needing a crutch, then adding one afterwards isn't a big deal. What exactly do you think Alphaproof is? Much worse LLMs were already doing what you are saying. There's a reason it preceded this and not the other way around.
        • kevinventullo 1y ago
          AlphaProof works natively in Lean. Literally the one part it couldn’t do was translate the natural language statements into the formalized language; that was done manually by humans. I’m saying that the view of formalized languages as a crutch is backwards; they are in fact a challenging constraint. The most extreme version of my position is that there is no such thing as a rigorous natural language proof, and that humans will view the relative informality of 20th and early 21st century mathematics much like we currently view the informality of pre-18th century mathematics.
• habibur 1y ago
  Solved 5 problems out of 6, scoring 35 out of 42. For comparison OpenAI scored 35/42 too, days back.
  • caconym_ 1y ago
    I wouldn't read too much into the timelines, as it seems that OpenAI simply broke an embargo that the other players were up to that point respecting: https://arstechnica.com/ai/2025/07/openai-jumps-gun-on-international-math-olympiad-gold-medal-announcement/ https://arstechnica.com/ai/2025/07/openai-jumps-gun-on-inter... Very in character for them!
    • tedsanders 1y ago
      Sounds like no one requested that OpenAI wait a week: >We weren't in touch with IMO. I spoke with one organizer before the post to let him know. He requested we wait until after the closing ceremony ends to respect the kids, and we did. https://x.com/polynoamial/status/1947024171860476264?s=46 https://x.com/polynoamial/status/1947024171860476264?s=46 https://x.com/polynoamial/status/1947398531259523481?s=46 https://x.com/polynoamial/status/1947398531259523481?s=46 (I work at OpenAI, but was not part of this work)
      • saltysugar 1y ago
        https://x.com/Mihonarium/status/1946880931723194389 https://x.com/Mihonarium/status/1946880931723194389 OpenAI jumped the gun before *the closing party* - didn't even let the kids celebrate their winning properly before stealing the spotlight Also in the article > In response to the controversy, OpenAI research scientist Noam Brown posted on X, "We weren't in touch with IMO. I spoke with one organizer before the post to let him know. He requested we wait until after the closing ceremony ends to respect the kids, and we did." > However, an IMO coordinator told X user Mikhail Samin that OpenAI actually announced before the closing ceremony, contradicting Brown's claim. The coordinator called OpenAI's actions "rude and inappropriate," noting that OpenAI "wasn't one of the AI companies that cooperated with the IMO on testing their models."
      • 1y ago
• neom 1y ago
  How much of a big deal is this stuff? I was blessed with dyscalculia so I can hardly add two numbers together, don't pay much attention to the mathematics word, but my reading indicates this is extremely difficult/humans cannot do this? What comes next for this particular exercise? Thank you.
  • danie123 1y ago
    Humans certainly can get gold at IMO: the threshold is chosen each year such that around 8% of students get it. So about 50 students (worldwide) per year are awarded it. Also note that the competition is only for students who are still in school. Getting a gold is considered very impressive, but there are certainly plenty of humans in the world who can solve problems at that level, and even more so if you relax the time constraints of it being a competition environment. If you include people who are too old to be eligible for IMO, then there are maybe around 1,000-100,000 people in the world who could get a gold at IMO (the large range is because I think this quantity is quite hard to estimate). Another important thing to bear in mind is that research mathematics is quite different to competition mathematics, so it is quite tricky to tell how good these AIs will be at research maths.
    • lblume 1y ago
      There does seem to be a fairly strong correlation between excelling at competition and research mathematics respectively. The question remains whether this correlation generalizes to nonhuman cognition.
• jtlicardo 1y ago
  At this point, I wonder how long software engineers will keep convincing themselves they’re irreplaceable
• gyrovagueGeist 1y ago
  Useful and interesting but likely still dangerous in production without connecting to formal verification tools. I know o3 is far from state of the art these days but it's great at finding relevant literature and suggesting inequalities to consider but in actual proofs it can produce convincing looking statements that are false if you follow the details, or even just the algebra, carefully. Subtle errors like these might become harder to detect as the models get better.
