MCPInstall

math-help

by parcadeiEducation & Science

Guide to the math cognitive stack - what tools exist and when to use each

Installs
543
Last 24h
—
Trending rank
—
Security
Not audited

Install

Works with every agent the skills CLI supports.

npx skills add https://github.com/parcadei/continuous-claude-v3 --skill math-help
  1. 01

    Install

    Run the command in your project. The CLI asks which agents to install for.

  2. 02

    Describe the task

    Ask your agent for something this skill covers. It loads math-help automatically when relevant.

  3. 03

    Review the result

    The agent follows the SKILL.md steps, scripts and references bundled with the skill.

SKILL.md

The instructions your agent reads when the skill is triggered.

Math Cognitive Stack Guide

Cognitive prosthetics for exact mathematical computation. This guide helps you choose the right tool for your math task.

Quick Reference

I want to...Use thisExample
Solve equationssympy_compute.py solvesolve "x**2 - 4 = 0" --var x
Integrate/differentiatesympy_compute.pyintegrate "sin(x)" --var x
Compute limitssympy_compute.py limitlimit "sin(x)/x" --var x --to 0
Matrix operationssympy_compute.py / numpy_compute.pydet "[[1,2],[3,4]]"
Verify a reasoning stepmath_scratchpad.py verifyverify "x = 2 implies x^2 = 4"
Check a proof chainmath_scratchpad.py chainchain --steps '[...]'
Get progressive hintsmath_tutor.py hinthint "Solve x^2 - 4 = 0" --level 2
Generate practice problemsmath_tutor.py generategenerate --topic algebra --difficulty 2
Prove a theorem (constraints)z3_solve.py proveprove "x + y == y + x" --vars x y
Check satisfiabilityz3_solve.py satsat "x > 0, x < 10, x*x == 49"
Optimize with constraintsz3_solve.py optimizeoptimize "x + y" --constraints "..."
Plot 2D/3D functionsmath_plot.pyplot2d "sin(x)" --range -10 10
Arbitrary precisionmpmath_compute.pypi --dps 100
Numerical optimizationscipy_compute.pyminimize "x**2 + 2*x" "5"
Formal machine proofLean 4 (lean4 skill)/lean4

The Five Layers

Layer 1: SymPy (Symbolic Algebra)

When: Exact algebraic computation - solving, calculus, simplification, matrix algebra.

Key Commands:

# Solve equation
uv run python -m runtime.harness scripts/sympy_compute.py \
    solve "x**2 - 5*x + 6 = 0" --var x --domain real

# Integrate
uv run python -m runtime.harness scripts/sympy_compute.py \
    integrate "sin(x)" --var x

# Definite integral
uv run python -m runtime.harness scripts/sympy_compute.py \
    integrate "x**2" --var x --bounds 0 1

# Differentiate (2nd order)
uv run python -m runtime.harness scripts/sympy_compute.py \
    diff "x**3" --var x --order 2

# Simplify (trig strategy)
uv run python -m runtime.harness scripts/sympy_compute.py \
    simplify "sin(x)**2 + cos(x)**2" --strategy trig

# Limit
uv run python -m runtime.harness scripts/sympy_compute.py \
    limit "sin(x)/x" --var x --to 0

# Matrix eigenvalues
uv run python -m runtime.harness scripts/sympy_compute.py \
    eigenvalues "[[1,2],[3,4]]"

Best For: Closed-form solutions, calculus, exact algebra.

Layer 2: Z3 (Constraint Solving & Theorem Proving)

When: Proving theorems, checking satisfiability, constraint optimization.

Key Commands:

# Prove commutativity
uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
    prove "x + y == y + x" --vars x y --type int

# Check satisfiability
uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
    sat "x > 0, x < 10, x*x == 49" --type int

# Optimize
uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
    optimize "x + y" --constraints "x >= 0, y >= 0, x + y <= 100" \
    --direction maximize --type real

Best For: Logical proofs, constraint satisfaction, optimization with constraints.

Layer 3: Math Scratchpad (Reasoning Verification)

When: Verifying step-by-step reasoning, checking derivation chains.

Key Commands:

# Verify single step
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
    verify "x = 2 implies x^2 = 4"

# Verify with context
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
    verify "x^2 = 4" --context '{"x": 2}'

# Verify chain of reasoning
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
    chain --steps '["x^2 - 4 = 0", "(x-2)(x+2) = 0", "x = 2 or x = -2"]'

# Explain a step
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
    explain "d/dx(x^3) = 3*x^2"

Best For: Checking your work, validating derivations, step-by-step verification.

Layer 4: Math Tutor (Educational)

When: Learning, getting hints, generating practice problems.

Key Commands:

# Step-by-step solution
uv run python scripts/cc_math/math_tutor.py steps "x**2 - 5*x + 6 = 0" --operation solve

# Progressive hint (level 1-5)
uv run python scripts/cc_math/math_tutor.py hint "Solve x**2 - 4 = 0" --level 2

# Generate practice problem
uv run python scripts/cc_math/math_tutor.py generate --topic algebra --difficulty 2

Best For: Learning, tutoring, practice.

