The US Math Olympiad (USAMO) serves as a qualifier for the Worldwide Math Olympiad and presents a a lot greater bar than assessments just like the American Invitational Arithmetic Examination (AIME). Whereas AIME issues are troublesome, 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 have been a part of the fashions’ coaching knowledge. 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 an enormous 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 practically 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 general and o4-mini-high scoring 19.05 p.c general on USAMO. Nevertheless, these outcomes are doubtlessly contaminated as a result of they have been measured after the competition occurred, which means that the newer OpenAI fashions may doubtlessly have included the options within the coaching knowledge.
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 Drawback 5. This downside requested fashions to seek out all constructive complete numbers “okay,” such {that a} particular calculation involving sums of binomial coefficients raised to the ability of “okay” would at all times lead to an integer, regardless of which constructive integer “n” was used. On this downside, Qwen’s QwQ mannequin made a notable error: It incorrectly excluded non-integer prospects at a stage the place the issue assertion allowed them. This error led the mannequin to an incorrect last reply regardless of having appropriately recognized the mandatory circumstances earlier in its reasoning course of.