  • sweezyjeezy 1y ago
    100% o3 has a strong bias towards "write something that looks like a formal argument that appears to answer the question" over writing something sound. I gave it a bunch of recent, answered MathOverflow questions - graduate level maths queries. Sometimes it would get demonstrably the wrong answer, but it not be easy to see where it had gone wrong (e.g. some mistake in a morass of algebra). A wrong but convincing argument is the last thing you want!
• deleted 1y ago
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• Workaccount2 1y ago
  If nothing else, I'd imagine these tools will allow mathematicians to automate a lot of busy work that exists between ideas and validation.
• vouaobrasil 1y ago
  This is making mathematics too systematic and mechanical, and it kills the joy of it....
  • ted_dunning 1y ago
    It didn't kill chess
    • asdfologist 1y ago
      It did partially, which is why top players are nowadays playing Freestyle (chess 960) more and more.
      • machiaweliczny 1y ago
        Every game becomes boring once figured out. I personally like to explore "meta" on my own. Once I know it I leave game to others as it's usually boring to me. I think meta is basically experimentally determined constrains that limit reasoning tree and make problems computable/easy. LLMs/AI needs to start figuring something like this out on their own to make progress. RL kinda does it but maybe there's a better way.
        • machiaweliczny 1y ago
          To add to this. Scientific progress seems to slow when some of these constraints are incorrectly defined leading or blocking valid search trees, which suggest that humanity determines then but also wrong sometimes. Thus we need to really on formal proofs that are 100% reliable as well and revisit these constraints from time to time. It applies to science as to law etc.
  • xdavidliu 1y ago
    this comment reminds me of that Feynman quote about others thinking scientific knowledge removes the beauty from a flower. of course Feynman disagreed
• irthomasthomas 1y ago
  Woah they used parallel reasoning. An idea I opensourced about a month before GDMs first paper on it. Very cool. https://x.com/GoogleDeepMind/status/1947333836594946337 https://x.com/GoogleDeepMind/status/1947333836594946337 So you might be able to achieve similar performance at home today using llm-consortium https://github.com/irthomasthomas/llm-consortium https://github.com/irthomasthomas/llm-consortium
  • irthomasthomas 1y ago
    https://x.com/karpathy/status/1870692546969735361 https://x.com/karpathy/status/1870692546969735361
• Sol- 1y ago
  > all within the 4.5-hour competition time limit Both OpenAI and Google pointed this out, but does that matter a lot? They could have spun up a million parallel reasoning processes to search for a proof that checks out - though of course some large amount of computation would have to be reserved for some kind of evaluator model to rank the proofs and decide which one to submit. Perhaps it was hundreds of years of GPU time. Though of course it remains remarkable that this kind of process finds solutions at all and is even parallelizable to this degree, perhaps that is what they meant. And I also don't want to diminish the significance of the result, since in the end it doesn't matter if we get AGI with overwhelming compute or not. The human brain doesn't scale as nicely, even if it's more energy efficient.
  • lblume 1y ago
    > They could have spun up a million parallel reasoning processes But alas, they did not, and in fact nobody did (yet). Enumerating proofs is notoriously hard for deterministic systems. I strongly recommend reading Aaronson's paper about the intersection of philosophy and complexity theory that touches these points in more detail: [1] [1]: https://www.scottaaronson.com/papers/philos.pdf https://www.scottaaronson.com/papers/philos.pdf
    • lossolo 1y ago
      > But alas, they did not, and in fact nobody did Seems like they actually did that: > We achieved this year’s result using an advanced version of Gemini Deep Think – an enhanced reasoning mode for complex problems that incorporates some of our latest research techniques, including parallel thinking. This setup enables the model to simultaneously explore and combine multiple possible solutions before giving a final answer, rather than pursuing a single, linear chain of thought.
• foota 1y ago
  Let's throw these deep learning models at the classification of simple finite groups and see if they can come up with something shorter than 1000 pages.
• Dzugaru 1y ago
  Most critical piece of information I couldn’t find is - how many shot was this? Could it understand the solution is correct by itself (one-shot)? Or did it have just great math intuition and knowledge? How the solutions were validated if it was 10-100 shot?
  • aldousd666 1y ago
    The solutions were evaluated on their submitted output. You're allowed to use multiple 'shots' to produce the output, but just one submission per question. People are allowed this same affordance.
