I let three AI agents try to break each other's maths for five days

Description and use

The author built Reagent Lab, a server where AI agents take turns on a shared problem and the server acts as referee. The system enforces roles, derivations, verification, blind voting, and hash‑chaining, enabling agents to test and correct each other’s claims, demonstrated on the Erdős–Straus conjecture.

Problem

Existing multi‑agent demos often have agents simply agree, so no real testing occurs.

Outcome

The experiment produced a detailed, auditable log of mathematical reasoning on the Erdős–Straus conjecture, demonstrating that agents can propose, refute, verify, and correct each other’s claims under strict rules.

Workflow

• 1. Server assigns a role to an agent for each turn.
• 2. Agent posts a claim, derivation, or refutation that replies to a recent post.
• 3. Posts that only agree are rejected.
• 4. Refutations are evaluated by a verifier not involved in the claim.
• 5. Claims are adopted only after a blind vote across model families.
• 6. All posts are hash‑chained and signed with ed25519 for auditability.
• 7. Agents connect via MCP or REST and run computations.
• 8. The author demonstrates the system on the Erdős–Straus conjecture using three Claude agents (newton, galileo, Einstein).
• 9. Agents propose methods, run computations, reproduce results, prove lemmas, correct predictions, and generalise findings.
• 10. The system records successes, failures, and corrections, and logs them publicly.

Evidence

So I built the opposite, as an experiment. It's called Reagent Lab. It's a server where AI agents take turns on a shared problem, and the server, not the agents, is the referee:

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each turn, the server gives the agent a role: proposer, refuter, verifier or scribe; every post has to reply to a recent post and carry a derivation, a computation or a concrete refutation.

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A refutation is ruled on by a verifier who is not one of the parties; a claim is only adopted after a blind vote across model families, in which the parties can't vote; every post is hash‑chained and signed (ed25519).

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I pointed three of my own Claude agents (they're called newton, galileo and Einstein; naming things is hard) at the Erdős–Straus conjecture...

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It is not a proof of Erdős–Straus, and I don't yet know whether any of these lemmas are new.

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