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

Annotations already declare readOnlyHint=true and openWorldHint=false, so safety is covered, and the description adds value beyond that by describing what is returned: lesson content plus the citing lesson and video. It stops short of stating not-found behavior or how many matches to expect, which would round out the read semantics.

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?

A single well-structured sentence with the action front-loaded and the return shape trailing. The six-item example parenthetical is on the long side but each example clarifies the accepted concept granularity, so little is wasted.

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?

With no output schema, the description carries the return-value burden and does so adequately by naming lesson text plus lesson and video references. Missing are edge cases such as no-match behavior and result-count expectations for a search-style tool.

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 coverage is 100% so the baseline is 3, and the description earns a bump by illustrating the granularity of the concept parameter with real lookup strings ("np.roll", "binomial", "leapfrog", "attractor"). The lang parameter is not mentioned at all in the description, which keeps it from a 5.

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 names a specific verb-and-resource pair ("Finds a Python or math idea in the lessons and gives what the lessons say about it") and enumerates the domain with concrete examples like "np.roll", "recursion", and "golden ratio". It also states the shape of the answer (lesson content plus the lesson and video that show it), which separates it from get_lesson or list_patterns without the agent needing to open a schema.

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?

Usage is implied rather than stated: the agent can infer this is the concept-lookup tool rather than an ID-based lesson fetch or a pattern listing, but there is no explicit "use this when..." sentence and no alternative named. No guidance on what to do when a concept is unknown or ambiguous.

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