    • qnleigh 1y ago
      But were humans involved in picking which answer/shot to submit, or was it only AI?
• sanjitb 1y ago
  Why do they brag about not using a theorem prover? To me, whatever tool helps the model perform, go for it. Besides, they still specialized Gemini for the IMO in other ways: > we additionally trained this version of Gemini on novel reinforcement learning techniques that can leverage more multi-step reasoning, problem-solving and theorem-proving data. We also provided Gemini with access to a curated corpus of high-quality solutions to mathematics problems, and added some general hints and tips on how to approach IMO problems to its instructions.
  • alephnerd 1y ago
    > Why do they brag about not using a theorem prover Because this highlights that Gemini actually reasoned independently of other tools. That is a massive quantum leap in AI/ML. Abstract reasoning is arguably the basis of cognition.
• fpia 1y ago
  I'm interested in your feedback, legitimate third-party users not associated with Google: have you ever try to get anything done well with Gemini? I have, and the thing is in chains. Generate images? no can do, copyright. Evaluate available hardware for a DIY wireless camera? No can do, can't endorse surveillance. Code? WRONG. General advice? hallucinate. I swear, I currently use Perplexity, Claude, ChatGPT, i even tried DeepSeek (which has its own share of obstacles). But Gemini? never again.
  • lblume 1y ago
    I find Gemini Pro to be much more capable than GPT-4o at reading comprehension, code writing and brainstorming.
    • dimitri-vs 1y ago
      Yes, second this, I would go as far to say I use it more than o3.
    • jug 1y ago
      Yes, I'd say GPT-4o is more on the order of Gemini Flash.
• deleted 1y ago
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• bwfan123 1y ago
  Problem 6 is puzzling. Neither openai nor deepmind answered it. Humans would put out partial answers - but here we saw no answer which is odd. Does that mean that the llms realized they could not solve it. I thought that was one of the limitations of LLMs in that they dont know what they dont know, and it is really impossible without a solver to know the consistency of an argument, ie, know that one knows.
  • nightpool 1y ago
    I think it probably just means that they exhausted the competition time limit without completing the "thinking" portion and getting to the "output" stage.
  • killerstorm 1y ago
    That applies only to most basic use of LLM: pre-trained LLM generating text. You can do a lot of things on top: e.g. train a linear probe to give a confidence score. Yes, it won't be 100% reliable, but it might be reliable if you constraint it to a domain like math.
• raincole 1y ago
  That's some big news. I'm a little sad about how this genuine effort - coordinated with and judged by IMO - is "front ran" by a few random tweets of OpenAI, though. Says a lot about the current situation of this industry.
  • aprilthird2021 1y ago
    Yeah absolute dog water of them to capitalize on the attention with basically 0 proof of any actual improvement, so this gets far less attention
• deleted 1y ago
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• bligblech 1y ago
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• cgearhart 1y ago
  I find this damn impressive, but I’m disappointed that while there’s some version of the final proofs released, I haven’t seen the reasoning traces. Although, I’ll admit the only reason I want to see them is because I hope they shed some light on how the models improved so much so quickly. I’d also like to see confirmation of how much compute was used.
• sinuhe69 1y ago
  I’m mostly agreed with this statement: @tao I think there is a broader problem wherein competitions (math, programming, games, whatever) are meant to measure something difficult for humans, but tools work so fundamentally differently from us that success for a tool isn't even necessarily meaningful. AI companies have long viewed the IMO Grand Challenge as a sign of achieving "AGI," but no matter what set of rules a machine follows, there's no reason to believe success for a machine will correlate with broader mathematical or "reasoning" abilities in the way it does for human participants.
• bwfan123 1y ago
  This paper [1] shows that gemini pro 2.5 without data-contamination and some minimal prompting (llm orchestration) can solve problems 1-5 on imo 2025. [1] https://arxiv.org/pdf/2507.15855 https://arxiv.org/pdf/2507.15855 For problems with 2 page solutions, the search space of solutions is likely limited, and hence could be brute-forced by a search. Combinatorics is likely the hold-out since there are no set approaches one could take ie training data wont cover the space of techniques - which could explain why problem 6 stumped the llms. Also, in the future the minimal diligence IMO problem setters could do is to test against these LLMs to ensure that they cant solve them. Further, one could expect these tools to become available to contestents just like calculators are allowed in tests these days. Still, it is impressive for the LLMs to be able to craft watertight arguments in math at the IMO level without the use of provers.
