1177 Math B6718919

MATH

!!! tip "Quick Start" bash mcpbr run -c config.yaml --benchmark math -n 20

Overview

MATH is a dataset of 12,500 competition mathematics problems drawn from AMC (American Mathematics Competitions), AIME (American Invitational Mathematics Examination), and other math competitions. The dataset was created to evaluate the mathematical problem-solving capabilities of language models on problems that require deep reasoning, multi-step solutions, and knowledge of advanced mathematical concepts.

Problems span 7 mathematical subjects and are rated across 5 difficulty levels, providing fine-grained evaluation of a model's mathematical capabilities. Unlike GSM8K, which tests grade-school arithmetic, MATH problems require knowledge of algebra, geometry, combinatorics, number theory, and calculus at a competition level.

In mcpbr, the MATH benchmark evaluates how effectively an MCP server assists the language model in solving challenging mathematics problems. The agent is expected to show its work step-by-step and provide a final answer in \boxed{answer} format.

Task Structure

Each MATH task contains the following fields:

Subjects (7 total):

Difficulty levels (5 total):

Example task:

Problem: What is the largest value of $x$ such that the expression
         $\dfrac{\sqrt{x-2}}{x^2+x-6}$ is defined?

Level: Level 3
Type: algebra

Solution: For the expression to be defined, we need $x-2 \ge 0$ and
          $x^2+x-6 \ne 0$. The first condition gives $x \ge 2$.
          Factoring the denominator: $x^2+x-6=(x+3)(x-2)$, so $x \ne -3$
          and $x \ne 2$. Combined: $x > 2$. There is no largest such
          value, but in context the answer is $\boxed{2}$.

Instance IDs are generated in the format math_{index} based on the position in the filtered/sampled task list.

Running the Benchmark

=== "CLI"

```bash
# Run MATH with default settings
mcpbr run -c config.yaml --benchmark math

# Run a small sample for quick testing
mcpbr run -c config.yaml --benchmark math -n 20

# Filter by subject
mcpbr run -c config.yaml --benchmark math --filter-category algebra

# Filter by difficulty level (Level 1 = easiest, Level 5 = hardest)
mcpbr run -c config.yaml --benchmark math --level 3

# Combine subject and difficulty filters
mcpbr run -c config.yaml --benchmark math \
  --filter-category geometry --level 2 -n 50

# Run with verbose output and save results
mcpbr run -c config.yaml --benchmark math -n 100 -v -o results.json -r report.md
```

=== "YAML Configuration"

```yaml
benchmark: "math"
sample_size: 10
timeout_seconds: 300
max_iterations: 20

mcp_server:
  command: "npx"
  args: ["-y", "@modelcontextprotocol/server-filesystem", "{workdir}"]

model: "sonnet"

# Optional: Filter by subject
filter_category:
  - "algebra"
  - "number_theory"

# Optional: Enable extended thinking for complex problems
thinking_budget: 10000
```

Evaluation Methodology

MATH evaluation extracts and compares mathematical answers with normalization:

1. Ground truth extraction: The expected answer is extracted from the task's solution field by finding the \boxed{answer} pattern. The parser handles nested braces up to 2 levels deep to support complex LaTeX expressions like \boxed{\frac{1}{2}}.

2. Agent answer extraction: The same \boxed{answer} extraction is applied to the agent's response. As a fallback, the evaluator looks for "The answer is" or "Final answer:" patterns.

3. Normalization: Both answers are normalized before comparison:

   • All whitespace is removed
   • LaTeX formatting commands are stripped: \left, \right, \,
   • The result is a compact string representation

4. Comparison: Normalized answers are compared as exact string matches. This means \frac{1}{2} and 0.5 would NOT match -- the agent should use the same mathematical notation as the ground truth.

5. Verdict: The task is marked as resolved if the normalized agent answer exactly matches the normalized ground truth answer.

!!! note "Evaluation is offline" Unlike code generation benchmarks, MATH evaluation does not execute code in the Docker container. The comparison is performed entirely on the extracted text answers. The Docker environment is still created (with Python/SymPy available) so the agent can use computation tools during problem solving.

Example Output

Successful resolution:

{
  "resolved": true,
  "agent_answer": "\\frac{1}{2}",
  "ground_truth_answer": "\\frac{1}{2}"
}

Failed resolution (wrong answer):

{
  "resolved": false,
  "agent_answer": "\\frac{1}{3}",
  "ground_truth_answer": "\\frac{1}{2}"
}

Failed resolution (answer not extracted):

{
  "resolved": false,
  "error": "Could not extract answer from solution"
}

Failed resolution (ground truth parse error):

{
  "resolved": false,
  "error": "Could not parse ground truth answer"
}

Troubleshooting

Agent provides correct answer but in different format

The MATH evaluator uses exact string matching after normalization. If the ground truth is \frac{1}{2} but the agent responds with 0.5 or 1/2, the match will fail. Instruct the agent to use \boxed{} format with proper LaTeX notation.

Agent does not use \boxed{} format

If the agent omits the \boxed{} wrapper, the evaluator falls back to "The answer is" pattern matching. For best results, ensure your prompt explicitly requests \boxed{answer} format. The default mcpbr prompt includes this instruction.

Complex LaTeX expressions fail to extract

The \boxed{} parser handles up to 2 levels of nested braces. Deeply nested expressions like \boxed{\sqrt{\frac{a+\sqrt{b}}{c}}} should extract correctly. If extraction fails, check for mismatched braces in the agent's output.

Filtering returns no tasks

Subject names must match exactly (case-insensitive): algebra, counting_and_probability, geometry, intermediate_algebra, number_theory, prealgebra, precalculus. Level filtering matches on the string "Level N" in the task's level field. Verify your filter values against these lists.

Best Practices

• Start with easier levels (Level 1-2) to verify your setup before attempting harder problems. Level 5 problems are extremely challenging even for frontier models.
• Use longer timeouts (120-300s) since competition math problems require more reasoning time than code generation tasks.
• Enable extended thinking with thinking_budget: 10000 or higher for Level 4-5 problems where deep reasoning is needed.
• Filter by subject to evaluate specific mathematical capabilities. Running algebra and prealgebra together gives a good baseline before trying harder subjects like geometry or number_theory.
• Instruct LaTeX format -- ensure the agent prompt explicitly requests \boxed{answer} format. The default prompt does this, but custom prompts should include the same instruction.
• Use Python/SymPy for verification -- the Docker environment includes SymPy. Encourage the agent to verify its symbolic computations programmatically.
• Pair with GSM8K -- run GSM8K for basic math reasoning and MATH for advanced reasoning to get a complete picture of mathematical capabilities.
• Set max_iterations to 15-20 since competition problems may require multiple rounds of reasoning and verification.

Related Links

• MATH Dataset Repository
• MATH Paper (Measuring Mathematical Problem Solving)
• MATH-lighteval Dataset on HuggingFace
• GSM8K Benchmark -- grade-school math reasoning
• Benchmarks Overview
• Configuration Reference
• CLI Reference