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PaperclipPerfector  1mo ago (text post)   33507 thread views

Culture War Roundup for the week of March 31, 2025

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Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad

Abstract: Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, o3-mini, achieving scores comparable to top human competitors. However, these benchmarks evaluate models solely based on final numerical answers, neglecting rigorous reasoning and proof generation which are essential for real-world mathematical tasks. To address this, we introduce the first comprehensive evaluation of full-solution reasoning for challenging mathematical problems. Using expert human annotators, we evaluated several state-of-the-art reasoning models on the six problems from the 2025 USAMO within hours of their release. Our results reveal that all tested models struggled significantly, achieving less than 5% on average. Through detailed analysis of reasoning traces, we identify the most common failure modes and find several unwanted artifacts arising from the optimization strategies employed during model training. Overall, our results suggest that current LLMs are inadequate for rigorous mathematical reasoning tasks, highlighting the need for substantial improvements in reasoning and proof generation capabilities.

Background: The 'official' American competitive high school math circuit has several levels, progressing from AMC 10/12 (25 question, multiple choice, 75 minutes total) to AIME (15 questions, 3 hours, answers are in the form of positive 3 digit integers) to USAMO (2 days, 6 proof-based questions total, 3 questions with 4.5 hours per day), with difficulty increasing commensurate with the decrease in # of questions. While most AIME questions can be ground out using a standard set of high school/introductory college level math knowledge and tricks, the USAMO requires more depth of understanding and specialized techniques. For example, problem 1 (theoretically, the easiest) is as follows:

Let k and d be positive integers. Prove that there exists a positive integer N such that for every odd integer n > N , the digits in the base-2n representation of n^k are all greater than d.

This problem can be solved fairly simply using induction on k.

I've also noticed this when plugging grad-level QM questions into Gemini/ChatGPT. No matter how many times I tell it that it's wrong, it will repeatedly apologize and make the same mistake, usually copied from some online textbook or solution set without being able to adapt the previous solution to the new context.

I've also noticed this when plugging grad-level QM questions into Gemini/ChatGPT. No matter how many times I tell it that it's wrong, it will repeatedly apologize and make the same mistake, usually copied from some online textbook or solution set without being able to adapt the previous solution to the new context.

Could you confirm the exact models used? Both Gemini and ChatGPT, through the standard consumer interface, offer a rather confusing list of options that's even broader if you're paying for them.

The quote the full model names in appendix A.1, but it's really such a short paper that it's worth at least scrolling through before discussing.

  • O3-MINI (HIGH)
  • O1-PRO (HIGH)
  • DEEPSEEK R1
  • QWQ-32B
  • GEMINI-2.0-FLASH-THINKING-EXP
  • CLAUDE-3.7-SONNET-THINKING

While surprisingly poor performing, it's not entirely out of line with my own experience experimenting with this class of models. They do seem to hallucinate at a very high rate for problems requiring subtle but extremely tight reasoning.

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.

I don't think I know anyone who:

has scored >50% on USMAO, IMO, or the Putnam.

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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