The US Math Olympiad (USAMO) serves as a qualifier for the Worldwide Math Olympiad and presents a a lot greater bar than checks just like the American Invitational Arithmetic Examination (AIME). Whereas AIME issues are tough, they require integer solutions. USAMO calls for contestants write out full mathematical proofs, scored for correctness, completeness, and readability over 9 hours and two days.
The researchers evaluated a number of AI reasoning fashions on the six issues from the 2025 USAMO shortly after their launch, minimizing any probability the issues had been a part of the fashions’ coaching information. These fashions included Qwen’s QwQ-32B, DeepSeek R1, Google’s Gemini 2.0 Flash Considering (Experimental) and Gemini 2.5 Professional, OpenAI’s o1-pro and o3-mini-high, Anthropic’s Claude 3.7 Sonnet with Prolonged Considering, and xAI’s Grok 3.
Whereas one mannequin, Google’s Gemini 2.5 Professional, achieved a better common rating of 10.1 out of 42 factors (~24 p.c), the outcomes in any other case confirmed a large efficiency drop in comparison with AIME-level benchmarks. The opposite evaluated fashions lagged significantly additional behind: DeepSeek R1 and Grok 3 averaged 2.0 factors every, Google’s Flash-Considering scored 1.8, Anthropic’s Claude 3.7 managed 1.5, whereas Qwen’s QwQ and OpenAI’s o1-pro each averaged 1.2 factors. OpenAI’s o3-mini had the bottom common rating at simply 0.9 factors (~2.1 p.c). Out of almost 200 generated options throughout all examined fashions and runs, not a single one acquired an ideal rating for any downside.
Whereas OpenAI’s newly launched 03 and o4-mini-high weren’t examined for this examine, benchmarks on the researchers’ MathArena web site present o3-high scoring 21.73 p.c total and o4-mini-high scoring 19.05 p.c total on USAMO. Nonetheless, these outcomes are doubtlessly contaminated as a result of they had been measured after the competition came about, that means that the newer OpenAI fashions might doubtlessly have included the options within the coaching information.
How the fashions failed
Within the paper, the researchers recognized a number of key recurring failure patterns. The AI outputs contained logical gaps the place mathematical justification was missing, included arguments based mostly on unproven assumptions, and continued producing incorrect approaches regardless of producing contradictory outcomes.
A particular instance concerned USAMO 2025 Downside 5. This downside requested fashions to search out all optimistic complete numbers “ok,” such {that a} particular calculation involving sums of binomial coefficients raised to the ability of “ok” would all the time end in an integer, irrespective of which optimistic integer “n” was used. On this downside, Qwen’s QwQ mannequin made a notable error: It incorrectly excluded non-integer potentialities at a stage the place the issue assertion allowed them. This error led the mannequin to an incorrect remaining reply regardless of having accurately recognized the mandatory circumstances earlier in its reasoning course of.
