Ultimath
The Ultimath server evaluates mathematical expressions across multiple independent numeric engines simultaneously to detect floating-point errors and verify numeric reliability.
evaluate: Run any math expression through 4 independent engines (multiprecision, exact decimal, IEEE-754 double, interval arithmetic) in parallel and compare results side by side. When engines disagree, it flags numerically unreliable values (e.g., floating-point sensitivity, catastrophic cancellation, singularities, branch cuts).list_functions: List all supported mathematical functions with name, arity, category, and description — optionally filtered by category (algebraic, trigonometric, hyperbolic, exponential, special, rounding, introspection).
Supported operations:
Arithmetic (
+,-,*,/,%), powers (x^y), roots (sqrt), factorial (!)Trigonometry (
sin,cos,tan), exponentials/logarithms (exp,ln,log)Complex numbers (e.g.
3+2i), alternate base literals (e.g.0xFF,0b1010)Built-in constants:
pi,e,PHI
Output control: Specify precision (1–50 decimal digits) and format (fixed, scientific, auto). Each engine returns structured diagnostics and warnings (e.g. precision loss, overflow, ULP errors).
Notes: Multiplication must be explicit (e.g. 2*pi). No type casts or constructors — complex numbers use 1+2i notation. Expressions are not stored; only anonymized usage metrics are retained.
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 |
| 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. |
| Its own error bound covers the first |
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.
Related MCP server: mcp-abacus
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 ratioPHI).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 (2piis an error). Expressions are purely mathematical — no type casts or constructors; write a complex number as1+2i.
Setup
Get a free API key at https://ultimath.ai.
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
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
Maintenance
Tools
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