Axiom — Advanced Math

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`.

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)

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.

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.

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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

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.

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