Layer 5: Lean 4 (Formal Proofs)

When: Rigorous machine-verified mathematical proofs, category theory, type theory.

Access: Use /lean4 skill for full documentation.

Best For: Publication-grade proofs, dependent types, category theory.

Numerical Tools

For numerical (not symbolic) computation:

NumPy (160 functions)

# Matrix operations
uv run python scripts/cc_math/numpy_compute.py det "[[1,2],[3,4]]"
uv run python scripts/cc_math/numpy_compute.py inv "[[1,2],[3,4]]"
uv run python scripts/cc_math/numpy_compute.py eig "[[1,2],[3,4]]"
uv run python scripts/cc_math/numpy_compute.py svd "[[1,2,3],[4,5,6]]"

# Solve linear system
uv run python scripts/cc_math/numpy_compute.py solve "[[3,1],[1,2]]" "[9,8]"

SciPy (289 functions)

# Minimize function
uv run python scripts/cc_math/scipy_compute.py minimize "x**2 + 2*x" "5"

# Find root
uv run python scripts/cc_math/scipy_compute.py root "x**3 - x - 2" "1.5"

# Curve fitting
uv run python scripts/cc_math/scipy_compute.py curve_fit "a*exp(-b*x)" "0,1,2,3" "1,0.6,0.4,0.2" "1,0.5"

mpmath (153 functions, arbitrary precision)

# Pi to 100 decimal places
uv run python scripts/cc_math/mpmath_compute.py pi --dps 100

# Arbitrary precision sqrt
uv run python -m scripts.mpmath_compute mp_sqrt "2" --dps 100

Visualization

math_plot.py

# 2D plot
uv run python scripts/cc_math/math_plot.py plot2d "sin(x)" \
    --var x --range -10 10 --output plot.png

# 3D surface
uv run python scripts/cc_math/math_plot.py plot3d "x**2 + y**2" \
    --xvar x --yvar y --range 5 --output surface.html

# Multiple functions
uv run python scripts/cc_math/math_plot.py plot2d-multi "sin(x),cos(x)" \
    --var x --range -6.28 6.28 --output multi.png

# LaTeX rendering
uv run python scripts/cc_math/math_plot.py latex "\\int e^{-x^2} dx" --output equation.png

Educational Features

5-Level Hint System

LevelCategoryWhat You Get
1ConceptualGeneral direction, topic identification
2StrategicApproach to use, technique selection
3TacticalSpecific steps, intermediate goals
4ComputationalIntermediate results, partial solutions
5AnswerFull solution with explanation

Usage:

# Start with conceptual hint
uv run python scripts/cc_math/math_tutor.py hint "integrate x*sin(x)" --level 1

# Get more specific guidance
uv run python scripts/cc_math/math_tutor.py hint "integrate x*sin(x)" --level 3

Step-by-Step Solutions

uv run python scripts/cc_math/math_tutor.py steps "x**2 - 5*x + 6 = 0" --operation solve

Returns structured steps with:

  • Step number and type
  • From/to expressions
  • Rule applied
  • Justification

Common Workflows

Workflow 1: Solve and Verify

  1. Solve with sympy_compute.py
  2. Verify solution with math_scratchpad.py
  3. Plot to visualize (optional)
# Solve
uv run python -m runtime.harness scripts/sympy_compute.py \
    solve "x**2 - 4 = 0" --var x

# Verify the solutions work
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
    verify "x = 2 implies x^2 - 4 = 0"

Workflow 2: Learn a Concept

  1. Generate practice problem with math_tutor.py
  2. Use progressive hints (level 1, then 2, etc.)
  3. Get full solution if stuck
# Generate problem
uv run python scripts/cc_math/math_tutor.py generate --topic calculus --difficulty 2

# Get hints progressively
uv run python scripts/cc_math/math_tutor.py hint "..." --level 1
uv run python scripts/cc_math/math_tutor.py hint "..." --level 2

# Full solution
uv run python scripts/cc_math/math_tutor.py steps "..." --operation integrate

Workflow 3: Prove and Formalize

  1. Check theorem with z3_solve.py (constraint-level proof)
  2. If rigorous proof needed, use Lean 4
# Quick check with Z3
uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
    prove "x*y == y*x" --vars x y --type int

# For formal proof, use /lean4 skill

Choosing the Right Tool

Is it SYMBOLIC (exact answers)?
  └─ Yes → Use SymPy
      ├─ Equations → sympy_compute.py solve
      ├─ Calculus → sympy_compute.py integrate/diff/limit
      └─ Simplify → sympy_compute.py simplify

Is it a PROOF or CONSTRAINT problem?
  └─ Yes → Use Z3
      ├─ True/False theorem → z3_solve.py prove
      ├─ Find values → z3_solve.py sat
      └─ Optimize → z3_solve.py optimize

