Now, in three papers that together exceed 150 pages, Guàrdia and two collaborators have proved for the first time that instability inevitably arises in a model of planets orbiting a sun.

“The result is really very spectacular,” said Gabriella Pinzari, a mathematical physicist at the University of Padua in Italy. “The authors proved a theorem that is one of the most beautiful theorems that one could prove.” It could also help explain why our solar system looks the way it does.