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Thank you for listing out the models in the paper, but I was more concerned with the ones you've personally used. If you say they're in the same tier, then I would assume that you mean o3-high, o1 pro but not Claude 3.7 Sonnet Thinking (since you didn't mention Anthropic). I will note that R1, QWQ and Flash 2.0 Thinking are worse than those two, even if they're still competent models.
The best that Gemini has to offer is Gemini 2.5 Pro Thinking, which is the state of the art at present (in most domains). Is that the one you've tried? If you're not paying, youre not getting it on the app. I use it through AI Studio, where it's free. For ChatGPT, what was the best model you tried?
If you don't want to go to the trouble of signing up to AI Studio yourself (note that it's very easy), feel free to share a prompt and I'll try it myself and report back. I obviously can't judge the quality of the answer on its own merits, so I'll have to ask you.
Ah, I'm not OP. I've tried O3 High, O1 Pro, and QwQ. For the paper they have the prompts and grading scheme on the corresponding github. USAMO questions are hard enough you definitely need some expertise to grade them accurately. I'm far from being capable of judging them accurately.
Very qualitatively, the current crop of LLMs impresses me with the huge breadth of topics they can talk about. But "talking" to them does not give the impression they are better at reasoning than anyone I know who has scored >50% on USMAO, IMO, or the Putnam.
They are still improving very quickly, and I don't see the rate of improvement leveling off. Gemini 2.5 recently answered with ease a test question of mine that Gemini 2.0 (and, honestly, everything prior to Claude 3.5) had been utterly confused by. But I admit that they're definitely lacking in reasoning skills still; they're much better at retrieval and basic synthesis of knowledge than they are at extrapolating it to anything too greatly removed from standard problems that I'd expect were in their training data sets.
Still, can we take a step back and look at the big picture here? The USAMO is an invitation-only math competition where they pick the top few hundred students from a bigger invitation-only competition winnowed from an open math competition, and the median score on it is still sub-50%. The Putnam has thousands of competitors, but they're typically the most dedicated undergrad math majors and yet the median score on it is often zero! How far have we moved the goal posts, to get to this point? It's the "Can a robot write a symphony?" "Can you?" movie scene made manifest.
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I don't think I know anyone who:
I think my younger cousin was an IMO competitor, but he didn't win AFAIK, even if he's now in a very reputable maths program.
I'm personally quite restricted myself in my ability to evaluate pure reasoning capabilitiy, since I'm not a programmer or mathematician. I know they're great at medicine, even tricky problems, but what makes medicine challenging is far more the ability to retain an enormous amount of information in your head rather than an unusually onerous demand on fluid intelligence. You can probably be a good doctor with an IQ of 120, if you have a very broad understanding of relevant medicine, but you're unlikely to be a good mathematician producing novel insights.
I did for all three, but it was many years ago, and I think I'd struggle with most IMO problems nowadays. Pretty sure I'm still better at proofs than the frontier CoT models, but for more mechanical applied computations (say, computing an annoying function's derivative) they're a lot better than me at churning through the work without making a dumb mistake. Which isn't that impressive, TBH, because Wolfram Alpha could do that too, a decade ago. But you have to consciously phrase things correctly for WA, whereas LLMs always correctly understand what you're asking (even if they get the answer wrong).
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