Is it NUMERICAL (approximate answers)?
  └─ Yes → Use NumPy/SciPy
      ├─ Linear algebra → numpy_compute.py
      ├─ Optimization → scipy_compute.py minimize
      └─ High precision → mpmath_compute.py

Need to VERIFY reasoning?
  └─ Yes → Use Math Scratchpad
      ├─ Single step → math_scratchpad.py verify
      └─ Chain → math_scratchpad.py chain

Want to LEARN/PRACTICE?
  └─ Yes → Use Math Tutor
      ├─ Hints → math_tutor.py hint
      └─ Practice → math_tutor.py generate

Need MACHINE-VERIFIED formal proof?
  └─ Yes → Use Lean 4 (see /lean4 skill)

Related Skills

  • /math or /math-mode - Quick access to the orchestration skill
  • /lean4 - Formal theorem proving with Lean 4
  • /lean4-functors - Category theory functors
  • /lean4-nat-trans - Natural transformations
  • /lean4-limits - Limits and colimits

Requirements

All math scripts are installed via:

uv sync

Dependencies: sympy, z3-solver, numpy, scipy, mpmath, matplotlib, plotly

FAQ

What does the math-help skill do?

Guide to the math cognitive stack - what tools exist and when to use each

How do I install math-help?

Run npx skills add https://github.com/parcadei/continuous-claude-v3 --skill math-help in your project. The skills CLI detects the agents you use and copies the skill into the right folder. For Claude Code you can also place the skill folder at ~/.claude/skills/math-help/ (personal) or .claude/skills/math-help/ (project).

Which AI agents can use math-help?

Any agent that supports the open Agent Skills format (a folder with a SKILL.md file), including Claude Code, Codex, Cursor, GitHub Copilot, Gemini CLI, Windsurf, Cline, OpenCode and more.

Is math-help safe to install?

No partner security audit is available yet. Skills can run commands and scripts, so read the SKILL.md and any bundled files before installing.

Who maintains math-help?

It is published by parcadei in parcadei/continuous-claude-v3. It has 543 recorded installs.

More from parcadei/continuous-claude-v3

View all →

discovery-interview

parcadei/continuous-claude-v3

Deep interview process to transform vague ideas into detailed specs. Works for technical and non-technical users.

4.1K installs

premortem

parcadei/continuous-claude-v3

Identify failure modes before they occur using structured risk analysis

886 installs

math

parcadei/continuous-claude-v3

Unified math capabilities - computation, solving, and explanation. I route to the right tool.

Education & Science876 installs

github-search

parcadei/continuous-claude-v3

Search GitHub code, repositories, issues, and PRs via MCP

AI & Agents732 installs

dead-code

parcadei/continuous-claude-v3

Find unused functions and dead code in the codebase

Code Quality & Workflow730 installs

refactor

parcadei/continuous-claude-v3

Code refactoring workflow - analyze → plan → implement → review → validate

Code Quality & Workflow621 installs

Popular education & science skills

View category →

teach

mattpocock/skills

Teach the user a new skill or concept, within this workspace.

Education & Science874K installs

scaffold-exercises

mattpocock/skills

Create exercise directory structures with sections, problems, solutions, and explainers that pass linting. Use when user wants to scaffold exercises, create exercise stubs, or set up a new course section.

Education & Science488.2K installs

paper-context-resolver

lllllllama/rigorpilot-skills

Rigor Paper Context helper for README-first deep learning repo reproduction. Use only when the README and repository files leave a narrow reproduction-critical gap and the task is to resolve a specific paper detail such as dataset split, preprocessing, evaluation protocol, checkpoint mapping, or runtime assumption from primary paper sources while recording conflicts. Do not use for general paper summary, repo scanning, environment setup, command execution, title-only paper lookup, or replacing README guidance by default.

Education & Science478.3K installs

caveman-learn

juliusbrussee/caveman

Act on a Caveman learn report - review the ranked token sinks, apply cost-lowering fixes with per-edit consent, and report what those fixes returned. Use when asked to lower an agent's token cost, what caveman has saved, to trim a heavy CLAUDE.md, or to offload re-pasted context into cavemem.

Education & Science107.9K installs

gsap-plugins

greensock/gsap-skills

Official GSAP skill for GSAP plugins — registration, ScrollToPlugin, ScrollSmoother, Flip, Draggable, Inertia, Observer, SplitText, ScrambleText, SVG and physics plugins, CustomEase, EasePack, CustomWiggle, CustomBounce, GSDevTools. Use when the user asks about a GSAP plugin, scroll-to, flip animations, draggable, SVG drawing, or plugin registration.

Education & Science67.9K installs

teach-impeccable

pbakaus/impeccable

DEPRECATED: Use /impeccable teach instead. This command has been folded into the impeccable skill.

Education & Science50K installs