Question: > 
> **Is the Solar System stable?** 
> 
> 
> 

You can see [this](https://en.wikipedia.org/wiki/Stability_of_the_Solar_System) Wikipedia page.  

In May 2015 I was at the conference of Cedric Villani at Sharif university of technology with this title: "Of planets, stars and eternity (stabilization and long-time behavior in classical celestial mechanics)"
, at the end of this conference one of the students asked him this question and he laughed strangely(!) with no convincing answer!  

**Edit**: The purpose of "long-time" is timescale more than [Lyapunov time](https://en.wikipedia.org/wiki/Lyapunov_time), hence billions of years.

Answer: 
[This paper](http://iopscience.iop.org/0004-637X/683/2/1207/fulltext/) (Batyrin and Laughlin, 2008) seems to indicate that we are doomed.
The work of Wisdom is relevant (for example, see <http://rspa.royalsocietypublishing.org/content/413/1844/109.short>) but not conclusive. Numerical work suggests overall stability over very long time periods.