competition-mathematics problem benchmark evaluation, subject-stratified mathematical domain evaluation, difficulty-stratified problem progression evaluation, step-by-step solution reference generation and validation, longitudinal model capability tracking and baseline comparison

MATH

DatasetFree

12.5K competition math problems across 7 subjects and 5 difficulty levels.

Open Source

/ 100

5 capabilities

Capabilities5 decomposed

competition-mathematics problem benchmark evaluation

Medium confidence

Provides a curated dataset of 12,500 authentic competition mathematics problems sourced from AMC, AIME, and similar olympiad-style competitions, enabling systematic evaluation of LLM mathematical reasoning across 7 subject domains. Each problem includes ground-truth step-by-step solutions that serve as reference implementations for answer verification and reasoning chain validation. The dataset uses a 5-level difficulty stratification to enable fine-grained performance analysis across problem complexity ranges, allowing researchers to identify capability thresholds and reasoning degradation patterns.

Solves for

Evaluate whether my LLM can solve authentic competition-level math problems end-to-endBenchmark my model's mathematical reasoning against published baselines (GPT-3 at 6.9%, o3 at 90%+)Identify which mathematical domains my model struggles with using subject-level performance breakdownsTrack improvement in mathematical reasoning capability across model iterations and training approaches

Best for

AI research teams developing reasoning-focused LLMs

Organizations evaluating LLM capabilities for STEM applications

Researchers studying scaling laws in mathematical problem-solving

Requires

Hugging Face Datasets library (datasets>=2.0.0) or direct JSON/CSV parsing capability

Computational resources for running inference on 12,500 problems (typically 2-8 hours depending on model size and hardware)

Mathematical answer parsing logic to extract and normalize solutions (handles fractions, decimals, symbolic expressions)

Limitations

Dataset is static — does not include new competition problems beyond collection date, limiting evaluation of model memorization vs generalization

Requires manual or LLM-based solution verification since problems expect numerical/symbolic answers, not multiple choice

Difficulty levels are subjective human annotations rather than derived from problem-solving success rates, creating potential mismatch with actual model difficulty perception

What makes it unique

Sourced directly from authentic competition mathematics (AMC, AIME) rather than synthetic or textbook problems, ensuring problems test genuine mathematical reasoning under time pressure and novelty constraints. Includes detailed step-by-step solutions for each problem, enabling not just answer verification but reasoning chain analysis and intermediate step correctness evaluation.

vs alternatives

More rigorous than general math benchmarks (SVAMP, MathQA) because competition problems are designed to be unsolvable by pattern-matching alone; more comprehensive than single-competition datasets because it spans 7 mathematical domains and 5 difficulty levels, enabling fine-grained capability profiling

subject-stratified mathematical domain evaluation

Medium confidence

Organizes the 12,500 problems across 7 discrete mathematical subjects (Prealgebra, Algebra, Number Theory, Counting and Probability, Geometry, Intermediate Algebra, Precalculus), enabling targeted performance analysis by mathematical domain. This stratification allows researchers to identify which mathematical reasoning capabilities their models have acquired and which remain deficient, rather than collapsing performance into a single aggregate score. The subject taxonomy maps to standard high school and early undergraduate mathematics curricula, making results interpretable to educators and curriculum designers.

Solves for

Identify which mathematical domains my model excels at and which require targeted training or fine-tuningCompare my model's relative strengths across geometry, algebra, number theory, and probability reasoningDetermine if my model has acquired foundational skills (Prealgebra) before attempting advanced topics (Precalculus)Validate that mathematical reasoning improvements from training generalize across all domains or are domain-specific

Best for

Researchers studying mathematical reasoning specialization in LLMs

Teams fine-tuning models for specific mathematical domains (e.g., geometry for CAD/design applications)

Educational technology companies evaluating LLM readiness for tutoring specific subjects

Requires

Ability to filter or group dataset by subject category field

Statistical analysis tools to compute per-subject accuracy, precision, and confidence intervals

Optional: domain-specific solution validators (e.g., geometric proof checkers for Geometry problems)

