Name: Anonymous 2011-06-03 18:48
The mathematicians Wiener and Banach lived at about the same time. Banach chose a much more abstract direction to take his mathematics, looking at general properties of infinite dimensional normed vector spaces beyond Hilbert spaces and spaces of continuous or measurable function. Wiener looked more to real life applications, and building on the work of Einstein put the phenominum of Brownian motion onto a rigourous mathematical foundation. Many very talented mathematicians have studied Banach spaces, but it has proven to be a remarkably barren field. On the other hand Wiener's approach has led to the rich theory of stochastic calculus, which has proved extremely useful in studing the heat equation, harmonic functions, and even economics.