Euclid

Euclid

"What is asserted without proof can be dismissed without proof, but what is proved, endures."In the spirit of Euclid of Alexandria

Twenty-three centuries ago, Euclid of Alexandria looked at the mathematics of his time, a tangle of folklore, intuition, and "trust me", and said: no more. He built geometry from the ground up on axioms and proofs. If something was true, you could show it was true. No hand-waving. No guessing.

Large language models have the same problem Euclid's contemporaries did. They don't calculate. They predict. When you ask an LLM "what's 247 x 389?", it pattern-matches against its training data and guesses what the answer probably looks like. Sometimes right, sometimes wrong. You'd never know the difference.

Deterministic computation tools for AI agents.

Euclid is a hosted MCP server that gives any AI agent access to real, deterministic computation engines. What is self-evident should not be guessed, and arithmetic is about as self-evident as it gets.

Quick Start

Claude Code

claude mcp add euclid --transport http https://mcp.euclidtools.com

Claude Desktop

Add to ~/Library/Application Support/Claude/claude_desktop_config.json (macOS) or %APPDATA%\Claude\claude_desktop_config.json (Windows):

{
  "mcpServers": {
    "euclid": {
      "url": "https://mcp.euclidtools.com"
    }
  }
}

Cursor

Add to .cursor/mcp.json in your project root (or ~/.cursor/mcp.json globally):

{
  "mcpServers": {
    "euclid": {
      "url": "https://mcp.euclidtools.com"
    }
  }
}

Windsurf

Add to ~/.windsurf/mcp.json:

{
  "mcpServers": {
    "euclid": {
      "url": "https://mcp.euclidtools.com"
    }
  }
}

VS Code (Copilot)

Add to .vscode/mcp.json in your project:

{
  "servers": {
    "euclid": {
      "type": "http",
      "url": "https://mcp.euclidtools.com"
    }
  }
}

Other MCP Clients

Any MCP client that supports HTTP transport will work. Point it at:

https://mcp.euclidtools.com

Authentication is handled automatically via OAuth 2.1. Your client will prompt you to sign in on first connection.

Verify It Works

After connecting, ask your AI agent:

"What is 247 times 389?"

If Euclid is working, the agent will call the calculate tool instead of predicting the answer. You'll see the tool call in the response. The correct answer is 96,083, and unlike mental math, it's guaranteed.

The Problem

LLMs are non-deterministic. Every token they produce is a prediction, including math:

• 247 × 389 → the model predicts 96,083 (sometimes it gets 96,183 or 95,983)
• sin(47.3°) × cos(12.1°) → the model predicts something close-ish
• 15% of $8,472.50 → the model predicts a dollar amount

Sometimes the predictions are correct. Sometimes they're subtly wrong. The problem is you can never be sure which is which.

Euclid makes this a non-issue. When an AI agent has Euclid available, it sends expressions to a real computation engine and returns the computed result. Deterministic. Correct. Every time.

Think of it like what grep did for AI code search. A simple, proven tool that gives the model a capability it fundamentally lacks.

Why Not Just Use Code Execution?

Many LLM environments have code execution tools (Python sandboxes, etc.) that can do math. The difference:

Enforce Deterministic Computation

Installing Euclid gives your AI access to a calculator. But access alone isn't enough: the AI needs to be instructed to reach for it. Without an explicit directive, models will still predict math from training data by default.

Add the following to your project's AI instruction file. Pre-built versions are in the rules/ directory:

The content is identical. Copy the one that matches your IDE into your project root, or append it to your existing instruction file.

