| name | select-tractable-problem |
| description | 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. |
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:
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.
