MCP Math Server

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries full burden. It states the formula but lacks behavioral details: it doesn't mention that this is a slow-converging series (important for performance), doesn't specify output format or precision, and omits any error handling or limitations. The description adds minimal context beyond the basic formula.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise and front-loaded, stating the purpose and formula in one sentence. The parenthetical domain/category adds minor metadata without verbosity. However, it could be more structured by separating usage guidance or parameter details, but as-is, it avoids waste.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity (mathematical computation with performance implications), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It omits critical context: expected output (e.g., float approximation of pi), convergence behavior, accuracy trade-offs with 'terms', and comparison to other pi-computation tools. This leaves significant gaps for an AI agent.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 0% description coverage, with one parameter 'terms' of type integer. The description does not explain what 'terms' means (e.g., number of series terms to sum), its typical range, or its impact on accuracy. Since schema coverage is low, the description fails to compensate adequately, providing no parameter semantics beyond what the bare schema indicates.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool computes pi using the Leibniz formula, specifying the mathematical method. It distinguishes itself from other pi-computation siblings (e.g., compute_pi_chudnovsky, compute_pi_machin) by naming the specific algorithm. However, it does not explicitly contrast with these siblings in the description text, missing full differentiation.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain (arithmetic) and category (mathematical_constants), but offers no explicit when/when-not instructions or references to sibling tools like compute_pi_chudnovsky for different precision needs or contexts.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.