Anyone have a link to an article exploring Lean plus MCP? EDIT: Here's a recent Arxiv paper: https://arxiv.org/abs/2404.12534v2, the keyword is "neural theorem proving"

I've just remembered: AlphaEvolve showed that LLMs can design their own "learning curricula", to help train themselves to do better at reasoning tasks. I recall these involve the AI suggesting problems that have the right amount of difficulty to be useful to train on.

I'll ramble a tiny bit more: Anybody who learns maths comes to understand that it helps to understand the "guts" of how things work. It helps to see proofs, write proofs, do homework, challenge yourself with puzzles, etc. I wouldn't be surprised if the same thing were true for LLMs. As such, I think having the LLM call out to symbolic solvers could ultimately undermine their intelligence - but using Lean to ensure rigour probably helps.

Long story short, it is great when humans interact with LLMs for imprecise queries, because, we can ascribe meaning to LLM output. But for precise queries, the human, or the LLM needs to speak a narrow interface to another machine.

Precision requires formalism, as what we mean by precise involves symbolism and operational definition. Where the genius of the human brain lies (and which is not yet captured in LLMs) is the insight and understanding of what it means to precisely model a world via symbolism - ie, the place where symbolism originates. As an example, humans operationally and precisely model the shared experience of "space" using the symbolism and theory of euclidean geometry.

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

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

    @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...

It's highly unlikely it's possible, even in theory. Symbolic solvers must explore many known "routes" to expand and simply given equations, without any theoretical guarantees. Even if you found a symbolic solution to your 20M system, it'd have so many terms in it that you'd have to settle for a numerical approximation, just to make sense of them all.

Numerical solvers are of course, a different matter, altogether.