Wired>>Science>>As Math Grow More Complex, Will Computers Reign?
I do not need to comment this article in the very detail - this Blog shows where my position is. On the side of Doron Zeilberger.
I have put together some foundations in the Background and tried to touch the principles of the innovative spiral of developing mathematical knowledge bases - experimenting - abstracting - proving - experimenting ... black-box and white-box principles ...
I started this Blog with Numbers or Symbols - and repeated that I like the AND-effect - especially in Asymptotic Mathematics.
But I am clear about one thing: unplugged, you can do only Axiomatic Mathematics (where 2 functions are identical, when their I/O relation is identical) and not Algorithmic Mathematics (where resource usage and performance is essential).
In "pure mathematics" a cube is modeled by a^3, but it really matters, if this model is represented by a wire frame, bounded geometry, solid object, octree, ... - dependent on the real life problem dealing with cubes.