For centuries, ever since Isaac Newton formulated his laws of motion and gravity, mathematicians and astronomers have grappled with the long-term stability of planetary orbits in the solar system. In the simplest model, which considers only the gravitational forces exerted by the sun, the planets follow their elliptical orbits like clockwork for eternity. But once you account for gravitational attraction between the planets themselves, everything gets more complicated. You can no longer explicitly calculate the planets’ positions and velocities over long periods of time, and must instead ask qualitative questions about how they might behave. Might the effects of the planets’ mutual attraction accumulate and break the clockwork? Now, in three papers that together exceed 150 pages, a trio of mathematicians have proved for the first time that instability inevitably arises in a model of planets orbiting a sun. Rafael de la Llave, a professor in the School of Mathematics, didn't work on the research but is quoted in the article.