Euclid - The Creation of Mathematics

The philosopher Immanuel Kant writes in the popular introduction to

his philosophy: "There is no single book about metaphysics like we

have in mathematics. If you want to know what mathematics is, just

look at Euclid's Elements." (Prolegomena Paragraph 4)

Even if the material covered by Euclid may be considered elementary

for the most part, the way in which he presents essential features of

mathematics in a much more general sense, has set the standards for

more than 2000 years. He displays the axiomatic foundation of a

mathematical theory and its conscious development towards the solution

of a specific problem. We see how abstraction works and how it

enforces the strictly deductive presentation of a theory. We learn

what creative definitions are and how the conceptual grasp leads to

the classification of the relevant objects.

For each of Euclid's thirteen Books, the author has given a general

description of the contents and structure of the Book, plus one or two

sample proofs. In an appendix, the reader will find items of general

interest for mathematics, such as the question of parallels, squaring

the circle, problem and theory, what rigour is, the history of the

platonic polyhedra, irrationals, the process of generalization, and

more.

This is a book for all lovers of mathematics with a solid background

in high school geometry, from teachers and students to university

professors. It is an attempt to understand the nature of mathematics

from its most important early source.