math
Unified math capabilities - computation, solving, and explanation. I route to the right tool.
When & Why to Use This Skill
This Claude skill provides a comprehensive, unified interface for advanced mathematical computation, symbolic solving, and conceptual explanations. By integrating powerful engines like SymPy for symbolic math, Z3 for constraint solving, and Pint for unit conversions, it transforms Claude into a high-performance mathematical assistant capable of handling everything from basic algebra to complex theoretical analysis.
Use Cases
- Symbolic Computation: Solving complex algebraic equations, performing calculus (integrals, derivatives, limits), and simplifying intricate mathematical expressions.
- Linear Algebra & Matrix Operations: Computing eigenvalues, eigenvectors, determinants, and performing matrix decompositions for engineering or data science tasks.
- Constraint Solving & Logic: Verifying if mathematical inequalities are always true or finding optimal values subject to specific constraints using the Z3 theorem prover.
- Scientific Unit Conversion: Converting between diverse physical units and measurement systems with high precision for scientific and technical workflows.
- Academic Tutoring: Providing deep conceptual explanations for advanced topics such as Category Theory, Real Analysis, Topology, and Differential Equations.
| name | math |
|---|---|
| description | Unified math capabilities - computation, solving, and explanation. I route to the right tool. |
| triggers | ["calculate", "compute", "solve", "integrate", "derivative", "eigenvalue", "matrix", "simplify", "factor", "limit", "series", "differential equation", "unit convert", "explain", "what is", "how does"] |
| allowed-tools | [Bash, Read, Write] |
| priority | high |
/math - Unified Math Capabilities
One entry point for all computation and explanation. I route to the right tool based on your request.
For formal proofs, use /prove instead.
Quick Examples
| You Say | I Use |
|---|---|
| "Solve x² - 4 = 0" | SymPy solve |
| "Integrate sin(x) from 0 to π" | SymPy integrate |
| "Eigenvalues of [[1,2],[3,4]]" | SymPy eigenvalues |
| "Is x² + 1 > 0 for all x?" | Z3 prove |
| "Convert 5 miles to km" | Pint |
| "Explain what a functor is" | Category theory skill |
Computation Scripts
SymPy (Symbolic Math)
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" <command> <args>
| Command | Description | Example |
|---|---|---|
solve |
Solve equations | solve "x**2 - 4" --var x |
integrate |
Definite/indefinite integral | integrate "sin(x)" --var x --lower 0 --upper pi |
diff |
Derivative | diff "x**3" --var x |
simplify |
Simplify expression | simplify "sin(x)**2 + cos(x)**2" |
limit |
Compute limit | limit "sin(x)/x" --var x --point 0 |
series |
Taylor expansion | series "exp(x)" --var x --point 0 --n 5 |
dsolve |
Solve ODE | dsolve "f''(x) + f(x)" --func f --var x |
laplace |
Laplace transform | laplace "sin(t)" --var t |
Matrix Operations:
| Command | Description |
|---|---|
det |
Determinant |
eigenvalues |
Eigenvalues |
eigenvectors |
Eigenvectors with multiplicities |
inverse |
Matrix inverse |
transpose |
Transpose |
rref |
Row echelon form |
rank |
Matrix rank |
nullspace |
Null space basis |
linsolve |
Linear system Ax=b |
charpoly |
Characteristic polynomial |
Number Theory:
| Command | Description |
|---|---|
factor |
Factor polynomial |
factorint |
Prime factorization |
isprime |
Primality test |
gcd |
Greatest common divisor |
lcm |
Least common multiple |
modinverse |
Modular inverse |
Combinatorics:
| Command | Description |
|---|---|
binomial |
C(n,k) |
factorial |
n! |
permutation |
P(n,k) |
partition |
Integer partitions p(n) |
catalan |
Catalan numbers |
bell |
Bell numbers |
Z3 (Constraint Solving)
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/z3_solve.py" <command> <args>
| Command | Use Case |
|---|---|
sat |
Is this satisfiable? |
prove |
Is this always true? |
optimize |
Find min/max subject to constraints |
Pint (Units)
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py" convert <value> <from_unit> <to_unit>
Example: convert 5 miles kilometers
Math Router (Auto-Route)
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/math_router.py" route "<natural language request>"
Returns the exact command to run. Use when unsure which script.
Topic Skills (For Explanation)
When the request is "explain X" or "what is X", I reference these:
| Topic | Skill Location | Key Concepts |
|---|---|---|
| Abstract Algebra | math/abstract-algebra/ |
Groups, rings, fields, homomorphisms |
| Category Theory | math/category-theory/ |
Functors, natural transformations, limits |
| Complex Analysis | math/complex-analysis/ |
Analytic functions, residues, contour integrals |
| Functional Analysis | math/functional-analysis/ |
Banach spaces, operators, spectra |
| Linear Algebra | math/linear-algebra/ |
Matrices, eigenspaces, decompositions |
| Mathematical Logic | math/mathematical-logic/ |
Propositional, predicate, proof theory |
| Measure Theory | math/measure-theory/ |
Lebesgue, σ-algebras, integration |
| Real Analysis | math/real-analysis/ |
Limits, continuity, convergence |
| Topology | math/topology/ |
Open sets, compactness, connectedness |
| ODEs/PDEs | math/odes-pdes/ |
Differential equations, boundary problems |
| Optimization | math/optimization/ |
Convex, LP, gradient methods |
| Numerical Methods | math/numerical-methods/ |
Approximation, error analysis |
| Graph/Number Theory | math/graph-number-theory/ |
Graphs, primes, modular arithmetic |
| Information Theory | math/information-theory/ |
Entropy, coding, channels |
Routing Logic
I decide based on your request:
"solve/calculate/compute" → SymPy (exact symbolic)
"is X always true?" → Z3 (constraint proving)
"convert units" → Pint
"explain/what is" → Topic skill for context
"prove formally" → Redirect to /prove
Examples
Solve Equation
User: Solve x² - 5x + 6 = 0
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" solve "x**2 - 5*x + 6" --var x
Result: x = 2 or x = 3
Compute Eigenvalues
User: Find eigenvalues of [[2, 1], [1, 2]]
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" eigenvalues "[[2,1],[1,2]]"
Result: {1: 1, 3: 1} (eigenvalue 1 with multiplicity 1, eigenvalue 3 with multiplicity 1)
Prove Inequality
User: Is x² + y² ≥ 2xy always true?
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/z3_solve.py" prove "x**2 + y**2 >= 2*x*y"
Result: PROVED (equivalent to (x-y)² ≥ 0)
Convert Units
User: How many kilometers in 26.2 miles?
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py" convert 26.2 miles kilometers
Result: 42.16 km
When to Use /prove Instead
Use /prove when you need:
- Machine-verified formal proof (Lean 4)
- Category theory proofs (functors, Yoneda, etc.)
- Publication-quality verification
- Abstract algebra proofs
/math is for computation. /prove is for verification.