> The view that mathematics should try to constrain itself to physical > reality is, in my opinion, not a crackpot position.
It's a meaningless position unless you can give "confine itself to physical reality" in connection to a subject which is not *about* physical reality a meaning.
> Let me use an example. 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.
Stephen, I suggest you confine yourself to topics you know something about, and cease spouting ignorant horseshit. A very famous incident--so famous it makes it dead obvious you don't know what the hell you are talking about--is Gelfand's proof of Wiener's theorem using Banach algebras. Wiener had proven that if Fourier series on a closed interval which converges absolutely to a function f such that f has no zero on the interval, then 1/f also has an absolutely convergent Fourier series on that interval. The proof was not easy, yet Gelfand proves it in a few lines using the theory of Banach algebras.