# Select Tractable Problem

> Filter open math problems for agent attackability: prefer actively discussed problems, demote those tied to major conjectures or requiring new theory. Use before long proof runs or when the user asks which Erdős/open problems to attempt.

- Skill: `meleantonio/select-tractable-problem` (Agent Skill)
- Install (CLI): `npx skillmds@latest add meleantonio/select-tractable-problem`
- Raw SKILL.md: https://api.skillmd.com/api/skills/meleantonio/select-tractable-problem/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- Author: meleantonio (https://skillmd.com/u/meleantonio)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/meleantonio/select-tractable-problem

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# Select a tractable open problem

Problem selection is the first secret of the workflow: burn long compute only
on problems that are cared about **and** plausibly within reach of current
agent search, not on fortress conjectures.

## Prefer

- Problems with recent active discussion by working mathematicians (forums,
  blogs, Tao/Bloom-style commentary, seminar notes).
- Sharply stated yes/no or exact-constant questions (clear success criterion).
- Problems where finite checks, constructions, or elementary/analytic toolkit
  pieces are known to matter.
- Instances where weaker order-of-magnitude results already exist (room for a
  sharp resolution without inventing a field).

## Demote or reject

- Clear special cases of RH, Twin Prime, Collatz-class, or other celebrity
  conjectures unless the user explicitly wants a partial conditional result.
- Problems whose community notes say “equivalent to …” a major open statement.
- Vague “describe the structure of all …” targets without a principal binary
  or asymptotic question.
- Problems that triage (below) rates as needing a new theory or decades of
  domain-specific machinery.

## AI triage prompt

Run this against one or more strong models; keep independence if using several:

```text
You are triaging an open mathematical problem for an autonomous proof agent.

Problem statement:
[STATEMENT]

Source / community notes:
[NOTES]

Answer with:
1. Care score (0–5): how much active research attention this problem has.
2. Fortress score (0–5): how tightly it is tied to a major named conjecture.
3. Theory-need score (0–5): likelihood a solution needs a new theory vs known tools.
4. Success-criterion clarity (0–5): how crisp the yes/no or exact-target is.
5. Agent-attackability (0–5): candid estimate for long multi-agent search with
   adversarial audit, not single-shot prompting.
6. Go / Conditional / No-go recommendation with one paragraph of reasons.
7. If Conditional: what narrowed principal question would be attackable.
```

## Decision rule

| Care | Fortress | Theory-need | Clarity | Action |
|------|----------|-------------|---------|--------|
| ≥3 | ≤2 | ≤3 | ≥4 | **Go** |
| ≥3 | ≤3 | ≤4 | ≥3 | **Conditional** (narrow the principal question) |
| else | | | | **No-go** (propose alternatives) |

Record the triage table in `problems/<id>/STATUS.md` before any long run.