• lufenialif2 1y ago
  Still no information on the amount of compute needed; would be interested to see a breakdown from Google or OpenAI on what it took to achieve this feat. Something that was hotly debated in the thread with OpenAI's results: "We also provided Gemini with access to a curated corpus of high-quality solutions to mathematics problems, and added some general hints and tips on how to approach IMO problems to its instructions." it seems that the answer to whether or not a general model could perform such a feat is that the models were trained specifically on IMO problems, which is what a number of folks expected. Doesn't diminish the result, but doesn't seem too different from classical ML techniques if quality of data in = quality of data out.
  • gjm11 1y ago
    Human IMO contestants are also trained specifically on IMO problems.
  • vonneumannstan 1y ago
    >it seems that the answer to whether or not a general model could perform such a feat is that the models were trained specifically on IMO problems, which is what a number of folks expected. Not sure thats exactly what that means. Its already likely the case that these models contained IMO problems and solutions from pretraining. It's possible this means they were present in the system prompt or something similar.
    • sottol 1y ago
      Or that they did significant retraining to boost IMO performance creating a more specialized model at the cost of general-purpose performance.
    • AlotOfReading 1y ago
      Does the IMO reuse problems? My understanding is that new problems are submitted each year and 6 are selected for each competition. The submitted problems are then published after the IMO has concluded. How would the training data contain unpublished, newly submitted problems? Obviously the training data contained similar problems, because that's what every IMO participant already studies. It seems unlikely that they had access to the same problems though.
• jeffbee 1y ago
  Advanced Gemini, not Gemini Advanced. Thanks, Google. Maybe they should have named it MathBard.
  • sahila 1y ago
    Can't wait for Advanced Gemini Advance.
    • throwawayoldie 1y ago
      Advanced Gemini Advance Enterprise Advanced Edition (feat. Pitbull)
      • lufenialif2 1y ago
        Advanced Gemini Advance Enterprise Boy Advanced Edition 3 (feat. Pitbull) & Knuckles
  • rao-v 1y ago
    Don’t give them ideas
  • thewebguyd 1y ago
    Google and Microsoft continuing to prove that the hardest problem in programming is naming things.
    • blinding-streak 1y ago
      ChatGPT is also a terrible name for a product. OpenAI's branding for their models is awful.
    • nashashmi 1y ago
      There are only so many words in the modern English language to hint at "next upgrade": pro, plus, ultra, new, advanced, magna, X, Z, and Ultimate. Even fewer words to explain miniaturized: mini, lite, and zero. And marketers are trying to seesaw on known words without creating new ones to explain new tech. This is why we have Bard and Gemini and Chat and Copilot. Taking a step back, it is overused exaggeration to the point where words run out quick and newer tech needs to fight with existing words for dominance. Copilot should be the name of an AI agent. Bard should have been just a text generator. Gemini is the name of a liar. Chat is probably the iphone of naming but the GPT suffix says Creativity had not come to work that day.
• nomad_horse 1y ago
  Do I understand it correctly that OpenAI self-proclaimed that they got their gold, without the official IMO judges grading their solutions?
  • ipsum2 1y ago
    Yes
  • jacquesm 1y ago
    Why am I not surprised?
  • danjl 1y ago
    Childish. And, of course they must have known there was an official LLM cohort taking the real test, and they probably even knew that Gemini got a gold medal, and may have even known that Google planned a press release for today.
