Euclid

Here's an introductory puzzle. In the totality of our intellectual heritage, which book is most studied and most edited? The answer is obvious: the Bible.

But which is the most studied and edited work after it? That is a little harder to say. The answer comes from a branch of science that we now take for granted, geometry. The work in Euclid's Elements. This is the work that codified geometry in antiquity. It was written by Euclid, who lived in the Greek city of Alexandria in Egypt around 300 BCE, where he founded a school of mathematics. Since 1482, there have been more than a thousand editions of Euclid's Elements printed! It has been the standard source for geometry for nearly 2000 years. It is only in recent decades that we have started to separate geometry from Euclid. In living memory--my memory of high school--geometry was still taught using the development of Euclid's definitions, axioms and postulates and his numbering of them.

We can identify two reasons for the importance of Euclid's Elements in our understanding of the foundations of science: its structure and the certitude of its results. First, Euclid's Elements solved an important problem. When we have a large body of knowledge, such as we have in geometry, how are we to organize it?

So, as our knowledge grows, how are we to organize it so that we capture in it all the truths that we want and do not let in things that don't property belong there? Euclid employed a quite profound method, deductive systematization. His elements were structured according to a series of propositions (see below)