Polymath

Polymath Split-Brain Workflow

A meta-method for mapping the possibility space of a problem before committing to an approach. Forces uncorrelated views by spawning parallel agents that each see the problem through a different disciplinary lens. The value comes from the spread of returned ideas, not from averaging them -- disagreement is the signal.

What You Get

• Landscape map: N sub-agent outputs covering uncorrelated disciplinary lenses
• Synthesis of disagreements in structured template (not averaged consensus)
• Actionable divergence points highlighting where frames conflict

Killer items -- silent failures if skipped

These are load-bearing. Skipping any produces output that looks successful but is wrong:

• [K1] Step 0 triage produced an explicit go-decision -- without this, the workflow burns lenses on a problem that didn't need them.
• [K2] Step 2 rosters were built by THREE PARALLEL sub-agents (close/mid/far tiers), each running max-distance walk within its tier WITHOUT looking at the problem's specific features -- without this, orchestrator bias leaks into tier construction and the composed polymath personas lose their spread.
• [K3] Step 7 pre-spawn checklist was filled out and announced to the user before any sub-agent call -- without this, the user has no chance to correct the framing or refuse the cost.
• [K4] All sub-agent dispatches went out in a SINGLE message with multiple tool blocks -- sequential dispatch silently wastes 10x wall-time.
• [K5] Each agent's brief contains a self-contained CONTEXT block with all 5 required sub-slots filled -- without this, agents confabulate from thin air.
• [K6] Synthesis followed the mandatory output template (Step 9), not free prose -- without this, "do not average" gets violated by accident.

When this is the right tool

Use ONLY when ALL hold: the problem is research/strategy/framing-level; the "right" frame is genuinely unknown; the cost of picking the wrong frame is high; a single deep Agent call would not suffice (value is in spread, not depth on one axis).

DO NOT use when: the problem is well-defined; the user needs a specific factual answer; the user is debugging a specific error/build/syntax; the user wants K<5 ideas (use a single Agent); the output would fit in one paragraph; the harness forbids parallel sub-agent spawning.

The core insight

Adjacent domains share assumptions with the substrate. You need lenses whose objects look the same as yours but whose intuitions are different -- isomorphism, not analogy. The generative move is parallel max-distance walks at three relatedness tiers (close/mid/far), then composing each agent as a polymath expert carrying one domain from each tier.

See core-insight.md for the full explanation of three-tier stratification and the isomorphism test.

Reading guide