Mathematics plays a strong role in the way we live our lives and the creation of the luxuries contained therein, without math much of our lives would of necessity be far simpler. None of our constructs and concepts we all take for granted would be possible, yet for something of such pivotal importance, mathematics, more specifically the origin and meaning of it, is little understood. I shall in this and a series of following essays, as an exercise to order my thoughts on this matter, attempt a rigorous treatment of the topic. However, before a meaning behind the mathematics can be deduced one must first explore its origins.
The Pivotal Breakthroughs - A Preview
There is much we take advantage of in modern mathematics, concepts we take so much for granted we do not realize their pivotal nature and great complexity, the intellectual feats their achievement were for mankind. The concept of the natural numbers [as abstract entities], the concept of addition and then general mathematical operations on numbers, the concept of zero as first a quantity denoting null and then as a placeholder. Such concepts are so important and complex that without their achievement we would still be measuring our wealth in cattle. But where did it all start?
The First Step - Grouping