MATH Benchmark — AI Glossary

Reference details

Related terms

• GSM8K
• Reasoning (LLM)
• Chain of Thought (CoT)

How it works

1. Problems come with step-by-step solutions, but the standard protocol compares only the final answer, so the solutions serve training rather than grading.
2. Answers are mathematical expressions in LaTeX, which means grading cannot be string comparison — a half written as a fraction and as a decimal are the same answer in different notation.
3. The grader therefore normalises and then tests equivalence, stripping formatting, ordering set elements, and evaluating simple expressions to compare values.
4. Those equivalence rules are a component of the benchmark, and two graders disagreeing about whether an unsimplified radical matches produce different scores for identical model output.
5. Process supervision changes the target rather than the grader: a model is trained against a signal that scores each step, so correctness of reasoning becomes something the reward can see.
6. That is the mechanism behind step-level reward models, and it is why a final-answer protocol and a process-supervised model are measuring different things even on the same problems.

Example: Right answer, wrong reasoning, full marks

Grading is on the final answer, so a model that reaches the correct value through invalid steps scores identically to one that reasons soundly — and on multiple-choice or small-integer answers, a lucky guess is indistinguishable from a solution. This is why process supervision exists: grading each step rather than the endpoint separates the two, and produces a reward signal that does not credit accidental correctness. When you read a result on a maths benchmark, the question that determines what it means is whether the steps were checked or only the answer.

Commonly confused with

Competition mathematics is not applied numeracy. Strong performance here says little about arithmetic on messy real data, unit handling, or reading figures out of a document — and a model that solves olympiad-style problems can still be unreliable adding a column of numbers, because that path runs through tokenization rather than reasoning.

When to use it

Reach for it when:

• Comparing reasoning-trained models, where extended deliberation is the variable of interest
• Measuring whether chain-of-thought or process supervision helped a specific model
• As one input among several on symbolic reasoning ability

Reach for something else when:

• Predicting reliability on business arithmetic or spreadsheet-style tasks
• Without checking contamination — problem sets of this kind are widely republished
• Reading final-answer accuracy as evidence of valid reasoning

Primary source

• Hendrycks et al., Measuring Mathematical Problem Solving With the MATH Dataset (arXiv)

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