FrontierMath Benchmark

A FrontierMath Benchmark is an AI system benchmark task that is a mathematics benchmark (for evaluating advanced mathematical reasoning capabilitys).

• AKA: Advanced Mathematics AI Benchmark, Research-Level Math Benchmark.
• Context:
  • Task Input: Mathematics Problems, AI System, Evaluation Criteria
    • Optional Input: Verification Methods, Time Constraints
  • Task Output: Solution Attempts, Performance Scores
  • Task Performance Measure: Solution Accuracy, Reasoning Depth, Completion Rate
  • ...
  • It can (typically) assess Mathematical Reasoning through research problems.
  • It can (typically) evaluate Problem Solving via novel challenges.
  • It can (typically) measure Advanced Capability using expert validation.
  • It can (typically) verify Solution Quality through automated checks.
  • It can (typically) maintain Benchmark Integrity via unpublished problems.
  • ...
  • It can (often) span Mathematics Fields through diverse problems.
  • It can (often) compare Model Performance via standardized tests.
  • It can (often) highlight System Limitations through challenge problems.
  • ...
  • It can range from being a Simple Mathematics Task to being a Complex Mathematics Task, depending on its problem difficulty.
  • It can range from being a Narrow Mathematics Domain to being a Broad Mathematics Domain, depending on its topic coverage.
  • It can range from being a Quick Solution Task to being a Long-Form Solution Task, depending on its time requirement.
  • It can range from being a Computational Mathematics Task to being a Theoretical Mathematics Task, depending on its problem type.
  • ...
• Example(s):
  • Category Theory Benchmarks (mathematics systems for abstract reasoning tasks), such as proof verification systems.
  • Algebraic Geometry Benchmarks (mathematics systems for geometric reasoning tasks), such as theorem proving systems.
  • Number Theory Benchmarks (mathematics systems for numerical reasoning tasks), such as conjecture testing systems.
  • Analysis Benchmarks (mathematics systems for analytical reasoning tasks), such as limit computation systems.
  • Applied Mathematics Benchmarks (mathematics systems for practical reasoning tasks), such as problem solving systems.
  • ...
• Counter-Example(s):
  • Basic Mathematics Benchmark, which tests elementary skills.
  • GSM8K Benchmark, which evaluates high school mathematics.
  • MATH Benchmark, which assesses undergraduate mathematics.
  • Standardized Test Benchmark, which lacks research-level complexity.
• See: Mathematics Benchmark, AI System Evaluation, Mathematical Reasoning, Advanced Problem Solving, Research Mathematics.

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