## Deterministic Computation (Euclid)

**NEVER predict, guess, or mentally compute numerical results.** LLMs produce answers by
pattern-matching against training data, sometimes right, sometimes subtly wrong, and
there is no way to tell which. Always use Euclid's MCP tools instead.

| Tool         | When to Use                                                                                                                            |
| ------------ | -------------------------------------------------------------------------------------------------------------------------------------- |
| `calculate`  | Arithmetic, percentages, margins, exponents, trig, logarithms, factorials. Any expression with a numerical answer                     |
| `convert`    | Unit conversions: m² to acres, km to miles, L/hr to gal/hr, °C to °F, bytes to kB, etc.                                               |
| `statistics` | Mean, median, mode, std deviation, variance, percentile, min, max, sum. Plus t-test, z-test, chi-squared, confidence intervals, correlation |
| `datetime`   | Date differences, add/subtract time, business days, age, day of week, quarter, leap year. Any calendar arithmetic                     |
| `encode`     | Base64, hex, URL, HTML encoding/decoding; SHA-256/512, SHA-1, MD5 hashing; HMAC signatures; JWT decoding                               |
| `finance`    | Loan payments, amortization, present/future value, NPV, IRR, CAGR, margin/markup, compound interest. Any financial formula             |
| `regex`      | Pattern testing, text extraction, match-all, replace, split. Execute patterns, never predict whether they match                        |
| `color`      | Color conversion (hex, RGB, HSL, etc.), contrast ratios, WCAG accessibility, lighten/darken, palette generation                        |
| `validate`   | Email, URL, UUID, credit card (Luhn check), IPv4, IPv6, IBAN. Structural validation with check digits                                  |
| `geo`        | Distances (Haversine/Vincenty), bearings, midpoints, destination points, polygon area, point-in-polygon, coordinate conversions        |

This applies everywhere, not just code. Analytics, business metrics, growth rates,
marketing numbers, cost calculations, date arithmetic, financial projections during
conversation. If there is a number to compute, a date to calculate, or data to
encode, hash, or validate, use Euclid. No exceptions.

Why this matters: LLMs will confidently produce incorrect arithmetic with no indication anything is wrong. A model that returns 247 × 389 = 96,183 looks just as confident as one that returns the correct 96,083. The only way to guarantee correctness is to compute, not predict.

Tools

Euclid has 10 tools.

calculate

Evaluates mathematical expressions deterministically.

calculate("(245 * 389) + (12^3 / 7)")  → 95,551.857...
calculate("sqrt(144)")                  → 12
calculate("sin(45 deg)")                → 0.707...
calculate("10!")                         → 3,628,800
calculate("e^(i * pi) + 1")            → 0  (Euler's identity)

Supports: arithmetic, order of operations, exponents, roots, trigonometry, logarithms, factorials, constants (pi, e, phi), complex numbers, Unicode math symbols (×, ÷, √, π, ², ³).

convert

Converts between units deterministically.

convert(100, "fahrenheit", "celsius")   → 37.778
convert(5, "km", "miles")              → 3.107
convert(1024, "bytes", "kB")           → 1.024
convert(60, "mph", "km/h")             → 96.561

Supports: length, mass, volume, temperature, area, speed, time, data, and 100+ units. Natural language aliases (e.g. "celsius", "miles per hour") are normalized automatically.

statistics

Statistical calculations, both descriptive and inferential.

statistics("mean", [23, 45, 12, 67, 34])          → 36.2
statistics("std", [23, 45, 12, 67, 34])            → 21.159
statistics("z_test_proportion", { ... })            → { significant: true, p_value: 0.023 }
statistics("confidence_interval", { data: [...] })  → { lower: 28.1, upper: 44.3 }

Descriptive: mean, median, mode, std, variance, min, max, sum, percentile.Inferential: z-test, t-test, chi-squared, confidence intervals, correlation, normal CDF/inverse.

datetime

Deterministic date and time arithmetic.

datetime("difference", { from: "2026-01-01", to: "2026-03-15", unit: "days" })  → 73
datetime("add", { date: "2026-01-01", amount: 90, unit: "days" })               → "2026-04-01"
datetime("age", { birthDate: "1990-06-15", asOf: "2026-03-21" })                → 35
datetime("business_days", { from: "2026-01-01", to: "2026-01-31" })             → 22

