solve-math git:20261104.7999338A

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---
name: solve-math
description: How to approach a math problem (Mathematician role and any model)
---
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# Procedure — solving a math question

## Step 1 — recall before reasoning

Before you compute anything, `pool math:<subfield> recall <topic>` for prior techniques. Subfields: `math:algebra`, `math:combinatorics`, `math:geometry`, `math:number-theory`, `math:calculus`, `math:probability`. If you find a relevant pattern, follow it.

## Step 2 — never trust mental arithmetic

Use the `calc` tool for every numeric computation, even simple ones. Mental math is a confidence trap. `calc` is exact and fast. Examples:

- `calc 17 * 23` → 391
- `calc polynomialRoot(6, -5, 1)` → roots of x^2 − 5x + 6 (coefficients constant term first) → [3, 2]
- `calc lusolve([[1,2],[3,4]], [5,6])` → solution of a linear system
- `calc simplify('x*2 + 3*x')`, `calc derivative('x^2', 'x')` → symbolic forms take the expression as a string
- `calc combinations(10, 3)`, `calc gcd(360, 420)`, `calc 17 mod 5`

## Step 3 — verify with an independent calc

Before committing to an answer, run a SECOND calc that gets to the same result by a different route. If they disagree, you have a bug — find it before answering.

## Step 4 — answer in the format the caller wants

- Numeric answer requested → bare number, no explanation in the final answer message.
- Multiple-choice math → letter only.
- If the caller didn't specify, default to bare answer with a one-line "by <method>" justification.

## Step 5 — deposit what you learned

If you discovered a useful technique (a substitution, a known identity, a counting trick), `pool math:<subfield> add <one-line summary>`. Future Mathematicians (you or successors) will find it. Store the technique only — never the problem, its numbers or its answer.

## Anti-patterns

- Don't show a 5-step worked solution in a `tell Sender` reply unless they asked. They want the answer.
- Don't hedge a result you verified with `calc` — that IS your answer. When you could not verify it, say so in one line.