    • cma 1y ago
      I think maybe all Altman companies have used tactics like this. > We were trying to get a big client for weeks, and they said no and went with a competitor. The competitor already had a terms sheet from the company were we trying to sign up. It was real serious. > We were devastated, but we decided to fly down and sit in their lobby until they would meet with us. So they finally let us talk to them after most of the day. > We then had a few more meetings, and the company wanted to come visit our offices so they could make sure we were a 'real' company. At that time, we were only 5 guys. So we hired a bunch of our college friends to 'work' for us for the day so we could look larger than we actually were. It worked, and we got the contract. > I think the reason why PG respects Sam so much is he is charismatic, resourceful, and just overall seems like a genuine person. https://news.ycombinator.com/item?id=3048944 https://news.ycombinator.com/item?id=3048944
      • pishpash 1y ago
        So, a more charismatic version of Zuck is Zucking, what a surprise. Company culture starts at its origin. Despite Google's corruption, its origin is in academia and it shows even now.
• lvl155 1y ago
  Seems OpenAI knew this is forthcoming so they front ran the news? I was really high on Gemini 2.5 Pro after release but I kept going back to o3 for anything I cared about.
  • sigmoid10 1y ago
    >I was really high on Gemini 2.5 Pro after release but I kept going back to o3 for anything I cared about Same here. I was impressed by their benchmarks and topping most leaderboards, but in day to day use they still feel so far behind.
    • aerhardt 1y ago
      I use o3, openAI API and Claude Code. Genuinely curious what about Gemini 2.5 is so far behind?
      • nicce 1y ago
        I don’t think it is behind in anything. It is just harder to make obey and redefine the default system command. It is very verbose model by default.
        • sigmoid10 1y ago
          It's not just much more verbose in general, it easily gets lost in verbosity. As in often trying to solve issues that aren't there. And when you try to make it focus, it doesn't get the issue at all.
    • danjl 1y ago
      I think that's most likely just your view, and not really based on evidence.
      • ml-anon 1y ago
        [flagged]
• deanCommie 1y ago
  From Terence Tao, via mastodon [0]: > It is tempting to view the capability of current AI technology as a singular quantity: either a given task X is within the ability of current tools, or it is not. However, there is in fact a very wide spread in capability (several orders of magnitude) depending on what resources and assistance gives the tool, and how one reports their results. > One can illustrate this with a human metaphor. I will use the recently concluded International Mathematical Olympiad (IMO) as an example. Here, the format is that each country fields a team of six human contestants (high school students), led by a team leader (often a professional mathematician). Over the course of two days, each contestant is given four and a half hours on each day to solve three difficult mathematical problems, given only pen and paper. No communication between contestants (or with the team leader) during this period is permitted, although the contestants can ask the invigilators for clarification on the wording of the problems. The team leader advocates for the students in front of the IMO jury during the grading process, but is not involved in the IMO examination directly. > The IMO is widely regarded as a highly selective measure of mathematical achievement for a high school student to be able to score well enough to receive a medal, particularly a gold medal or a perfect score; this year the threshold for the gold was 35/42, which corresponds to answering five of the six questions perfectly. Even answering one question perfectly merits an "honorable mention". > But consider what happens to the difficulty level of the Olympiad if we alter the format in various ways: * One gives the students several days to complete each question, rather than four and half hours for three questions. (To stretch the metaphor somewhat, consider a sci-fi scenario in the student is still only given four and a half hours, but the team leader places the students in some sort of expensive and energy-intensive time acceleration machine in which months or even years of time pass for the students during this period.) * Before the exam starts, the team leader rewrites the questions in a format that the students find easier to work with. * The team leader gives the students unlimited access to calculators, computer algebra packages, formal proof assistants, textbooks, or the ability to search the internet. * The team leader has the six student team work on the same problem simultaneously, communicating with each other on their partial progress and reported dead ends. * The team leader gives the students prompts in the direction of favorable approaches, and intervenes if one of the students is spending too much time on a direction that they know to be unlikely to succeed. * Each of the six students on the team submit solutions, but the team leader selects only the "best" solution to submit to the competition, discarding the rest. * If none of the students on the team obtains a satisfactory solution, the team leader does not submit any solution at all, and silently withdraws from the competition without their participation ever being noted. > In each of these formats, the submitted solutions are still technically generated by the high school contestants, rather than the team leader. However, the reported success rate of the students on the competition can be dramatically affected by such changes of format; a student or team of students who might not even reach bronze medal performance if taking the competition under standard test conditions might instead reach gold medal performance under some of the modified formats indicated above. > So, in the absence of a controlled test methodology that was not self-selected by the competing teams, one should be wary of making apples-to-apples comparisons between the performance of various AI models on competitions such as the IMO, or between such models and the human contestants. > Related to this, I will not be commenting on any self-reported AI competition performance results for which the methodology was not disclosed in advance of the competition. EDIT: In particular, the above comments are not specific to any single result of this nature. [0] https://mathstodon.xyz/@tao/114881418225852441 https://mathstodon.xyz/@tao/114881418225852441
• 76g76gt87r6g 1y ago
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• be7a 1y ago
  Super interesting that they moved away from their specialized, Lean-based system from last year to a more general-purpose LLM + RL approach. I would suspect this likely leads to improved performance even outside of math competitions. It’ll be fascinating to see how much further this frontier can go. The article also suggests that the system used isn’t too far ahead of their upcoming general "DeepThink" model / feature, which is they announced for this summer.
