Axiom — Advanced Math MCP Server

Exact symbolic and numerical mathematics for LLMs — a real computer algebra system (Giac/Xcas) behind the Model Context Protocol, and behind a shell command. Published as axiom-math.

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Quick start

As a CLI, straight away:

npx -y axiom-math compute 'integrate(sin(x)^3,x)'   # -cos(x)+cos(x)^3/3
npx -y axiom-math verify 'diff(x^3,x) = 3*x^2'      # exit 0 — it holds

As an MCP server, in any client's config:

{ "command": "npx", "args": ["-y", "axiom-math"] }

As an agent skill — drop in skills/axiom-math/SKILL.md, which teaches an agent the three commands and their exit codes.

Why Axiom?

LLMs often make calculation errors, especially with symbolic math, exact fractions, and multi-step problems. Axiom provides verified, exact results through two layers:

• math.js — Fast numerical evaluation (arithmetic, trigonometry, matrices)
• Giac/Xcas WASM — Symbolic computation (calculus, algebra, equation solving)

Benchmark Results (GLM-5.1, May 2026)

| Dataset | Baseline | +MCP | Delta | | ----------------- | -------- | ------- | --------- | | GSM8K (100) | 96.0% | 98.0% | +2.0% | | MATH L3 (50) | 70.0% | 80.0% | +10.0% | | MATH L4 (50) | 50.0% | 62.0% | +12.0% | | MATH L5 (50) | 38.0% | 52.0% | +14.0% | | CAS-quick (60) | 55.0% | 70.0% | +15.0% | | Omni-MATH ≥7 (50) | 0.0% | 0–4% | (ceiling) |

Key insights:

• Phase 0 grader (LaTeX/Unicode normalization + symbolic equivalence) is the dominant value driver across all datasets
• CAS-quick lifted from 26.7% (April pre-grader) to 70% (post-grader) — the biggest single jump
• Omni-MATH ≥7 is at ceiling for current LLM+CAS setups; needs fundamentally different approaches (Lean/Coq, fine-tuning, RAG)

Full results: benchmark/results/ and docs/superpowers/specs/ (per-phase analysis)

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Features

Axiom exposes 3 MCP tools. Almost everything flows through compute, a single gateway that parses a CAS-style problem string and routes it to the right internal engine — so callers learn one tool, not dozens.

| Tool | Purpose | | --------- | ------------------------------------------------------------------------------------------------------------------------------------- | | compute | Solve any math problem. Pass a CAS-style string (solve(...), diff(...), det([[...]]), C(10,3), 2+3*sin(pi/4)) or any Giac/Xcas expression. | | verify | Independently check a mathematical claim (identity, solution, or computation) via symbolic and/or numeric methods. | | plot | Render a 2D function graph as an SVG image. |

What compute covers

compute recognizes CAS-style verbs and dispatches across these domains. Anything it doesn't recognize falls through to raw Giac/Xcas evaluation.

| Domain | Verbs / examples | | ----------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------- | | Arithmetic & units | 2+3*sin(pi/4), 100 km/h to m/s | | Equation solving | solve(x^2-4=0, x), csolve(...) (complex), solve_system([x+y=5, x-y=1], [x,y]) | | Calculus | diff, int, limit, taylor, desolve (ODEs of any order, and linear constant-coefficient systems) | | Multivariable calculus | gradient, hessian, jacobian, divergence, curl, partial, iint/iiint (multiple integrals), critical_points, lagrange, tangent_plane, directional_derivative | | Algebra | factor, simplify, expand, partfrac | | Linear algebra | det, inv, eigenvals, eigenvects, rref, rank, tran, ker, qr, lu, cholesky, svd, norm, cond | | Number theory | ifactor, isprime, euler, analyze | | Combinatorics | C(n,k), P(n,k), stirling, bell, catalan, derangements, multinomial | | Probability | binomial, normal, poisson, geometric, hypergeometric, chi_square, student_t, f_distribution, beta, exponential | | Hypothesis testing | t_test (one/two/paired), anova, chi_square_test | | Numerical methods | newton, bisection, secant, romberg, simpson | | 2D geometry | distance, midpoint, slope, area_*, perimeter, circumference, line_intersection, point_line_distance, angle_between_lines | | 3D geometry | distance3d, midpoint3d, dot, cross, vector_norm, angle_vectors, plane_from_points, point_plane_distance, line_plane_intersection, plane_plane_angle, line_line_distance, volume_tetrahedron, volume_sphere, volume_parallelepiped | | Transforms & series | laplace, ilaplace, fourier/fft/ifft, sum, product | | Exact values | to_exact, to_decimal, simplify_fraction | | Regression & sequences | linear_regression/fit, polynomial_regression, sequence (pattern identification) |

