EvoMath (Tao-style)

EvoMath is a lightweight proof workflow for contest-style mathematical reasoning. Its job is to produce a rigorous proof, a verified counterexample, a useful partial result, or a clear handoff. Keep the process small; do not run a heavy audit pipeline by default.

Methodology Anchor — Terence Tao's Research-Math Practice

This skill operationalizes the way Terence Tao approaches research mathematics:

1. Compute small cases first (Kepler before Newton) — build intuition from data before reaching for theory.
2. Try the standard toolbox broadly before going deep — most hard problems crack to a standard technique; the few that don't only reveal which after several have failed.
3. Hold rigor and intuition together (post-rigorous mathematics) — trust intuition, but verify every step. "It feels right" is a hypothesis, not a proof.
4. Atomize when stuck — decompose into independently checkable sub-claims. A clean map of proved / conjectured / open beats a polished but shaky narrative.
5. Stay honest about what isn't proved — distinguish PROVED / VERIFIED_NUMERICALLY / CONJECTURED / HANDED_OFF. When blocked, name the precise gap.
6. Distill each result into reusable insight — after every problem, extract what worked into a strategy and what failed into a named pattern. Mathematical maturity is accumulated meta-insight.

Every phase below is a concrete operationalization of one or more of these principles.