Skip to content

README.md

Latest commit

 

History

History
112 lines (80 loc) · 3.93 KB

README.md

File metadata and controls

112 lines (80 loc) · 3.93 KB
Raw

Discover Math Problems

Chinese guide: README.zh-CN.md

discover-math-problems helps a coding agent turn fuzzy mathematical background into a concrete research-state packet.

When To Use It

Use this skill when you have:

  • scattered notes, definitions, examples, or failed proof attempts;
  • an open-ended mathematical direction but no clear problem ranking;
  • immature theorem ideas that need counterexample pressure before proof work;
  • a need for a resumable record of conjectures, evidence, and uncertainty.

What It Produces

The agent should produce ranked problem menus, conjecture lattices, evidence ledgers, counterexample pressure notes, proof obligations, work orders, and a research_state_packet.

Skill Entry Points

Load this package directory when using it directly:

discover-math-problems/

Core files:

  • SKILL.md: shared Skill layer and main entrypoint.
  • agents/openai.yaml: agent metadata.
  • references/autonomous-research-protocol.md: end-to-end discovery loop.
  • references/conjecture-generation-protocol.md: conjecture lattice and stress testing.
  • references/artifact-contract.md: artifact names, fields, and status labels.

Installation

Copy this to your coding agent:

Please install the `discover-math-problems` skill from https://github.com/VeryMath/AI4Math-Auto-Research.git. Read the package `SKILL.md`, install the declared Skill entrypoint, verify that `$discover-math-problems` is discoverable, and tell me whether I need to restart the agent.

If you already have this skill repository locally, replace the repository URL with the local folder path. The coding agent should handle cloning, linking, configuration, reload/restart checks, and verification.

Quick Start

Use $discover-math-problems.

I have background notes and a few immature theorem ideas. Build a research state,
rank candidate problems, generate a conjecture lattice, pressure-test the
strongest candidates, and produce proof obligations for later review.

Useful inputs include domain background, source notes, definitions, examples, failed proof attempts, open-ended research goals, and partially formed conjectures.

How To Interact

Use a checkpoint loop:

background or immature idea
  -> background map
  -> problem menu
  -> conjecture lattice
  -> evidence ledger and counterexample pressure
  -> proof obligations
  -> approve / revise / reject / skip
  -> next discovery pass or final research-state packet

Use approve to run the proposed next discovery step, revise to adjust the domain, assumptions, source scope, or candidate ranking, reject to stop the current direction, and skip to move past a nonessential phase. The agent should ask before changing the central mathematical object, accepting a strong external theorem as a black box, discarding a user-preferred direction, spending a long run on source acquisition or computational search, or promoting a candidate to verification_ready.

Artifact Contract

Substantive discovery work should create or update:

  • background_map.md and background_map.json
  • problem_menu.md and problem_menu.json
  • conjecture_lattice.md and conjecture_lattice.json
  • evidence_ledger.json
  • counterexample_pressure.md
  • proof_obligations.md and proof_obligations.json
  • work_orders.md and work_orders.json
  • research_state_packet.json
  • human_decision_brief.md

Status labels should stay honest: background_map, candidate_problem_menu, candidate_conjecture, stress_tested_conjecture, proof_obligations_ready, or verification_ready. verification_ready means ready for verification work, not already verified. Never call a conjecture a theorem.

Maintainer Checks

Validate the Skill shape after edits:

python3 "${CODEX_HOME:-$HOME/.codex}/skills/.system/skill-creator/scripts/quick_validate.py" skills/discover-math-problems

Repository-level adapter checks live in the parent AI4Math Skill Library.