In 1922, Lewis Fry Richardson imagined a vast hall, a theatre in the round, filled with sixty four thousand human beings, each computing the weather for one small patch of atmosphere. A conductor stood at the centre on a raised dais, shining a spotlight on any section that fell behind. Richardson called it a “forecast factory.” He published the idea in a book ahead of its time, and died in 1953, three years after a machine called ENIAC had vindicated his method.

Last week, OpenAI filled a room that Richardson would have recognised. Not with people but with ten thousand artificial intelligence agents, each trained on a model the company says is significantly more capable than anything it has released to the public. They set the agents to work on the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize Problems posted by the Clay Mathematics Institute in the year 2000, each worth a million dollars to the first solver. The equations describe how fluids move. They underpin weather forecasting, aircraft design, blood flow modelling, and ocean current prediction. For ninety years, a complete proof of their smoothness, the guarantee that solutions do not blow up into infinities, has eluded mathematicians.

Eighty eight hours later, the agents had exchanged nearly three million messages and consumed a hundred and thirty billion output tokens. OpenAI announced it had resolved two of the four statements required by the Millennium Prize. The company estimated the effort would have cost roughly ten million dollars at its own published pricing. It then added, with studied modesty, that it did not intend to claim the........

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