evomath-tao
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:
- Compute small cases first (Kepler before Newton) — build intuition from data before reaching for theory.
- 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.
- Hold rigor and intuition together (post-rigorous mathematics) — trust intuition, but verify every step. "It feels right" is a hypothesis, not a proof.
- Atomize when stuck — decompose into independently checkable sub-claims. A clean map of proved / conjectured / open beats a polished but shaky narrative.
- Stay honest about what isn't proved — distinguish PROVED / VERIFIED_NUMERICALLY / CONJECTURED / HANDED_OFF. When blocked, name the precise gap.
- 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.
More from evoscientist/evoskills
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Guides self-review of YOUR OWN academic paper before submission with adversarial stress-testing. Core method: 5-aspect checklist (contribution sufficiency, writing clarity, results quality, testing completeness, method design), counterintuitive protocol (reject-first simulation, delete unsupported claims, score trust, promote limitations, attack novelty), reverse-outlining, and figure/table quality checks. Use when: user wants to self-review or self-check their own paper draft before submission, stress-test their claims, prepare for reviewer criticism, or mentions 'self-review', 'check my draft', 'is my paper ready'. Do NOT use for writing a peer review of someone else's paper, and do NOT use after receiving actual reviews (use paper-rebuttal instead).
290paper-writing
Guides writing academic papers section by section using an 11-step workflow with LaTeX templates and counterintuitive writing tactics. Covers Abstract, Introduction, Method, Experiments, Related Work, Conclusion, and Supplementary. Use when: user asks to write or draft a paper section, needs LaTeX templates, wants to improve academic writing quality, optimize novelty framing, or mentions 'write introduction', 'draft method', 'paper writing'. Do NOT use for pre-submission review (use paper-review), experiment execution (use experiment-pipeline), or paper planning/story design (use paper-planning).
268paper-rebuttal
Guides writing effective rebuttals after receiving peer review feedback. Covers review diagnosis (score-driven color-coding), response strategy (champion identification, common-theme consolidation), tactical writing (18 rules), and counterintuitive rebuttal principles. Use when: user received reviewer scores/comments, needs to write a rebuttal or author response, wants to respond to specific criticism (e.g. 'limited novelty', 'missing baselines'), mentions 'rebuttal', 'reviewer comments', 'author response', or 'respond to reviewers'. Do NOT use for pre-submission self-review (use paper-review instead).
264paper-planning
Guides pre-writing planning for academic papers with 4 structured steps: story design (task-challenge-insight-contribution-advantage), experiment planning (comparisons + ablations), figure design (pipeline + teaser), and 4-week timeline management. Includes counterintuitive planning tactics (write a mock rejection letter to identify weaknesses before writing, narrow before broad claims, design ablations first). Use when: user wants to plan a paper before writing, design story/contributions, plan experiments, create figure sketches, set a writing timeline, or write a pre-emptive rejection letter for planning purposes. Do NOT use for actual writing (use paper-writing), running experiments (use experiment-pipeline), self-reviewing a finished draft (use paper-review), or finding research problems (use research-ideation).
256research-ideation
End-to-end research ideation pipeline: literature grounding → multi-track idea generation (3 personas: innovator/pragmatist/critic) → iterative refinement → ELO tournament ranking → update evo-memory (IDE) → user selects direction → expand into manuscript-quality proposal. Use when: user wants to find a research direction, brainstorm ideas, evaluate idea novelty, design a novel solution, rank/compare research ideas, or generate a research proposal. Do NOT use for finding/searching/reading papers (use paper-navigator), literature survey reports (use research-survey), or planning a paper (use paper-planning).
254experiment-pipeline
Guides structured 4-stage experiment execution with attempt budgets and gate conditions: Stage 1 initial implementation (reproduce baseline), Stage 2 hyperparameter tuning, Stage 3 proposed method validation, Stage 4 ablation study. Integrates with evo-memory (load prior strategies, trigger IVE/ESE) and experiment-craft (5-step diagnostic on failure). Use when: user has a planned experiment, needs to reproduce baselines, organize experiment workflow, or systematically validate a method. Do NOT use for debugging a specific experiment failure (use experiment-craft) or designing which experiments to run (use paper-planning).
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