# Ten Claude agents wrote a 17,895-line proof for a 1904 physics problem > Source: > Published: 2026-09-30 06:46:04+00:00 *Ten Claude Sonnet 5.5 agents spent 15 hours proving a century-old physics puzzle in the formal language Lean, and a machine checked their work line by line. Nobody had to trust them.* In 1904, the physicist J.J. Thomson asked a deceptively simple question: if you scatter a set number of repelling charges across the surface of a sphere, what's the arrangement that costs the least energy? He was trying to work out where electrons sit inside an atom. The atomic model he was building toward turned out to be wrong, but the geometry question he left behind, now called the Thomson problem, kept mathematicians busy for over a hundred years. Exact answers exist for only a handful of small cases. Seven charges was one of the ones nobody had nailed down with a computer-checked proof, until this month. According to a report from AlphaSignal, the AI benchmarking startup Vals AI set ten instances of Anthropic's Claude Sonnet 5.5 loose on the seven-charge case in September, told them to work in Lean, the proof assistant mathematicians use when they want a computer to verify every logical step, and let them run for about 15 hours. The agents traded 1,270 messages coordinating the work between themselves. What came out the other end was a single file, Solution.lean, spanning 17,895 lines, that establishes the pentagonal bipyramid, a shape made of two pyramids glued base to base, as the unique lowest-energy configuration for seven points on a sphere, up to rotation, reflection and relabeling. That's not a claim resting on the agents' word. Lean's kernel, the small trusted core that checks every step of a formal proof against strict logical rules, accepted the file. According to AlphaSignal's account of the project, a second independent kernel implementation called nanoda also checked it, accepting all 47,854 declarations the proof produces without error. Two separately built verifiers agreeing is about as close to certainty as formal mathematics gets. The method itself is worth pausing on, because it shows the agents weren't just brute-forcing symbols. AlphaSignal reports the proof splits the problem by the smallest inner product between any two of the seven points, essentially a measure of how close two charges get to sitting on opposite sides of the sphere from each other. Configurations where no pair gets close to antipodal are handled by a single semidefinite bound involving any three points. The remaining cases get carved into five slabs and a cap, each covered by its own three-point certificate, built from exact integer or rational numbers rather than approximations. That structure follows earlier human work: the project's own documentation credits the N=8 approach from mathematicians Kryvonos, Liehr and Taylor, and a Lean formalization method from Tooby-Smith and Zughaid. The agents extended a known technique into unproven territory. They didn't invent one from nothing. [DeepSeek open sources chip tools that could let Huawei replace Nvidia in China](https://startupfortune.com/deepseek-open-sources-chip-tools-that-could-let-huawei-replace-nvidia-in-china/) DeepSeek has open sourced a full programming toolkit for Huawei's Ascend AI chips, led by TileLang, a CUDA alternative, alongside components for matrix computation, chip communication, and attention. The release follows Huawei's Ascend 910C reaching roughly 60% of Nvidia H100 inference performance and DeepSeek's decision to give Chinese... - [how to replace Nvidia with Huawei chips](https://startupfortune.com/deepseek-open-sources-chip-tools-that-could-let-huawei-replace-nvidia-in-china/) - [DeepSeek open source Huawei Ascend chip tools](https://startupfortune.com/deepseek-open-sources-chip-tools-that-could-let-huawei-replace-nvidia-in-china/) Vals AI, for its part, isn't a research lab dabbling in a side project for fun. It's an AI benchmarking company that just closed a $40 million Series A led by Andreessen Horowitz, according to TechCrunch's reporting, at a $400 million valuation. Its business is stress-testing models against hard, real tasks in law, finance and coding rather than generic trivia. A formally verified math proof is exactly the kind of demonstration that plays well for a company selling the idea that it can tell you what a model can actually do, not just what it says it can do. Here's the honest caveat, and it matters. The GitHub repository hosting the proof, at github.com/huwngtran/thomson-n7-lean, carries its own disclaimer front and center: the statement is not human-certified, and the work is not peer reviewed. That's not a small footnote. A Lean kernel can tell you that a proof is logically valid given its starting assumptions. It cannot tell you that a human mathematician correctly translated the real-world Thomson problem into those assumptions in the first place. Getting that translation, called the formalization step, wrong is exactly how a technically valid Lean proof can end up proving the wrong thing. Nobody with a math PhD has signed off on this one yet. This isn't Anthropic's first swing at using agents for pure mathematics this year, either. The company has previously described an unreleased research version of Claude coordinating around 60 subagents to push a lower bound on the Riemann hypothesis from 41.6% to 67.2%, and a separate multi-agent effort that generated 13 million lines of Lean code over eleven days to formalize Fermat's Last Theorem, producing over 30,000 theorems along the way. The Thomson problem run is smaller and faster by comparison, a day's work instead of a week and a half, but it's a third data point in the same direction: give a frontier model enough agents, enough time, and a formal language that won't let it bluff, and it can now chip away at problems that sat unsolved since before airplanes were common. Frankly, the interesting thing isn't that AI can do math. Calculators could always do math. It's that nobody had to check the agents' work by hand, because Lean did it for them, twice. **Also read:** [DeepSeek open sources chip tools that could let Huawei replace Nvidia in China](https://startupfortune.com/deepseek-open-sources-chip-tools-that-could-let-huawei-replace-nvidia-in-china/) • [China's AI hardware stocks are having their worst quarter as the rally unwinds](https://startupfortune.com/chinas-ai-hardware-stocks-are-having-their-worst-quarter-as-the-rally-unwinds/) • [OpenAI's Cheaper GPT-6.1 Sol Beats Pokemon Red's First Gym for $2.60](https://startupfortune.com/openais-cheaper-gpt-61-sol-beats-pokemon-reds-first-gym-for-260/) *This article is posted in [AI News](https://startupfortune.com/category/ai/), check it out for more related stories.* [OpenAI's Cheaper GPT-6.1 Sol Beats Pokemon Red's First Gym for $2.60](https://startupfortune.com/openais-cheaper-gpt-61-sol-beats-pokemon-reds-first-gym-for-260/) OpenAI's GPT-6.1 Sol set a new PokeBench record on September 29, clearing Pokemon Red's Brock gym in 244 turns for about $2.60, undercutting GPT-6 Astra's $13.49 run and Claude Opus 5.5's $8.44 run. The launch came a day after OpenAI shelved GPT-6.1 Astra over safety test regressions. - [openai gpt 6.1 sol pokemon benchmark results](https://startupfortune.com/openais-cheaper-gpt-61-sol-beats-pokemon-reds-first-gym-for-260/) - [cheapest ai model inference cost comparison test](https://startupfortune.com/openais-cheaper-gpt-61-sol-beats-pokemon-reds-first-gym-for-260/) ## Join the discussion [Open in the community →](https://startupfortune.com/community/) Almost there. Sign in and your reply posts straight away.