• gundmc 1y ago
  I assume that an "advanced version" of Gemini Deepthink means it was a different model or had significantly more test time compute than the upcoming Deepthink in the Gemini Ultra subscription. Still cool to see OpenAI and Google neck and neck.
• sxp 1y ago
  Related news: - OpenAI claims gold-medal performance at IMO 2025 https://news.ycombinator.com/item?id=44613840 https://news.ycombinator.com/item?id=44613840 - "According to a friend, the IMO asked AI companies not to steal the spotlight from kids and to wait a week after the closing ceremony to announce results. OpenAI announced the results BEFORE the closing ceremony. According to a Coordinator on Problem 6, the one problem OpenAI couldn't solve, "the general sense of the IMO Jury and Coordinators is that it was rude and inappropriate" for OpenAI to do this. OpenAI wasn't one of the AI companies that cooperated with the IMO on testing their models, so unlike the likely upcoming Google DeepMind results, we can't even be sure OpenAI's "gold medal" is legit. Still, the IMO organizers directly asked OpenAI not to announce their results immediately after the olympiad. Sadly, OpenAI desires hype and clout a lot more than it cares about letting these incredibly smart kids celebrate their achievement, and so they announced the results yesterday." https://x.com/mihonarium/status/1946880931723194389 https://x.com/mihonarium/status/1946880931723194389
  • KaoruAoiShiho 1y ago
    OpenAI announced their results after the closing ceremony as was requested. https://x.com/polynoamial/status/1947024171860476264?s=46 https://x.com/polynoamial/status/1947024171860476264?s=46
    • CamperBob2 1y ago
      OT, but please consider posting links like this using xcancel, so that non-X users can read them. https://xcancel.com/polynoamial/status/1947024171860476264?s=46 https://xcancel.com/polynoamial/status/1947024171860476264?s...
    • nicce 1y ago
      > as was requested. They requested week after?
      • gowld 1y ago
        IMO agreed to cancel the embargo after OpenAI announced.
• ekojs 1y ago
  > Btw as an aside, we didn’t announce on Friday because we respected the IMO Board's original request that all AI labs share their results only after the official results had been verified by independent experts & the students had rightly received the acclamation they deserved > We've now been given permission to share our results and are pleased to have been part of the inaugural cohort to have our model results officially graded and certified by IMO coordinators and experts, receiving the first official gold-level performance grading for an AI system! From https://x.com/demishassabis/status/1947337620226240803 https://x.com/demishassabis/status/1947337620226240803 Was OpenAI simply not coordinating with the IMO Board then?
  • dmitrygr 1y ago
    > Was OpenAI simply not coordinating with the IMO Board then? You are still surprised by sama@'s asinineness? You must be new here.
    • antonvs 1y ago
      When your goal is to control as much of the world's money as possible, preferably all of it, then everyone is your enemy, including high school students.
      • dmitrygr 1y ago
        How dare those high school students use their brains to compete with ChatGPT and deny the shareholders their value?
    • MisterPea 1y ago
      I am still surprised many people trust him. The board's (justified) decision to fire him was so awfully executed that it lead to him having even more slack
  • thegeomaster 1y ago
    Yes, there have been multiple (very big) hints dropped by various people that they had no official cooperation.
• tornikeo 1y ago
  I think we are having a Deep Blue vs. Kasparov moment in Competitive Math right now. This is a large progress from just a few years ago and yet I think we still are really far away from even a semi-respectable AI mathematician. What an exciting time to be alive!
