History of Mathematics: From a Mathematician's Vantage Point - hardcover

This book offers a very interesting panorama of the development of mathematics from the ancient Babylonians and Greeks to the present. It is written in a lucid style with very readable mathematical content. Understanding the material requires some broad mathematical education, but not a lot of specialized knowledge. One of the strongest sections deals with the accomplishments of the Greeks. The author clearly explains the problems tackled in ancient Greece, places them in context, outlines the accomplishments (some with concise proofs), and compares these with our present understanding of the subject. He also places the mathematical achievements of ancient Greece in the context of early Ionian Philosophy, Platonism, Aristotelism, or in the mindset of the Alexandrians. The chapters on the seventeenth and eighteenth centuries are presented clearly with emphasis on the great figures of these two centuries. Mathematics of the nineteenth and twentieth centuries are presented more thematically than chronologically. Analysis, in particular functional analysis, receives a very good overview. An appendix contains a transcript of the talk by Laurent Schwartz on the historical roots and basic notions of the theory of distributions. Other chapters discuss topics such as modern algebra, set theory, logic, group representations, calculus of variations, celestial mechanics, fractals, the fast Fourier transform, and wavelets. The book is supplemented with a chronological table and two detailed indices. It is suitable for graduate students, research mathematicians, and those interested in the history of mathematics and related areas.