Limitations

Subject categories are mutually exclusive but problems often require cross-domain reasoning (e.g., geometry + algebra), potentially underestimating integrated reasoning capability

No explicit tagging of prerequisite relationships (e.g., Prealgebra → Algebra → Intermediate Algebra), limiting analysis of hierarchical skill acquisition

Subject distribution is uneven — some domains may have 1,500+ problems while others have <1,000, creating statistical power imbalances in domain-level comparisons

What makes it unique

Explicitly organizes problems by 7 mathematical subject domains rather than treating mathematics as a monolithic capability, enabling fine-grained capability profiling. This mirrors how mathematical education is structured (separate courses for Algebra, Geometry, etc.), making results actionable for curriculum-aligned training and evaluation.

vs alternatives

More granular than aggregate math benchmarks (GSM8K, MATH500) which report single accuracy scores; enables identification of domain-specific weaknesses that aggregate metrics would mask, critical for targeted model improvement and application-specific evaluation

difficulty-stratified problem progression evaluation

Medium confidence

Stratifies all 12,500 problems across 5 difficulty levels (1-5), enabling researchers to construct difficulty-aware evaluation curves and identify at what problem complexity threshold model performance degrades. This enables analysis of whether mathematical reasoning scales smoothly with problem difficulty or exhibits sharp capability cliffs. The difficulty stratification allows researchers to evaluate whether models have acquired robust reasoning or are brittle to increased complexity, and to identify the 'frontier' difficulty level where models transition from reliable to unreliable performance.

Solves for

Determine the maximum difficulty level my model can reliably solve (e.g., 'reliable up to level 3, unreliable at level 4+')Analyze whether my model's mathematical reasoning scales smoothly with problem complexity or exhibits sharp performance cliffsEvaluate whether training improvements generalize to harder problems or only improve performance on easier problemsCompare my model's difficulty frontier against published baselines (e.g., GPT-3 solves ~7% across all difficulties, o3 solves ~90%)

Best for

Researchers studying scaling laws and capability emergence in mathematical reasoning

Teams evaluating whether models are ready for production use (e.g., tutoring systems need reliable performance on level 3+ problems)

Organizations analyzing whether training approaches improve robustness or just memorization

Requires

Ability to filter dataset by difficulty level (1-5)

Computational resources to evaluate model on all 5 difficulty subsets (potentially 2,500 problems per level)

Plotting/visualization tools to generate difficulty-stratified performance curves

Limitations

Difficulty levels are human-annotated subjective judgments, not derived from empirical model performance data, creating potential mismatch with actual model difficulty perception

No explicit mapping between difficulty level and problem characteristics (e.g., 'level 4 requires 5+ reasoning steps'), limiting interpretability of why certain difficulties are harder

Difficulty distribution across subjects is uneven — some subjects may have more level-5 problems than others, confounding difficulty and domain effects

What makes it unique

Provides explicit 5-level difficulty stratification across all 12,500 problems, enabling construction of difficulty-aware evaluation curves rather than single aggregate scores. This enables researchers to identify capability cliffs and scaling behavior, critical for understanding whether models have acquired robust reasoning or brittle pattern-matching.

vs alternatives

More nuanced than pass/fail benchmarks (MATH500) because it enables difficulty-stratified analysis; more interpretable than raw problem sets because difficulty annotations guide researchers to focus evaluation on capability frontiers rather than averaging across trivial and impossible problems

step-by-step solution reference generation and validation

Medium confidence

Provides detailed step-by-step solutions for all 12,500 problems, enabling not just binary answer correctness evaluation but intermediate reasoning chain validation. These reference solutions serve as ground truth for analyzing whether models generate correct reasoning steps in correct order, enabling fine-grained evaluation of reasoning quality beyond final answer accuracy. The solutions can be used to train models via supervised fine-tuning on step-by-step reasoning, or to validate intermediate steps in chain-of-thought outputs, enabling detection of 'right answer, wrong reasoning' failure modes.

