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Glossary · Measuring and comparing

FrontierMath

FrontierMath is an advanced mathematics benchmark developed by Epoch AI with mathematical specialists. It uses difficult original problems and verifiable answers to evaluate models’ problem-solving capabilities, rather than providing a general measure of everyday usefulness, teaching quality or the complete ability to conduct original scientific research.

FrontierMath: the explanation

A system receives a demanding mathematical problem and tries to produce an answer in the required form. Solving it may involve several reasoning stages, substantial calculations or code, depending on the permitted tools. Evaluation uses checks suited to the expected answers. The benchmark therefore targets abilities beyond routine school exercises. Success means the system produced an accepted solution within that setup. It does not automatically establish that every explanation is correct, easy to follow or useful to someone learning the underlying mathematical ideas.

FrontierMath was designed around challenging problems created and reviewed by mathematicians. Using original, unpublished problems aims in part to reduce the risk that solutions were memorized during training. The collection covers different mathematical areas, and its problems do not all have the same difficulty. The [FrontierMath research paper](https://arxiv.org/abs/2411.04872) describes this approach. For you, the benchmark offers evidence about advanced mathematical problem solving rather than the overall qualities of a conversational assistant, a document tool or an agent carrying out office tasks.

Read results alongside the problem selection, difficulty level and computing resources used. Access to code or mathematical tools can change how a system approaches the task. It is also important to distinguish producing a verifiable answer from constructing a complete proof that a person can inspect and understand. Aggregate scores may hide substantial differences between mathematical areas. For a practical need, examine relevant results and check how the system explains its assumptions, verifies calculations and responds when an intermediate step appears uncertain or incorrect.

A concrete example

You want an assistant to support your work on advanced mathematics exercises. A FrontierMath result provides evidence about a model’s ability to solve some difficult problems. You then give it an exercise with an available solution and ask it to justify each step. You compare the answer, assumptions and explanation. A correct final result is not sufficient when your main goal is understanding how the reasoning works.

Why it matters

FrontierMath can be relevant when comparing systems for demanding mathematical reasoning. It is less directly useful when choosing a writing assistant or browser agent. Check the allowed tools, problem categories and computing budget behind a result. For your own work, add requirements for verifiability and clear explanations. Performance on the benchmark does not guarantee error-free calculations in your situation or establish a general ability to carry out independent research.

Common misconceptions

  • A strong FrontierMath score does not mean a model teaches mathematics well to every audience, because finding a difficult answer and presenting a clear, rigorous explanation suited to your level are different abilities that require separate evaluation.
  • Original problems reduce some memorization risks without making contamination impossible, because data protection, later publication and evaluation practices still need scrutiny when interpreting whether a result reflects the ability to solve genuinely unfamiliar mathematical problems.

Related terms: measuring and comparing

benchmark
Benchmark is a structured test with defined rules for comparing system performance.
Epoch Capabilities Index
Epoch Capabilities Index is a composite measure that combines results from multiple benchmarks to compare AI models.
SWE-bench
SWE-bench is a benchmark for resolving software issues drawn from real projects.
GPQA Diamond
GPQA Diamond is a selected subset of GPQA containing difficult multiple-choice science questions.
OSWorld
OSWorld is a family of benchmarks and environments for evaluating agents that perform computer tasks.
Terminal-Bench
Terminal-Bench is a collection of tests for measuring how well an AI agent completes tasks through a terminal, an interface controlled with text commands.
SimpleQA
SimpleQA is a benchmark for checking how accurately a language model answers short factual questions.
AIME (benchmark)
AIME (benchmark) refers to using problems from the American Invitational Mathematics Examination to evaluate language models.

Where this site covers it

The term appears on 95 pages of this site. A few of them:

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Frequently asked questions

Is it a mental arithmetic test?

No. It concerns advanced mathematical problems that may require reasoning, substantial computation or code. Available tools depend on the evaluation protocol. Read the specific conditions before comparing scores or assuming the model performed every calculation without external assistance.

Does the score measure proof quality?

Not necessarily in every respect. Checking an expected answer is not always equivalent to evaluating a complete, readable and rigorous proof. If your task requires a demonstration, explicitly inspect the reasoning steps, assumptions and treatment of exceptional cases.

Does it help choose an everyday assistant?

It provides specialized evidence about difficult mathematics. For everyday assistance, document understanding, clarity, response times and reliable tool use may matter more. Combine this result with practical trials that represent what you actually want the assistant to do.

Neutrality. No affiliate links. No vendor pays to be reviewed, rated or ranked. Reviews are directed by François Chollet, neutral and factual, and every data point is dated and sourced. How we score