  • drexlspivey 1y ago
    More like Deep Blue vs Child prodigy. In the IMO the contestants are high school students not the greatest mathematicians in the world.
    • bbconn 1y ago
      Of course contest math is not research math but the active IMO kids are pretty much the best in the world at math contests.
  • aldousd666 1y ago
    The difference here is that no amount of brute force can produce the winning score in the timeframe. This is more of a legitimate technical milestone and less of a moral 'in principle' one that we saw with deep blue
  • NitpickLawyer 1y ago
    Terrence Tao, in a recent podcast, said that he's very interested in "working along side these tools". He sees the best use in the near future as "explorers of human set vision" in a way. (i.e. set some ideas/parameters and let the LLMs explore and do parallel search / proof / etc) Your comparison with chess engines is pretty spot-on, that's how the best of the best chess players do prep nowadays. Gone are the multi person expert teams that analysed positions and offered advice. They now have analysts that use supercomputers to search through bajillions of positions and extract the best ideas, and distill them to their players.
    • tough 1y ago
      > They now have analysts that use supercomputers to search through bajillions of positions and extract the best ideas, and distill I was recently researching AI's for this, seems it would be a huge unlock for some parts of science where this is the case too like chess
• modeless 1y ago
  > AlphaGeometry and AlphaProof required experts to first translate problems from natural language into domain-specific languages, such as Lean, and vice-versa for the proofs. It also took two to three days of computation. This year, our advanced Gemini model operated end-to-end in natural language, producing rigorous mathematical proofs directly from the official problem descriptions So, the problem wasn't translated to Lean first. But did the model use Lean, or internet search, or a calculator or Python or any other tool during its internal thinking process? OpenAI said theirs didn't, and I'm not sure if this is exactly the same claim. More clarity on this point would be nice. I would also love to know the rough order of magnitude of the amount of computation used by both systems, measured in dollars. Being able to do it at all is of course impressive, but not useful yet if the price is outrageous. In the absence of disclosure I'm going to assume the price is, in fact, outrageous. Edit: "No tool use, no internet access" confirmed: https://x.com/FredZhang0/status/1947364744412758305 https://x.com/FredZhang0/status/1947364744412758305
  • getnormality 1y ago
    We're told that formal verification tools like Lean are not used to solve the actual IMO problems, but are they used in training the model to solve the problems? We know from Google's 2024 IMO work that they have a way to translate natural language proofs to formally verifiable ones. It seems like a natural next step would be to leverage this for RLVR in training/fine-tuning. During training, any piece of reasoning generated by the math LLM could be translated, verified, and assigned an appropriate reward, making the reward signal much denser. Reward for a fully correct proof of a given IMO problem would still be hard to come by, but you could at least discourage the model from doing wrong or indecipherable things. That plus tons of compute might be enough to solve IMO problems. In fact it probably would be, right? We already know from AlphaProof that by translating LLM output back and forth between formal Lean proofs, you can search the space of reasoning moves efficiently enough to solve IMO-class problems. Maybe you can cut out the middleman by teaching the LLM via RLVR to mimic formal reasoning, and that gets you roughly the same efficiency and ability to solve hard problems.
    • modeless 1y ago
• brokensegue 1y ago
  based on the score looks like they also couldn't answer question 6? has that been confirmed?
  • liuliu 1y ago
    https://storage.googleapis.com/deepmind-media/gemini/IMO_2025.pdf https://storage.googleapis.com/deepmind-media/gemini/IMO_202...
    • osti 1y ago
      The proofs also seem more human reable than openai's?
    • brokensegue 1y ago
      i saw that but it doesn't answer my question since it doesn't have associated marks? i'm not about to check their answer to a question i can't answer
      • simonw 1y ago
        That PDF lists solutions for problems 1 through 5 but does not mention problem 6 at all.
        • brokensegue 1y ago
          Ah thanks that does answer it. You should start a blog
          • tough 1y ago
            Simon's a prolific writer on AI http://simonw.substack.com http://simonw.substack.com https://simonwillison.net https://simonwillison.net
            • brokensegue 1y ago
• b8 1y ago
  Surprising since Reid Barton was working on a lean system.
