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

With no annotations, the description carries the full behavioral burden. It usefully discloses the expected return contents (record, source, submission instructions, example, leaderboard), but it does not state error behavior if problem_id is invalid, required permissions, or that the operation is read-only beyond what 'get' implies.

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 a single compact sentence with no wasted wording, and the core resource is front-loaded. The colon-list construction is slightly telegraphic, but it efficiently conveys the main contents.

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 simple one-parameter read tool without an output schema, the description is reasonably complete about return contents. However, it leaves gaps around parameter sourcing and comparison to sibling tools, which are important for correct invocation in this dense math-related tool family.

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 sole parameter problem_id has zero schema description coverage, and the description adds no meaning about its format, origin, or whether it comes from math_problems. The parameter is only implied by the tool's noun phrase, leaving the agent to infer how to obtain a valid ID.

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 indicates a single math problem retrieval and enumerates the record, source, submission instructions, example construction, and leaderboard. It distinguishes itself from the likely sibling math_problems list by specifying 'one math problem,' though it omits an explicit verb like 'get' or 'retrieve.'

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?

There is no guidance on when to use this tool versus siblings such as math_problems, math_mine, or math_claims. Usage is only implied by the name and the mention of problem-specific contents; no prerequisites or exclusions are given.

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