How does the LLM know that it can use the factor tool to factor integers? Just by looking at the string "factor an integer"?

Yes, and I believe this is what the article is referring to when it says “a stochastic black box that communicates through a complex web of JSON schemas attached to docstring annotations”. Specifically, in the function definition:

    @mcp.tool()
    def factor(a: int) -> int:
        """Factor an integer"""
        return factor_number(a)

The documentation and source code seem to be:

- (official SDK): https://github.com/modelcontextprotocol/python-sdk/blob/e80c... -> using the function's docstring: https://github.com/modelcontextprotocol/python-sdk/blob/e80c...

- (v2?): https://gofastmcp.com/servers/tools#the-%40tool-decorator and https://github.com/jlowin/fastmcp/blob/998de22a6e76fc8ae323e... -> using the function's docstring: https://github.com/jlowin/fastmcp/blob/998de22a6e76fc8ae323e...

Yup

this is what the tools response for the mcp server looks like:

{ tools: [ 0: { name: "factor" description: "Factor an integer" inputSchema: { ... } 4 items } ] }

They give it a list of tool commands it can use in the context I believe.