GAUSS: Benchmarking Structured Mathematical Skills for Large Language Models

We introduce $\mathbf{\text{GAUSS}}$ ($\mathbf{\text{G}}$eneral $\mathbf{\text{A}}$ssessment of $\mathbf{\text{U}}$nderlying $\mathbf{\text{S}}$tructured $\mathbf{\text{S}}$kills in Mathematics), a benchmark that evaluates LLMs’ mathematical abilities across twelve core skill dimensions, grouped into three domains: knowledge and understanding, problem solving and communication, and meta-skills and creativity. By categorizing problems according to cognitive skills and designing tasks that isolate specific abilities, GAUSS constructs comprehensive, fine-grained, and interpretable profiles of models’ mathematical abilities. These profiles faithfully represent their underlying mathematical intelligence. To exemplify how to use the $\text{textsc}GAUSS$ benchmark, we have derived the skill profile of $\text{textsc}GPT-5-thinking$, revealing its strengths and weaknesses as well as its differences relative to $\text{textsc}o4-mini-high$, thereby underscoring the value of multidimensional, skill-based evaluation.