The server defines 5 tools with clear names and documented docstrings. All tools have proper input schemas with type definitions and parameter descriptions. Descriptions are adequate (60-200 chars) but generic, lacking specificity about when to use each tool or prerequisites. No output schemas are formally documented, return types are inferred from docstrings. Error handling is present in 2 tools (matrix_multiply, eigen_decomposition) but sparse. Tools follow a consistent verb_noun naming pattern, which aids discoverability. Security baseline met (no secrets in params, read-only operations). Composition is clean, each tool does one thing. However, the server lacks output schema documentation, lacks error recovery guidance, and descriptions do not indicate dependencies or use cases that would optimize LLM selection.

• Document output schemas explicitly in the tool registration, not just docstrings. Define the return type as a JSON Schema object. E.g., for statistical_analysis, register output schema: {type: 'object', properties: {mean: {type: 'number'}, median: {type: 'number'}, std: {type: 'number'}, min: {type: 'number'}, max: {type: 'number'}}}.
• Add validation logic to each tool and return structured error messages. E.g., polynomial_fit should validate len(x) == len(y) and degree >= 0, degree < len(x), then return: {'error': 'Invalid degree: degree must be less than data length. Got degree=5, data length=3.'}
• Expand tool descriptions to 100-200 chars and include use-case context. E.g., 'Add two numbers and return their sum. Use this for basic arithmetic operations, not matrix operations, see matrix_multiply for higher-dimensional data.' This helps LLMs select the right tool.
• Specify numeric parameter bounds in descriptions. E.g., 'degree (int, optional): Degree of polynomial. Must be >= 0 and less than the number of data points. Defaults to 2.'
• Add error recovery guidance to tools lacking it. E.g., in polynomial_fit docstring, add 'Raises: ValueError: If x and y have different lengths, or degree is negative.'
• Consider adding a tool annotation (readOnlyHint: true) to signal that all 5 tools are safe read-only operations, this is implicitly true now but would help LLMs understand safety in a structured way (if tool annotations are exposed by FastMCP).