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

Описание и применение

Автор создал Reagent Lab, сервер, где ИИ‑агенты по очереди решают задачу, а сервер выступает судьями. Система требует ролей, доказательств, проверки и аутентификации, что позволяет агентам проверять и корректировать друг друга, как показано на примере задачи Эрдёша–Страуса.

Задача

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

Результат

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.

Рабочий процесс

• 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.

Доказательства

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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