  An open problem in numerical analysis is to explain why molecular dynamics
works. The difficulty is that numerical trajectories are only accurate for very
short times, whereas the simulations are performed over long time intervals. It
is believed that statistical information from these simulations is accurate,
but no one has offered a rigourous proof of this. In order to give
mathematicians a clear goal in understanding this problem, we state a precise
mathematical conjecture about molecular dynamics simulation of a particular
system. We believe that if the conjecture is proved, we will then understand
why molecular dynamics works.
