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An archival-style black-and-white photograph of a mathematician working at a chalkboard, with a constant Jacobian determinant and three distinct inputs mapping to one output.

Jacobian

Atomic mathematics for agents: discover one typed operation, run it, and compose its bounded result.

CI PyPI npm Supported Python versions MIT license

Jacobian is an MCP server that gives AI agents atomic, composable tools for
higher mathematics. It exposes two tools: math.find searches an immutable
library of typed mathematical operations, and math.run executes exactly one
of them and returns its concrete typed result. Each operation is one bounded,
exact computation: a typed request in and a typed mathematical value out. The
same mathematical library is also available through a CLI and native Python
API.

Jacobian's hypothesis is that mathematical reasoning benefits from an
executable vocabulary of small, exact operations. Rather than exposing large
domain solvers or precomposed workflows, Jacobian exposes mathematical
primitives that agents can search for and compose into solutions beyond what
any individual operation was designed to solve. The library supplies
trustworthy mathematical moves; the reasoning model decides which moves to
make, how to combine their results, and when to stop. Keeping the operations
small and domain-owned preserves that search space instead of baking one proof
strategy or workflow into the tools themselves.

Quickstart

Run the canonical Python MCP command without installing Jacobian globally:

uvx --from jacobian jacobian-mcp

Where an MCP host requires an npm command, the npm package is a deterministic
carrier for that same command:

npx jacobian mcp

For a persistent installation:

python -m pip install jacobian
jacobian-mcp

That package includes Jacobian's exact maintained Python backend stack: SymPy,
NetworkX, Z3, and Python-FLINT. A normal Python or npm installation
therefore exposes the same built-in Python-backed operation portfolio. The
tested binary-install contract is CPython 3.12 or 3.13 on glibc Linux x86-64;
the release gate installs the built wheel and starts Jacobian on both Python
versions. Other systems may have compatible upstream wheels, but are not part
of the tested release contract yet. In particular, Alpine/musl cannot install
the complete mandatory stack from PyPI.

The Python distribution contains the mathematical kernel, CLI, and MCP server.
The npm package deterministically maps its exact package version to the
corresponding uvx invocation.

Compute one bounded result

An ordinary operation returns mathematics first. For example,
matrix.determinant.compute accepts one exact rational matrix and returns its
determinant directly. Callers compose results by passing their typed values to a
subsequent operation.

Available mathematics

The built-in portfolio covers work in:

  • polynomial maps and polynomial algebra;
  • exact linear algebra;
  • graphs, paths, colorings, and isomorphism;
  • bounded SAT and SMT solving;
  • finite algebra, probability, geometry, and topology; and
  • Lean source elaboration.

SAT and SMT operations use the maintained Z3 Python binding directly. The
optional lean.check operation runs one bounded source snippet in the fixed
Lean service environment, using a request-scoped temporary directory and
returning typed diagnostics. Use math.find to search for an operation, browse
an unfamiliar domain, and inspect one operation before calling math.run once.

See the domain operation library
for the maintained operation portfolio and
backend requirements.

Status

Jacobian 0.12.0 is pre-stable. Its published package and operation contracts
describe the supported surface; experimental operation contracts may change
between releases.

Documentation

Contributing

Jacobian uses Python 3.12, uv, and a small Makefile:

make setup
make test-math
make check

Read CONTRIBUTING.md before changing code. It documents
focused test commands, verification rules, documentation placement, and
pull-request expectations.

License

MIT