Dan Abramov vibes Conway conjecture proof in Lean

Abramov’s proof reveals that human steering combined with formal verification can push LLMs to solve open math problems, but unconstrained multi-agent swarms quickly degenerate without rigid ground-truth feedback.

• –Lean 4 served as the indispensable truth engine, filtering out plausible-sounding hallucinations and pseudo-proofs that models repeatedly generated.
• –Multi-agent collaboration without formal boundaries suffered severe epistemic drift, manufacturing private jargon and circular reasoning until partitioned into adversarial auditing and isolated verification roles.
• –Burning an estimated 40 billion tokens (~$40,000 API equivalent) highlights the massive brute-force compute and steering overhead still required to keep reasoning models aligned on complex goals.
• –Strict architectural hygiene—such as separating peer-reviewed reference formalization from speculative lemma generation in isolated worktrees—was essential to prevent context contamination.