The inner planets (Mercury, Venus, the Earth and Mars) have chaotic motions. Numerical evidence was given by Jacques Laskar in 1994. Since numerical errors grow exponentially because of the sensitivity to initial conditions, it was impossible to keep control on the position of the planets over long periods of times (hundreds of millions of years), and Laskar derived and simulated an averaged system of equations. At the time, the simulations showed that the orbit of Mercury could cross that of Venus for some period of time. Laskar could explain this chaotic behaviour by exhibiting resonances in some periodic motions of the orbits of the inner planets. Another way to study chaotic systems is to make numerous simulations in parallel with close initial conditions, and deriving probabilities of future behaviours. The shadowing lemma guarantees that a simulated trajectory resembles a real trajectory for a close initial condition. In 2009, Laskar announced in Nature the results of an ambitious program of 2000 parallel simulations of the Solar system over periods of the order of 5 billions of years. The new model of the Solar system was much more sophisticated, and included some relativistic effects. The simulations showed a 1% chance that Mercury could be destabilized and encounter a collision with the Sun or Venus. A much smaller number of simulations showed that all the inner planets could be destabilized, with a potential collision between the Earth and, either Venus, or Mars, in around 3.3 billion years.