MCP Math Server

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

With no annotations provided, the description carries the full burden. It clearly indicates this is a read-only operation that returns a specific mathematical constant value (ζ(3) ≈ 1.20206). It doesn't mention computational complexity, precision, or error handling, but for a zero-parameter constant lookup tool, the behavioral disclosure is reasonably complete.

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 perfectly concise: one sentence stating the constant value and its mathematical definition, followed by domain/category tags. Every element earns its place - the value, definition, and context tags all provide essential information with zero 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?

For a zero-parameter tool with no annotations and no output schema, the description provides complete context: what constant is returned, its approximate value, its mathematical definition, and domain/category classification. The only minor gap is lack of precision/format information about the returned value, but for a constant lookup tool, this is reasonably complete.

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 tool has zero parameters with 100% schema description coverage (empty schema). The description appropriately doesn't discuss parameters since none exist. It focuses instead on what constant is returned, which is the correct semantic information for this tool type.

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's purpose: 'Get Apéry's constant ζ(3) ≈ 1.20206' with the specific mathematical definition 'Sum of cubes reciprocals: 1 + 1/8 + 1/27 + ...'. It distinguishes itself from all 300+ sibling tools by focusing on this specific mathematical constant, which is unique in the list.

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 implied usage through the domain/category tags 'Domain: arithmetic, Category: general', suggesting this is a general arithmetic constant lookup. However, it doesn't explicitly state when to use this tool versus alternatives (like computing ζ(3) through other methods or accessing other mathematical constants from sibling tools).

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