Those number theoretical results or problems are quite simple to state
and have one point in common. It turns out that they can be
reinterpreted and investigated with methods from discrete dynamical
systems and ergodic theory: Mahler measures are topological entropies,
Hindman's theorem is a consequence of a topological modification of
ideas related to Poincaré recurrence, Margulis discussed
invariant measures of group actions on Lie groups and the work of
Green and Tao combines ergodic Ramsey theory in the spirit of
Furstenberg's approach to Szeméredi's theorem with deep results
from analytic number theory.