Solves for

Validate not just whether my model gets the right answer, but whether it generates correct intermediate reasoning stepsTrain my model on step-by-step solutions via supervised fine-tuning to improve reasoning chain qualityDetect 'right answer, wrong reasoning' failure modes where models arrive at correct answers through incorrect logicAnalyze which reasoning steps models struggle with most (e.g., algebraic manipulation vs conceptual understanding)

Best for

Teams training reasoning-focused models via supervised fine-tuning on step-by-step solutions

Researchers studying intermediate reasoning quality and chain-of-thought correctness

Organizations implementing step-by-step solution verification in production systems

Requires

Text parsing and comparison logic to match model-generated steps against reference solutions

Optional: semantic similarity metrics (embeddings, BLEU, ROUGE) to handle paraphrased but equivalent steps

Optional: symbolic math library (SymPy) to validate mathematical equivalence of algebraic expressions

Limitations

Solutions are human-written and may not cover all valid solution paths — models generating correct but alternative solutions may be incorrectly marked as wrong

No explicit step-level annotations (e.g., which steps are 'conceptual understanding' vs 'mechanical computation'), limiting fine-grained reasoning analysis

Solutions are text-based and may not capture visual/geometric reasoning required for Geometry problems, limiting validation of spatial reasoning

What makes it unique

Includes detailed step-by-step solutions for all 12,500 problems rather than just final answers, enabling intermediate reasoning validation and supervised fine-tuning on reasoning chains. This enables training approaches like outcome supervision and process supervision that have shown significant improvements in mathematical reasoning capability.

vs alternatives

Richer than answer-only benchmarks (SVAMP, MathQA) because it enables reasoning chain validation; more actionable than problem-only datasets because solutions provide training signal for supervised fine-tuning and intermediate step verification

longitudinal model capability tracking and baseline comparison

Medium confidence

Provides published baseline scores from multiple model generations (GPT-3 at 6.9%, o3 at 90%+, DeepSeek R1, etc.), enabling researchers to position their models within the landscape of known capabilities and track improvement over time. The dataset's stability and fixed problem set enable longitudinal comparison — researchers can evaluate their models against the same 12,500 problems and directly compare results to published baselines, identifying whether improvements come from better reasoning or from model scale/compute. This enables tracking of progress in mathematical reasoning as a research community.

Solves for

Compare my model's mathematical reasoning capability against published baselines (GPT-3, o3, DeepSeek R1)Track improvement in my model's mathematical reasoning across training iterations and model versionsIdentify whether my improvements come from better reasoning or from increased model scale/computeContribute my model's results to the community benchmark and track progress in mathematical reasoning capability

Best for

Researchers developing new reasoning approaches and wanting to benchmark against known baselines

Organizations tracking mathematical reasoning capability improvements across model iterations

Teams evaluating whether their training approach is competitive with state-of-the-art

Requires

Published baseline scores and evaluation methodology documentation

Standardized evaluation protocol to ensure fair comparison (same prompting, same number of attempts, same answer parsing logic)

Leaderboard or tracking system to aggregate and compare results across models and teams

Limitations

Published baselines may use different evaluation protocols (e.g., different prompting strategies, number of attempts), making direct comparison problematic

Baseline scores are snapshots in time — models may have been updated or re-evaluated with different settings, creating ambiguity about what exactly was measured

No explicit documentation of evaluation methodology for published baselines (e.g., zero-shot vs few-shot, temperature settings, max tokens), limiting reproducibility

What makes it unique

Provides published baseline scores from multiple model generations (GPT-3, o3, DeepSeek R1) on the same fixed problem set, enabling direct longitudinal comparison and tracking of progress in mathematical reasoning capability. The fixed problem set ensures that improvements over time reflect genuine capability gains rather than dataset changes.

vs alternatives

More useful for tracking progress than one-off benchmarks because the fixed problem set enables direct comparison across time and models; more interpretable than relative rankings because absolute scores on the same problems enable understanding of capability gaps and improvement trajectories

Capabilities are decomposed by AI analysis. Each maps to specific user intents and improves with match feedback.

Related Artifactssharing capabilities

Artifacts that share capabilities with MATH, ranked by overlap. Discovered automatically through the match graph.

