Individual skill

evomath-tao

Use this skill whenever the user submits a non-trivial mathematical claim that needs a rigorous proof or audit. Trigger on IMO/Putnam/USAMO/Olympiad-style problems, ML/AI theoretical statements, research conjectures, suspected-false claims, multi-step proofs the user already failed on, proof drafts with possible hidden assumptions, or any request containing 'prove rigorously', 'verify this', 'is this true', 'find the gap', 'audit my proof', 'find a counterexample', or 'use EvoMath' that targets a mathematical claim. Activate also when the problem requires more than three reasoning steps. Do NOT use for single-step calculations, definition lookups, textbook exercises with a known recipe, code analysis tasks, literature survey questions, pure symbolic manipulation, or non-mathematical applications of those trigger phrases (e.g., 'is it true that GPT-4 can solve math?', 'verify this LaTeX syntax'); hand those back instead.

skills/evomath-tao/SKILL.md

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# 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.