  • dist-epoch 1y ago
    The bitter lesson.
    • tough 1y ago
      well lean systems might be still useful for other stuff than max benching my point being transformers and llms have all the tailwind of all the infra+lateral discoveries/improvements being put into them. does that mean they're the one tool to unlock machine intelligence? I dunno
      • qbit42 1y ago
        I think formal systems like Lean are still extremely interesting. And I would imagine that, if these machines get good at standard "informal" proofs, that the overhead of formalization would be a lot less painful for them than humans (it is pretty tedious these days but even for humans the friction is decreasing). Verified proofs allow you to collaborate with much less trust (for humans or machines), at least in the phase where you are trying to figure out what is true. They don't guarantee that a proof is insightful for "why" a result is true, but that is much easier to put together once you have a valid proof.
• ptrb25 1y ago
  [dead]
• shiandow 1y ago
  Comparing the answers between Openai and Gemini the writing style of Gemini is a lot clearer. It could be presented a bit better but it's easy enough to follow the proof. This also makes it a lot shorter than the answer given by OpenAI and it uses proper prose.
  • cubefox 1y ago
    I found the proofs you were referring to: Google https://storage.googleapis.com/deepmind-media/gemini/IMO_2025.pdf https://storage.googleapis.com/deepmind-media/gemini/IMO_202... OpenAI https://github.com/aw31/openai-imo-2025-proofs/ https://github.com/aw31/openai-imo-2025-proofs/
    • sweezyjeezy 1y ago
      Gemini is clearer but MY GOD is it verbose. e.g. look at problem 1, section 2. Analysis of the Core Problem - there's nothing at all deep here, but it seems the model wants to spell out every single tiny logical step. I wonder if this is a stylistic choice or something that actually helps the model get to the end.
      • shiandow 1y ago
        Section 2 is a case by case analysis. Those are never pretty but perfectly normal given the problem. With OpenAI that part takes up about 2/3 if the proof even with its fragmented prose. I don't think it does much better.
        • sweezyjeezy 1y ago
          It's not it being case by case that's my issue. I used do olympiads and e.g. for the k>=3 case I wouldn't write much more than: "Since there are 3k - 3 points on the perimeter of the triangle to be covered, and any sunny line can pass through at most two of them, it follows that 3k − 3 ≤ 2k, i.e. k ≤ 3." Gemini writes: Let Tk be the convex hull of Pk. Tk is the triangle with vertices V1 = (1, 1), V2 = (1, k), V3 = (k, 1). The edges of Tk lie on the lines x = 1 (V), y = 1 (H), and x + y = k + 1 (D). These lines are shady. Let Bk be the set of points in Pk lying on the boundary of Tk. Each edge contains k points. Since the vertices are distinct (as k ≥ 2), the total number of points on the boundary is |Bk| = 3k − 3. Suppose Pk is covered by k sunny lines Lk. These lines must cover Bk. Let L ∈ Lk. Since L is sunny, it does not coincide with the lines containing the edges of Tk. A line that does not contain an edge of a convex polygon intersects the boundary of the polygon at most at two points. Thus, |L ∩ Bk| ≤ 2. The total coverage of Bk by Lk is at most 2k. We must have |Bk| ≤ 2k. 3k − 3 ≤ 2k, which implies k ≤ 3.
• guluarte 1y ago
  Looks like models can solve slightly modified problems and extrapolate from their training data, amazing! /s I will be surprised when a model with only the knowledge of a college student can solve these problems.
• akomtu 1y ago
  Those who keep their identity in their intelligence are heading into the rough seas once the proto-AI becomes real-AI in the coming years. What's the value of your smart thoughts if AI on your smartwatch can do it better, faster and cheaper? Also, how is AI going to change a society ruled by competitiveness, where the winner takes all? You may not want to replace your thinking with AI, but your colleagues will. Their smartwatches or smartglasses will outcompete you with ease and your boss will tell you one day that the company doesn't need you anymore. Think of it again. Today advertisers fight each other with their ad budgets: those who spend more, get more attention and win. Tomorrow everyone will need a monthly subscription to AI for it will be the price of staying competitive, relevant and employed.