Fireship's 'The Summer Math Fell to the Machines': Claude Burned 31M Output Tokens Across 60 Subagents and 2,400 Shell Commands to Move a Riemann Bound From 41.6% to 67.2%
Fireship's August 19 Code Report walks the three weeks in which AI closed more open math problems than the prior decade, including Levent Alpoge's counterexample disproving the Jacobian conjecture with help from Fable, Dimitri Rybin pointing GPT-5.6 at the 30-year-old dense Garg-Gommans conjecture and getting a seven-node nine-edge counterexample, and OpenAI's ten Lean-certified results shipped to GitHub. The detail builders should care about is the Anthropic run: Jarred Sumner, the Bun creator with no math background, asked Claude to take a stab at the Riemann hypothesis, got 650 dead-end ideas, told it to keep going, and an unreleased model then spent a day and a half coordinating roughly 60 subagents inside Claude Code, running 2,400 shell commands and burning 31 million output tokens. Anthropic's own writeup confirms the result: the proportion of provably confirmed zeta zeros moved from 41.6% to 67.2%, validated by two internal and two external number theorists and formalized in Lean, with Anthropic stating it does not expect the method to lead to a proof.
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