Thoughts on Evolution

Whilst I was showering this morning, thoughts on evolution were bouncing around in my head. This led to some contemplation on the matter. Let me start off by saying this is not a post about creationism vrs evolution. This is simply me sorting out some of my thoughts regarding evolution and my particular evaluation of it.
Most times when I hear people discussing this subject invariably you here that there is a single point of origin. Whether it was a single celled organism, or that we evolved from "Eve" in Africa, or that we evolved from apes. Whatever the case, this seems a bit too simple in my opinion.
Evolution is the Theory of a "process". Much like mathematics. In math 4 has always existed, but the process in witch to arrive at 4 can take many different forms. What if the same were true of Evolution? Instead of thinking everything evolved from a single point, what if everything evolved from multiple single points around the world? Since the "process" of evolution was hard at work, what if it simply took different paths to arrive at similar solutions simultaneously. Wouldn't this be a more accurate way to explain the differences between species? I mean if when the process of evolution was started whether from the formation of the planet, or from a large meteor impact, once it began it would continue using the material at hand in order to continue life. Now the next question would be are homosapiens the end result, or just another step? hehe.. that's something I would love to see science predict... What we may look like in a thousand, or million years....
Maybe this is just my ignorance about evolution, but i would suggest that there was not a "single" beginning. Instead there were multiple beginnings everywhere. Each of those beginnings using a different "formula" or "process" with the materials at hand to arrive at a particular result. In my opinion this seems to answer the diversity of life better.