10 Claude agents prove 122-year-old Thomson problem N=7 in 15-hour overnight run with 17,895-line Lean proof

新智元 · wechat · 2026-09-30

ValsAI researcher Hung Tran tasked 10 Claude Sonnet 5.5 agents with formally proving the N=7 Thomson problem — that the pentagonal bipyramid is the minimum-energy arrangement of 7 electrons on a sphere — a question open since 1904.

Fully autonomous: given only two Lean theorem statements and nine exploration directions, the agents exchanged 1,270 messages over 15 hours, self-organized, and one agent took on an integrator role merging verified parts into Solution.lean
The 17,895-line proof splits configuration space by the minimum inner product m between electron pairs, handles each region with certified bounds, and rounds all numerical certificates to exact integers/rationals — eliminating floating-point error entirely
Verification: Lean kernel compiled in 599s; independent kernel nanoda checked 47,854 declarations with zero errors; flipping a single integer breaks the build

The experiment signals AI moving from solving problems to conducting research: route-finding, parallel exploration, adjudication, code merging, and machine-checked acceptance — all without human intervention.

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10 Claude agents prove 122-year-old Thomson problem N=7 in 15-hour overnight run with 17,895-line Lean proof

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