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 mathematical logic but omits critical behavioral details: computational complexity (factorials grow rapidly), input limitations (e.g., n must be positive integer), error handling, or performance characteristics. For a primality test with no annotation coverage, this is a significant gap.

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 with the core purpose in the first sentence. The second sentence adds domain/category context efficiently. No wasted words, though it could benefit from slightly more detail given the lack of annotations.

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 of a primality test, no annotations, no output schema, and low parameter coverage, the description is incomplete. It explains the theorem but misses practical implementation details, return format (e.g., boolean result), error cases, and performance warnings, leaving the agent under-informed for reliable use.

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?

Schema description coverage is 0%, with one parameter 'n' undocumented in the schema. The description adds minimal semantics by implying 'n' is the number to test for primality, but doesn't specify constraints (e.g., n > 0, integer type), domain, or examples. It partially compensates for the schema gap but insufficiently for a tool with computational implications.

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: 'Test primality using Wilson's theorem' with the specific mathematical condition '(n-1)! ≡ -1 (mod n) iff n is prime.' It distinguishes itself from sibling tools like 'aks_primality_test', 'fermat_primality_test', and 'miller_rabin_test' by specifying the unique theorem-based approach.

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 implies usage context through 'Domain: arithmetic, Category: wilson_theorem', suggesting it's for mathematical primality testing. However, it lacks explicit guidance on when to choose this method over alternative primality tests available among siblings, such as efficiency considerations or input constraints.

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