How do I install the Math Help skill?

Run npx skillmds@latest add dojogenesis/math-help in your terminal (requires Node.js), paste this page's agent-chat prompt into Claude, Cursor, or any MCP-connected agent, or download the SKILL.md file and copy it into your agent's skills directory.

What does the Math Help skill do?

Guide to the math cognitive stack - what tools exist and when to use each It is listed under Coding & Dev Tools on SkillMD.

Is Math Help safe to use?

This skill has not completed SkillMD's automated safety review yet. SkillMD never runs a skill's scripts for you; review the SKILL.md before installing.

Which AI agents work with Math Help?

This skill is tagged as working with Claude Code, Claude.ai, OpenAI Codex. SKILL.md is an open format, so most agents that read a skills directory can load it too.

Is Math Help free to use?

Yes. Installing skills from SkillMD is free, and the skill stays under its author's original license.

Who published Math Help?

DojoGenesis (@dojogenesis) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Math Help by dojogenesis — Agent Skill

Name: Math Help
Author: DojoGenesis

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 this	Example
Solve equations	sympy_compute.py solve	`solve "x**2 - 4 = 0" --var x`
Integrate/differentiate	sympy_compute.py	`integrate "sin(x)" --var x`
Compute limits	sympy_compute.py limit	`limit "sin(x)/x" --var x --to 0`
Matrix operations	sympy_compute.py / numpy_compute.py	`det "[[1,2],[3,4]]"`
Verify a reasoning step	math_scratchpad.py verify	`verify "x = 2 implies x^2 = 4"`
Check a proof chain	math_scratchpad.py chain	`chain --steps '[...]'`
Get progressive hints	math_tutor.py hint	`hint "Solve x^2 - 4 = 0" --level 2`
Generate practice problems	math_tutor.py generate	`generate --topic algebra --difficulty 2`
Prove a theorem (constraints)	z3_solve.py prove	`prove "x + y == y + x" --vars x y`
Check satisfiability	z3_solve.py sat	`sat "x > 0, x < 10, x*x == 49"`
Optimize with constraints	z3_solve.py optimize	`optimize "x + y" --constraints "..."`
Plot 2D/3D functions	math_plot.py	`plot2d "sin(x)" --range -10 10`
Arbitrary precision	mpmath_compute.py	`pi --dps 100`
Numerical optimization	scipy_compute.py	`minimize "x*2 + 2x" "5"`
Formal machine proof	Lean 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

Level	Category	What You Get
1	Conceptual	General direction, topic identification
2	Strategic	Approach to use, technique selection
3	Tactical	Specific steps, intermediate goals
4	Computational	Intermediate results, partial solutions
5	Answer	Full 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

Solve with sympy_compute.py
Verify solution with math_scratchpad.py
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

Generate practice problem with math_tutor.py
Use progressive hints (level 1, then 2, etc.)
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

Check theorem with z3_solve.py (constraint-level proof)
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

Math Help

File contents

Math Cognitive Stack Guide

Quick Reference

The Five Layers

Layer 1: SymPy (Symbolic Algebra)

Layer 2: Z3 (Constraint Solving & Theorem Proving)

Layer 3: Math Scratchpad (Reasoning Verification)

Layer 4: Math Tutor (Educational)

Layer 5: Lean 4 (Formal Proofs)

Numerical Tools

NumPy (160 functions)

SciPy (289 functions)

mpmath (153 functions, arbitrary precision)

Visualization

math_plot.py

Educational Features

5-Level Hint System

Step-by-Step Solutions

Common Workflows

Workflow 1: Solve and Verify

Workflow 2: Learn a Concept

Workflow 3: Prove and Formalize

Choosing the Right Tool

Related Skills

Requirements

Frequently asked questions

Math Help

File contents

Math Cognitive Stack Guide

Quick Reference

The Five Layers

Layer 1: SymPy (Symbolic Algebra)

Layer 2: Z3 (Constraint Solving & Theorem Proving)

Layer 3: Math Scratchpad (Reasoning Verification)

Layer 4: Math Tutor (Educational)

Layer 5: Lean 4 (Formal Proofs)

Numerical Tools

NumPy (160 functions)

SciPy (289 functions)

mpmath (153 functions, arbitrary precision)

Visualization

math_plot.py

Educational Features

5-Level Hint System

Step-by-Step Solutions

Common Workflows

Workflow 1: Solve and Verify

Workflow 2: Learn a Concept

Workflow 3: Prove and Formalize

Choosing the Right Tool

Related Skills

Requirements

Related skills

Frequently asked questions

How do I install the Math Help skill?

What does the Math Help skill do?

Is Math Help safe to use?

Which AI agents work with Math Help?

Is Math Help free to use?

Who published Math Help?