Ultimath Mcp

Ultimath MCP

Stop hallucinating numbers. An MCP server that runs every math expression through eight independent engines in parallel — exact symbolic, ball, interval, three different arbitrary-precision floats, deferred symbolic and IEEE 754, each with its own failure modes — and returns all eight readings side by side, so when they disagree you know the answer is numerically unreliable.

Engine	What it does
Exact symbolic	Exact arithmetic: decides a value instead of approximating it
Multiprecision	Ball arithmetic, rigorous radius carried through
Interval	Rigorous lower/upper bounds (guaranteed enclosure)
Binary float	Arbitrary-precision binary floats, no GMP below
PARI/GP	Built without GMP: its own integer and transcendental kernels
NTL RR	Exact integer mantissa × 2^e; only operations round
Deferred symbolic	Rewrites before evaluating: a cancellation never rounds
IEEE-754 double	Standard hardware floating point

What each engine stands behind

Reading eight numbers is only half the answer. Each engine also says how far it underwrites its own — and the three answers are not degrees of one another:

Field	What the engine is saying
"exact": true	It holds the value. The reading is a truncation of it: every further digit you ask for is a digit of the number, not a closer approximation.
"digits": N	Its own error bound covers the first N significant digits. 0 is a real answer — that is what catastrophic cancellation does to a value.
neither	It carries no error bound. It printed as many digits as you asked for and can say nothing about any of them.

That last row is not 0, and it is the reason the other engines exist. Five of the eight are there by construction.

On exp(pi*sqrt(163)) - 262537412640768744, one engine prints 63 digits of which 34 are right — and says nothing about it. Two others prove 33 and stop. One holds the value exactly. Reading the eight numbers alone would not tell you which was which.

No engine is ever asked about another: each statement is about itself.

The exact engine

calcium settles an equality rather than comparing digits, reaches poles the others can only approach (tan(pi/2) is uinf), and when the printed digits are just a truncation it also returns the closed form — sqrt(2)+1 comes back with Add(Sqrt(2), 1), in plain form and in LaTeX, and acosh(0.5) with Div(Mul(NumberI, Pi), 3) — the named value, not the field element it is stored in.

The closed form is opt-in on the HTTP API ("closed_form": true) because proving one costs more than reading the digits. This client always asks for it: quoting an exact value is what its output schema promises.

Tools

• evaluate — evaluate an expression on all eight engines and compare. Supports arithmetic, trig (sin, cos, tan), exp/log (exp, ln, log), roots and powers (sqrt, x^y), factorial, complex numbers (3+2i), alternate bases (0xFF, 0b1010), and constants (pi, e, golden ratio PHI).
• list_functions — list every function the engines expose (name, arity, category, description). Optionally filter by category.

Comparisons do not mean the same thing on every engine. On the enclosure engines, !=, < and > are true only once proven; ==, <= and >= are true as soon as they are not disproven. A true == there is not a proof of equality — calcium decides that one exactly — but a true != is a proof of difference.

Multiplication must be explicit: write 2*pi, 2*sin(x), (a+b)*(c+d). Adjacency is not a product (2pi is an error). Expressions are purely mathematical — no type casts or constructors; write a complex number as 1+2i.

Setup

1. Get a free API key at https://ultimath.ai.
2. Add the server to your MCP client config (example for Claude Desktop):

{
  "mcpServers": {
    "ultimath": {
      "command": "npx",
      "args": ["-y", "ultimath-mcp"],
      "env": {
        "ULTIMATH_API_KEY": "your_api_key_here"
      }
    }
  }
}

That's it — npx fetches and runs the server on demand.

Requirements

• Node.js ≥ 18
• An Ultimath API key (ULTIMATH_API_KEY)

Links

• Website: https://ultimath.ai
• Source: https://github.com/Flupke68/ultimath-mcp

Under the hood

Ultimath's engines build on FLINT/Arb, Calcium, GMP/MPFR and MPFI — full credits at https://ultimath.ai/credits.

Privacy

Ultimath stores only a hash of your API key and basic usage metrics to run and secure the service; expressions are evaluated, not retained for training. Full policy: https://ultimath.ai/privacy/

License

MIT