Benchmark39

MATH Benchmark

12.5K competition math problems — AMC/AIME/Olympiad level, 7 subjects, standard math benchmark.

competition-mathematics problem dataset loading with multi-subject stratificationproblem difficulty and solution complexity analysissubject-stratified accuracy metric aggregation and analysismulti-model comparative evaluation and leaderboard generation

4 shared capabilities

Benchmark39

FrontierMath

Expert-level math problems created by mathematicians.

expert-level mathematical reasoning evaluation across multiple domainsmulti-domain mathematical problem classification and organizationbenchmark dataset access and evaluation infrastructureresearch-level mathematical problem inclusion and unsolved problem assessment

4 shared capabilities

Benchmark39

MathVista

Visual mathematical reasoning benchmark.

domain-specific mathematical reasoning assessmentmultimodal mathematical reasoning evaluation

2 shared capabilities

Dataset48

APPS (Automated Programming Progress Standard)

10K coding problems across 3 difficulty levels with test suites.

multi-difficulty benchmark evaluation for code generation modelsdifficulty-stratified performance analysis

2 shared capabilities

Benchmark39

GSM8K

8.5K grade school math problems — multi-step reasoning, verifiable solutions, reasoning benchmark.

multi-step mathematical reasoning benchmark evaluationmulti-step reasoning complexity stratification (2-8 steps)

2 shared capabilities

Dataset48

CodeContests

13K competitive programming problems from AlphaCode research.

difficulty-calibrated-problem-stratification

1 shared capability

Best For

✓AI research teams developing reasoning-focused LLMs
✓Organizations evaluating LLM capabilities for STEM applications
✓Researchers studying scaling laws in mathematical problem-solving
✓Teams implementing chain-of-thought or step-by-step reasoning training
✓Researchers studying mathematical reasoning specialization in LLMs
✓Teams fine-tuning models for specific mathematical domains (e.g., geometry for CAD/design applications)
✓Educational technology companies evaluating LLM readiness for tutoring specific subjects
✓Organizations analyzing whether mathematical reasoning is a unified capability or domain-specific skill

Known Limitations

⚠Dataset is static — does not include new competition problems beyond collection date, limiting evaluation of model memorization vs generalization
⚠Requires manual or LLM-based solution verification since problems expect numerical/symbolic answers, not multiple choice
⚠Difficulty levels are subjective human annotations rather than derived from problem-solving success rates, creating potential mismatch with actual model difficulty perception
⚠No built-in support for partial credit — problems are typically binary correct/incorrect, missing intermediate reasoning quality assessment
⚠Skewed toward high school competition math; limited coverage of undergraduate-level or applied mathematics domains
⚠Subject categories are mutually exclusive but problems often require cross-domain reasoning (e.g., geometry + algebra), potentially underestimating integrated reasoning capability

Requirements

Hugging Face Datasets library (datasets>=2.0.0) or direct JSON/CSV parsing capabilityComputational resources for running inference on 12,500 problems (typically 2-8 hours depending on model size and hardware)Mathematical answer parsing logic to extract and normalize solutions (handles fractions, decimals, symbolic expressions)Optional: LaTeX rendering or symbolic math library (SymPy, Mathematica) for solution verificationAbility to filter or group dataset by subject category fieldStatistical analysis tools to compute per-subject accuracy, precision, and confidence intervalsOptional: domain-specific solution validators (e.g., geometric proof checkers for Geometry problems)Ability to filter dataset by difficulty level (1-5)

Input / Output

Accepts: problem statement (text with optional LaTeX mathematical notation), problem metadata (subject category, difficulty level 1-5, competition source), problem statement with subject category label, problem metadata (subject: 'Algebra' | 'Geometry' | 'Number Theory' | etc.), problem statement with difficulty level annotation (1-5), problem metadata including subject and difficulty, problem statement, reference step-by-step solution (text with optional LaTeX notation), model-generated solution or reasoning chain, model evaluation results on MATH dataset (accuracy, per-subject breakdown, per-difficulty breakdown), model metadata (name, size, training approach, evaluation date)

