math-help
Reference guide to choosing the correct tools for specific mathematical and computational tasks.
Install
mkdir -p .claude/skills/math-help && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/2125" && unzip -o skill.zip -d .claude/skills/math-help && rm skill.zipInstalls to .claude/skills/math-help
Activation
This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.
Guide to the math cognitive stack - what tools exist and when to use eachKey capabilities
- →Solve algebraic equations and perform calculus operations
- →Verify logical reasoning steps and proof chains
- →Check constraint satisfiability and optimize functions
- →Generate educational practice problems and progressive hints
- →Plot 2D and 3D mathematical functions
How it works
The skill maps mathematical tasks to a five-layer stack of specialized Python scripts, including SymPy for symbolic algebra, Z3 for constraint solving, and a scratchpad for reasoning verification.
Inputs & outputs
When to use math-help
- →Choosing a math solver library
- →Verifying a logic proof
- →Finding tools for numerical optimization
About this skill
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 + 2*x" "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
/mathor/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
When not to use it
- →Tasks requiring formal machine-verified proofs beyond the scope of Z3
- →Situations where the user lacks the required Python environment
Prerequisites
Limitations
- →Numerical tools provide approximate rather than symbolic answers
- →Requires specific script invocation for each mathematical layer
How it compares
It provides a programmatic interface for specific mathematical domains instead of relying on general-purpose calculators or manual derivation.
Compared to similar skills
math-help side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| math-help (this skill) | 9 | 7mo | Review | Beginner |
| exploratory-data-analysis | 15 | 2mo | Review | Intermediate |
| model-compare | 7 | 7mo | Review | Advanced |
| astropy | 6 | 7mo | Review | Advanced |
Try saying
Example prompts that trigger this skill in your AI assistant.
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