Is the Solar System stable?

Rare events can be very important if their large impact compensates for their low probability. And what impact could be larger than the destabilization of the Earth's orbit or collision between the Earth and another planet of our solar system?! In the present talk, I will thus raise again the fascinating question of the stability of the Solar System: this adventure started with Newton's discovery of the law of gravitation about three centuries ago and is still not fully answered. In the past 30 years, a breakthrough occurred with the numerical discovery that planetary collisions are possible between the four smallest terrestrial planets within a timescale of a few hundred million years, but are very rare events. First discovered in the field of statistical physics, the generic phenomenology of rare events is that, conditioned to the fact that the event occurs, the path chosen by the system to realize the rare event can be predicted. I will show that the same phenomenology is valid for rare destabilization paths of the Solar System.