Produces: model-generated solution (free-form text or step-by-step reasoning chain), ground-truth solution (step-by-step walkthrough with final answer), evaluation metrics (accuracy, subject-level breakdown, difficulty-stratified performance), per-subject accuracy metrics (e.g., 92% on Algebra, 67% on Geometry), subject-level performance rankings and comparative analysis, domain-specific error patterns and failure mode categorization, difficulty-stratified accuracy curves (e.g., 98% at level 1, 85% at level 2, 60% at level 3, 20% at level 4, 5% at level 5), difficulty frontier identification (threshold where performance drops below acceptable threshold), scaling analysis (does performance degrade linearly, exponentially, or with sharp cliffs?), step-level correctness annotations (which steps are correct/incorrect), intermediate reasoning quality metrics (e.g., 'correct steps: 4/6, correct answer: yes'), fine-tuning datasets (problem + reference solution pairs for supervised training), comparative performance metrics (e.g., 'my model: 45%, GPT-3: 6.9%, o3: 90%'), improvement tracking over time (e.g., 'improved from 35% to 45% with new training approach'), leaderboard rankings and capability positioning

UnfragileRank

Adoption70%(35% weight)

Quality28%(25% weight)

Ecosystem40%(20% weight)

Match Graph10%(15% weight)

Freshness100%(5% weight)

UnfragileRank is computed from adoption signals, documentation quality, ecosystem connectivity, match graph feedback, and freshness. No artifact can pay for a higher rank.

Type: Dataset

5 capabilities

Visit MATH→

About

UC Berkeley's benchmark of 12,500 competition mathematics problems from AMC, AIME, and other math competitions covering 7 subjects: Prealgebra, Algebra, Number Theory, Counting and Probability, Geometry, Intermediate Algebra, and Precalculus. Each problem includes a detailed step-by-step solution. Difficulty levels 1-5. Tests genuine mathematical reasoning capability. Scores have climbed from 6.9% (GPT-3) to 90%+ (o3, DeepSeek R1), making it a key reasoning benchmark.

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Capabilities5 decomposed

competition-mathematics problem benchmark evaluation

Medium confidence

Solves for

Best for

AI research teams developing reasoning-focused LLMs

Organizations evaluating LLM capabilities for STEM applications

Researchers studying scaling laws in mathematical problem-solving

Requires

Hugging Face Datasets library (datasets>=2.0.0) or direct JSON/CSV parsing capability

Computational resources for running inference on 12,500 problems (typically 2-8 hours depending on model size and hardware)

Mathematical answer parsing logic to extract and normalize solutions (handles fractions, decimals, symbolic expressions)

Limitations

Dataset is static — does not include new competition problems beyond collection date, limiting evaluation of model memorization vs generalization

Requires manual or LLM-based solution verification since problems expect numerical/symbolic answers, not multiple choice

Difficulty levels are subjective human annotations rather than derived from problem-solving success rates, creating potential mismatch with actual model difficulty perception

What makes it unique

vs alternatives

subject-stratified mathematical domain evaluation

Medium confidence

Solves for

Best for

Researchers studying mathematical reasoning specialization in LLMs

Teams fine-tuning models for specific mathematical domains (e.g., geometry for CAD/design applications)

Educational technology companies evaluating LLM readiness for tutoring specific subjects

Requires

Ability to filter or group dataset by subject category field

Statistical analysis tools to compute per-subject accuracy, precision, and confidence intervals

Optional: domain-specific solution validators (e.g., geometric proof checkers for Geometry problems)

Limitations

Subject categories are mutually exclusive but problems often require cross-domain reasoning (e.g., geometry + algebra), potentially underestimating integrated reasoning capability

No explicit tagging of prerequisite relationships (e.g., Prealgebra → Algebra → Intermediate Algebra), limiting analysis of hierarchical skill acquisition

Subject distribution is uneven — some domains may have 1,500+ problems while others have <1,000, creating statistical power imbalances in domain-level comparisons

What makes it unique

vs alternatives

difficulty-stratified problem progression evaluation

Medium confidence

Solves for

Best for

Researchers studying scaling laws and capability emergence in mathematical reasoning