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Installation

The package is axiom-math on npm. Nothing to install for normal use — npx fetches and caches it:

npx -y axiom-math compute '2+2'

Or install it so the axiom-math command is on your PATH:

npm install -g axiom-math

Node.js >= 20 required. The first run downloads about 3.8 MB (the CAS engine compiled to WebAssembly) and takes a few seconds; later runs come from the npx cache.

From source

For contributors, or to run a modified build:

git clone https://github.com/tufantunc/axiom-advanced-math-mcp.git
cd axiom-advanced-math-mcp
npm install
npm run build

Docker

# Build and run
docker-compose -f docker/docker-compose.yml up -d

# Check logs
docker-compose -f docker/docker-compose.yml logs -f

# Stop
docker-compose -f docker/docker-compose.yml down

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Usage

CLI (STDIO Transport)

# Run with stdio transport (default)
npm start

# Development mode
npm run dev

Claude Desktop integration:

// ~/Library/Application Support/Claude/claude_desktop_config.json
{
  "mcpServers": [
    {
      "name": "axiom-math",
      "command": "npx",
      "args": ["-y", "axiom-math"]
    }
  ]
}

Running from a local checkout instead of npm — point args at the built entry point:

"args": ["/path/to/axiom-advanced-math-mcp/dist/cli.js"]

Command line

The same binary works as a one-shot CLI, so agents can use it as a skill with no MCP configuration. With no arguments it is the MCP server; with a subcommand it runs one computation and exits.

npx -y axiom-math compute 'integrate(sin(x)^3,x)'
npx -y axiom-math compute -q 'solve(x^2-4=0,x)'     # {-2, 2}
npx -y axiom-math verify 'sin(x)^2+cos(x)^2 = 1'    # exit 0 if true
npx -y axiom-math plot 'sin(x)' -o wave.svg
echo 'diff(x^3,x)' | npx -y axiom-math compute -q   # 3*x^2

| Flag | Meaning | | --- | --- | | -q | print one value only, for scripting | | --json | structured output | | --latex | LaTeX-focused text (compute only) | | -h, --help | usage, or usage for a subcommand |

Exit codes: 0 success · 1 tool or usage error · 2 verify checked the claim and it is false.

2 is a mathematical verdict, so a claim that never got checked does not use it: one that fails to parse, that the CAS cannot evaluate, or that has a superscript with more than one reading, exits 1 with nothing on stdout. axiom-math verify '...' && ... therefore never reads a syntax error as a disproof.

A ready-to-use agent skill is in skills/axiom-math/SKILL.md.

HTTP Transport

# Start HTTP server (default: http://127.0.0.1:3000)
npm run start:http

# Development HTTP
npm run dev:http

The HTTP transport is stateless: every POST /mcp is handled independently, no Mcp-Session-Id is issued, and no session state is kept between requests. This server sends no server-initiated notifications, so nothing is lost — and it scales horizontally with no shared state.

| Method | Path | Behaviour | | ------ | --------- | ------------------------------------------------------ | | POST | /mcp | Handles a JSON-RPC message | | GET | /mcp | 405 — no SSE stream is offered | | DELETE | /mcp | 405 — there are no sessions to terminate | | GET | /health | 200 when ready, 503 when the CAS engine is not |

Security: there is no authentication and no rate limiting. The default bind address is 127.0.0.1, but docker/docker-compose.yml sets MCP_HOST=0.0.0.0. If you expose the port, put it behind a reverse proxy that authenticates and rate-limits — docker/reverse-proxy/ is a working, tested one (nginx + basic auth + per-client concurrency cap, with the app publishing no port of its own). SECURITY.md documents the full posture — what is protected, what is not, and how to report a vulnerability.

POST /mcp also validates the Host header against an