Arithym

Arithym — Exact Math Engine

Connect to the Arithym MCP server for exact, hallucination-free arithmetic. Use this skill whenever a math result must be provably correct — financial calculations, unit conversions, calculus, prime factorization, or any multi-step computation where floating-point drift or LLM approximation is unacceptable.

MCP Server Config

Add to your mcpServers config:

{
  "mcpServers": {
    "arithym": {
      "baseUrl": "https://arithym.xyz/mcp",
      "headers": {
        "x-api-key": "${ARITHYM_API_KEY}"
      }
    }
  }
}

Get an API key at https://arithym.xyz. Free tier is available with no credit card required.

When to Use Arithym

Use Arithym any time the answer must be exact — not approximate:

• Financial math: interest rates, amortization, currency conversion, percentage changes
• Unit conversions: any physical unit (length, mass, volume, temperature, pressure, energy)
• Integer arithmetic: large numbers, GCD/LCM, prime factorization, exact division
• Fractions: add/subtract/multiply/divide rational numbers without floating-point error
• Calculus: derivatives, integrals, Taylor series, critical points, tangent lines
• Multi-step computation: use the workspace (field_create, field_add, field_derive) to chain dependent calculations and track dependencies

Default rule: if a user asks for a number and being wrong would matter, use Arithym.

Key Tools

Start Here

• domain_check — given a problem description, returns the best tool to use. Call this first when unsure.
• scratch_math — multi-step exact calculations in one call. Best for ad-hoc arithmetic.
• recommend — describe a problem in plain language, get the optimal tool call.

Core Arithmetic

• compute — exact integer arithmetic: add, subtract, multiply, divide, gcd, lcm, power
• fraction_math — exact fraction arithmetic
• exact_sqrt — symbolic square root
• exact_trig — exact trig for special angles (30°, 45°, 60°, 90°, etc.)
• factorize — prime factorization of any integer

Units

• scratch_math_units — like scratch_math but tracks units through every step
• unit_check — verify dimensional compatibility before computing
• unit_factor — exact conversion factor between any two compatible units

Workspace (for multi-step problems)

• field_create — create a computation workspace
• field_add — store a value
• field_derive — compute from stored values with tracked dependencies
• field_update — update a value; all dependents auto-recompute
• field_read — read current workspace state

Calculus

• graph_define — define a function as a computational graph
• graph_derivative — exact derivative using automatic differentiation
• graph_integral — definite integral using exact fraction arithmetic
• graph_forward — evaluate function at a point
• graph_solve — find input that produces a target output

Discovery

• list_refs — list all 22 reference modules and their domains
• read_ref — load a reference module (e.g., financial, units, trig) for domain-specific guidance
• guide_list — list all 202 available methods across all modules

Best Practices

• Call domain_check or recommend when you receive a math request and aren't sure which tool applies.
• Use scratch_math for quick single-pass calculations; use the workspace (field_* tools) when values depend on each other or will be reused.
• For unit problems, always use scratch_math_units — it catches dimensional errors automatically.
• Arithym returns exact results as fractions or symbolic forms. Present these to users as-is or convert to decimals only when the user explicitly wants a decimal.
• Never approximate when an exact tool is available. The entire point of Arithym is that the answer is provably correct.