Teams evaluating whether models are ready for production use (e.g., tutoring systems need reliable performance on level 3+ problems)

Organizations analyzing whether training approaches improve robustness or just memorization

Requires

Ability to filter dataset by difficulty level (1-5)

Computational resources to evaluate model on all 5 difficulty subsets (potentially 2,500 problems per level)

Plotting/visualization tools to generate difficulty-stratified performance curves

Limitations

Difficulty levels are human-annotated subjective judgments, not derived from empirical model performance data, creating potential mismatch with actual model difficulty perception

No explicit mapping between difficulty level and problem characteristics (e.g., 'level 4 requires 5+ reasoning steps'), limiting interpretability of why certain difficulties are harder

Difficulty distribution across subjects is uneven — some subjects may have more level-5 problems than others, confounding difficulty and domain effects

What makes it unique

vs alternatives

step-by-step solution reference generation and validation

Medium confidence

Solves for

Best for

Teams training reasoning-focused models via supervised fine-tuning on step-by-step solutions

Researchers studying intermediate reasoning quality and chain-of-thought correctness

Organizations implementing step-by-step solution verification in production systems

Requires

Text parsing and comparison logic to match model-generated steps against reference solutions

Optional: semantic similarity metrics (embeddings, BLEU, ROUGE) to handle paraphrased but equivalent steps

Optional: symbolic math library (SymPy) to validate mathematical equivalence of algebraic expressions

Limitations

Solutions are human-written and may not cover all valid solution paths — models generating correct but alternative solutions may be incorrectly marked as wrong

No explicit step-level annotations (e.g., which steps are 'conceptual understanding' vs 'mechanical computation'), limiting fine-grained reasoning analysis

Solutions are text-based and may not capture visual/geometric reasoning required for Geometry problems, limiting validation of spatial reasoning

What makes it unique

vs alternatives

longitudinal model capability tracking and baseline comparison

Medium confidence

Solves for

Best for

Researchers developing new reasoning approaches and wanting to benchmark against known baselines

Organizations tracking mathematical reasoning capability improvements across model iterations

Teams evaluating whether their training approach is competitive with state-of-the-art

Requires

Published baseline scores and evaluation methodology documentation

Standardized evaluation protocol to ensure fair comparison (same prompting, same number of attempts, same answer parsing logic)

Leaderboard or tracking system to aggregate and compare results across models and teams

Limitations

Published baselines may use different evaluation protocols (e.g., different prompting strategies, number of attempts), making direct comparison problematic

Baseline scores are snapshots in time — models may have been updated or re-evaluated with different settings, creating ambiguity about what exactly was measured

No explicit documentation of evaluation methodology for published baselines (e.g., zero-shot vs few-shot, temperature settings, max tokens), limiting reproducibility

What makes it unique

vs alternatives

Capabilities are decomposed by AI analysis. Each maps to specific user intents and improves with match feedback.

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MATH

Capabilities5 decomposed

competition-mathematics problem benchmark evaluation

subject-stratified mathematical domain evaluation

difficulty-stratified problem progression evaluation

step-by-step solution reference generation and validation

longitudinal model capability tracking and baseline comparison

Related Artifactssharing capabilities

MATH Benchmark

FrontierMath

MathVista

APPS (Automated Programming Progress Standard)

GSM8K

CodeContests

Best For

Known Limitations

Requirements

Input / Output

UnfragileRank

About

Categories

Alternatives to MATH

Are you the builder of MATH?

Get the weekly brief

Data Sources

MATH

Capabilities5 decomposed

competition-mathematics problem benchmark evaluation

subject-stratified mathematical domain evaluation

difficulty-stratified problem progression evaluation

step-by-step solution reference generation and validation

longitudinal model capability tracking and baseline comparison

Related Artifactssharing capabilities

MATH Benchmark

FrontierMath

MathVista

APPS (Automated Programming Progress Standard)

GSM8K

CodeContests

Best For

Known Limitations

Requirements

Input / Output

UnfragileRank

About

Categories

Alternatives to MATH

Are you the builder of MATH?

Get the weekly brief

Data Sources