Applying topological dynamics to prove Van der Waerden's theorem on the existence of monochromatic arithmetic progression has now become a somewhat classical example of the power of topological dynamics techniques.
However, since the statement of the theorem is purely algebraic or number theoretic, I wonder whether there is a proof without using the machinery from dynamics and I guess such a proof might give more insight on the matter of the fact.
Thanks!
ps: How come there is no "topological dynamics"tag?