9 operations: difference, add, subtract, business_days, days_in_month, age, quarter, day_of_week, is_leap_year.

encode

Deterministic encoding, decoding, hashing, and JWT inspection.

encode("base64_encode", { input: "hello world" })               → "aGVsbG8gd29ybGQ="
encode("sha256", { input: "hello world" })                      → "b94d27b9..."
encode("hmac", { input: "data", key: "secret", algorithm: "sha256" }) → "1b779..."
encode("jwt_decode", { input: "eyJhbGci..." })                  → { header, payload, signature }

16 operations: base64, base64url, hex, url, html (encode/decode), sha256, sha512, sha1, md5, hmac, jwt_decode.

finance

Financial calculations using arbitrary-precision decimal arithmetic.

finance("loan_payment", { principal: 350000, rate: 6.5, periods: 360 })   → $2,212.24/mo
finance("irr", { cashflows: [-100000, 30000, 35000, 40000, 45000] })      → 17.094%
finance("compound_growth", { start_value: 2.1M, end_value: 4.8M, periods: 4 }) → 22.958% CAGR

16 operations: loan_payment, amortization, present_value, future_value, periods, interest_rate, npv, irr, roi, markup, margin, discount, percentage_change, compound_growth, simple_interest, compound_interest.

color

Color conversion, accessibility checks, and palette generation.

color("convert", { color: "#FF6B35", to_space: "hsl" })
color("contrast_ratio", { foreground: "#FFFFFF", background: "#2563EB" })  → "4.62:1"
color("wcag_level", { foreground: "#FFFFFF", background: "#2563EB" })      → "AA"
color("analogous", { color: "#2563EB", count: 5 })

14 operations across conversion, accessibility (WCAG), manipulation, and palette generation. 8 color spaces: hex, rgb, hsl, hsv, cmyk, lab, oklab, oklch.

regex

Safe regex execution (guaranteed linear-time, no ReDoS).

regex("test", { pattern: "^\\d{3}-\\d{4}$", subject: "555-1234" })     → true
regex("matchAll", { pattern: "\\d+", subject: "abc 123 def 456" })     → ["123", "456"]
regex("replace", { pattern: "\\s+", subject: "a  b  c", replacement: " " }) → "a b c"

6 operations: test, match, matchAll, replace, split, escape.

validate

Structural validation with check digits.

validate("email", { input: "[email protected]" })        → { valid: true }
validate("credit_card", { input: "4111111111111111" })   → { valid: true, type: "Visa" }
validate("iban", { input: "GB82WEST12345698765432" })    → { valid: true }

Formats: email, url, uuid, credit_card (Luhn), ipv4, ipv6, iban.

geo

Geospatial calculations.

geo("distance", { from: [lat, lon], to: [lat, lon] })        → km (Haversine or Vincenty)
geo("bearing", { from: [lat, lon], to: [lat, lon] })         → degrees
geo("point_in_polygon", { point: [lat, lon], polygon: [...] }) → true/false

Distance, area, midpoint, bearing, destination point, point-in-polygon, coordinate conversions.

Pricing

Every account starts with 1,000 free tool calls. No credit card required.

After that, top up credits at app.euclidtools.com.

Philosophy

Everything an LLM produces is a prediction. For creative writing and reasoning, that's fine. For math, it's a problem.

The solution isn't to make models better at predicting math. It's to give them a calculator.

This is part of a broader principle: wherever a model does something predictive that should be deterministic, give it a deterministic tool. Math is the most obvious case, but the same logic applies to unit conversions, date arithmetic, regex evaluation, encoding, and more.

License

The Euclid MCP server is proprietary software. This repository contains connection instructions, skills, and documentation for integration purposes.

All rights reserved. See LICENSE for details.

Euclid of Alexandria formalized mathematical proof 2,300 years ago. We're just giving his tools to the machines.