You've seen this before.
You ask your AI agent: "Find ∫ x·e^x dx"
It confidently replies: e^x + C, complete with a plausible-looking derivation. You nod. Then you check — the correct answer is (x−1)·e^x + C. It was wrong by a mile, and you almost shipped it.
This is the fundamental problem with AI math today: LLMs can talk, but they can't verify their own work. They sound convincing while being catastrophically wrong. And the more complex the problem, the better the hallucination.
Math.skill changes that. It's an open-source mathematical reasoning skill for AI agents — install it, and your agent stops guessing and starts verifying.
What Makes It Different
| Typical AI Math Plugin | Math.skill | |
|---|---|---|
| Workflow | Prompt → LLM → answer | Prompt → 7-step pipeline → ≥2 verifications → answer |
| Verification | None | Answer blocked if verification fails |
| Open problems | Might hallucinate a "solution" | Honestly says "this is unsolved" |
| Error recovery | No mechanism | Auto-backtrack, fix, recompute, re-verify |
The core differentiator: a verification engine that runs at least 2 of 11 independent checks on every answer. No answer leaves the pipeline unverified. Period.
The 7-Step Pipeline
Every problem flows through this:
| Step | What Happens | Why It Matters |
|---|---|---|
| 1. Parse | Extract conditions, goals, variables, implicit domain constraints | Catches misread problems before they waste your time |
| 2. Model | Build formal representation: equation, function, matrix, probability space, etc. | Prevents building the wrong mathematical structure |
| 3. Select | Choose the optimal method from 30+ strategies | Avoids brute-forcing when elegance exists |
| 4. Solve | Step-by-step with mathematical justification at every transformation | Full traceability — nothing hidden |
| 5. Verify | Apply ≥2 of 11 independent verification methods | The differentiator — catches what LLMs miss |
| 6. Correct | If verification fails: backtrack to last known-good step, fix, recompute, re-verify | No "doubling down" on wrong answers |
| 7. Deliver | Exact answer (not approximate), domain conditions, verification summary | You know it's right, and you know why |
The Verification Engine: 11 Independent Methods
This is the heart of Math.skill. Each method catches a different class of errors:
| ID | Method | What It Catches |
|---|---|---|
| A | Back-substitution | Extraneous roots, sign errors — plug the answer back in |
| B | Domain check | Division by zero, negative radicands, log(0), arcsin(2) |
| C | Boundary analysis | Missed interval endpoints, parameter edge cases |
| D | Reverse derivation | Irreversible step errors — work backwards from answer |
| E | Numerical sampling | Coefficient drift, off-by-factor — test with specific values |
| F | Dimensional analysis | Unit mismatches, P > 1, variance < 0 |
| G | Limits & special cases | Degenerate behavior as parameters approach 0 or ∞ |
| H | Cross-validation | Solve with a completely different independent method |
| I | Counterexample search | Disprove false universal claims by construction |
| J | Formal logic check | ∀∃ order errors, necessary vs. sufficient, circular reasoning |
| K | Computational consistency | det(A−λI) = 0, total probability = 1, trace = sum of eigenvalues |
At least two methods per problem. The engine selects which ones based on the problem type. You don't have to think about it — it just works.
34 Math Categories. One Skill.
Math.skill covers everything from arithmetic to abstract algebra. Each category has its own verification protocol and common-error checklist:
Arithmetic · Algebra · Equations/Inequalities · Functions
Geometry · Trigonometry · Sequences · Combinatorics
Probability/Statistics · Limits · Differentiation · Integration
Multivariable Calculus · Linear Algebra · ODEs
Complex Analysis · Real Analysis · Abstract Algebra
Topology · Number Theory · Discrete Math · Optimization
Mathematical Modeling · Proofs · Counterexamples
Solution Checking · Problem Generation · Research-Level Problems
Not a one-size-fits-all. Each category gets targeted handling.
It Won't Lie About Unsolved Problems
Ask it to "prove the Riemann Hypothesis" and you won't get a hallucinated Nobel-worthy breakthrough. You'll get:
"This is a known open problem. Here's what I can provide: partial results, known bounds, and why this remains unsolved."
Honesty is the baseline. If a problem is open, it says so. If it can only give partial results, it clearly labels what's proven vs. conjectured.
Preemptive Error Prevention: 8 Guard Categories
The most common AI math failures are blocked before they happen:
- Algebra: Check division by zero before dividing. Verify roots after squaring. Re-expand after factoring.
- Inequalities: Sign reversal on multiply-by-negative. Case analysis for variable expressions.
- Functions: Find domain first. Distinguish critical points from extrema. Check non-differentiable points.
- Probability: Reject P ∉ [0,1]. Reject negative variance. Verify total probability = 1.
-
Calculus: Verify L'Hôpital conditions. State Taylor remainder order. Always add
+C. Check improper integral convergence. - Linear Algebra: Check matrix dimensions. Verify Av = λv. Verify A = PDP⁻¹.
- Geometry: Don't rely on visual intuition. State theorem conditions explicitly. Explain auxiliary constructions.
- Abstract Math: Verify all definition components. Check quantifier order (∀ε∃δ ≠ ∃δ∀ε). Verify well-definedness.
One Command to Install
npx skills add Wholiver/Math.Skill
That's it. No config. No API keys. No dependencies to wrestle with.
Works with: Claude Code · GitHub Copilot · Cursor · Windsurf · Codex · OpenCode — any AI agent that supports skills.sh.
MIT Licensed. Free to use. Free to modify. Free to ship with your product.
Who Is This For?
- Students — homework help with verified solutions. Learn the how and the why, not just the answer.
- Teachers — generate well-posed problems with full solutions. Check student answers against verified references.
- Researchers — quickly validate intermediate derivations. Catch errors before they propagate into your paper.
- Developers — if your AI coding agent touches math, stop it from hallucinating incorrect calculations.
- Everyone who's been burned by AI math — you know the feeling. This is the antidote.
The Bottom Line
Your AI agent is brilliant at many things. Math isn't one of them — unless you give it the right tools.
Math.skill gives your agent what it's missing: a mathematician's discipline. Parse, model, solve, verify, correct, deliver. Every time. No exceptions.
"One question. A verified answer."
npx skills add Wholiver/Math.Skill