> I've just been reading "After Thought". The premise of this book is that
> Mathematics has passed through 2 major stages up to today; Geometry, then
> Algebraic/formulaic. He proposes that we are, after four hundred years of
> the dominance of Cartesian, linear thought, about to move into the third
> great epoch of Mathematics; that of concurrent, computationally intensive
> methods. This includes such techniques as Neural Networks, Cellular
> Automata, Genetic Algorithms, and other such wonderful voodoo.
This is an interesting supposition, but I don't buy it. Now, most of my friends
are either mathematicians, or computer scientists (I'm in the latter camp), and
from the discussions we've had it looks like the place that Mathematics is
headed are the fields of descriptive frameworks. Such things as rings, groups,
lattices and other mathematical structures are a step in this direction. As are
function valued functions (functors? functionals? I forget what they are
called.) Now, this is not divorced from computer science, as such things as
type theory and category theory have direct application to the designs of
programs. The items you list, such as Neural Networks and Genetic Algorithms
are currently mathematically intractable, and most mathematicians I've talked
to don't have much to good to say about them.
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