Is there a simpler proof of Van der Waerden's Theorem when there are only two colors?

Question

http://en.wikipedia.org/wiki/Van_der_Waerden%27s_theorem

The usual approach is to induct on the length of the arithmetic progression, which is difficult to simplify directly to the case of two colors.

Does anyone know a different approach?

Thank you.

Answer 1

There is Shelah's approach for the Hales Jewett theorem (of which Van der Waerden is a special case). See, http://www.math.unh.edu/~dvf/532/Shelah's_proof

Not sure whether it is simpler, though.