Professor Morris Kline wrote this book in 1953. He started out strong, from the first page of his preface, and kept going from there: "...educated people almost universally reject mathematics as an intellectual interest. This attitude toward the subject is, in a sense,...
Professor Morris Kline wrote this book in 1953. He started out strong, from the first page of his preface, and kept going from there: "...educated people almost universally reject mathematics as an intellectual interest. This attitude toward the subject is, in a sense, justified. School course and books have presented `mathematics'' as a series of apparently meaningless technical procedures. Such material is as representative of the subject as an account of the name, position, and function of every bone in the human skeleton is representative of the living, thinking, and emotional being called man." (As for the quaint last word, please recall the year it was written.) Kline supports his assertion with a like one, which serves as the book''s epigraph, from René Descartes, a portion of which reads: "...the earliest pioneers of Philosophy in bygone ages refused to admit to the study of wisdom anyone who was not versed in Mathematics..."
Kline''s work is a tour-de-force of Western scientific achievement, and its impact on the culture and lives of its citizens. Most fundamentally, science requires a solid mathematical basis. He is never heavy-handed in his assertions, but he demonstrates the numerous times that the religious establishment is opposed to the scientific method. The High Priests of Ancient Egypt knew that the solar year was 365 and a quarter days long, but hide this knowledge in order to retain their power over the people by predicting the annual flooding of the Nile. He quotes St. Augustine: "The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell." And Kline also details the efforts of the Catholic Church against Galileo in order to retain an earth-centered universe, just like the Bible proclaimed.
It really all did start in Greece, with Pythagoras, Euclid, and several others whose mathematical concepts still shape the world in which we live. As the author points out, it was Alexander who was so instrumental in spreading these concepts throughout a large swath of the inhabited world. He moved the center of the world''s learning to a town named after himself in Egypt. Upon the burning of the library there, in the 600''s, there was an "interlude," as the author puts it, and others have referred to as a "dark age." The light would shine again, numerous centuries later, as Kline says: "The Polish Copernicus, the German Kepler, the Italian Galileo, the French Descartes and the English Newton received light and warmth from the sun of Greece."
As the title suggests, Kline includes several chapters that demonstrate the impact of mathematics in the cultural arenas. There is one devoted to the development of perspective in painting, and the author dedicates three chapters dedicated to Newton''s impact on religion, literature and aesthetics, and philosophy. There is also a chapter dedicated to the influence of mathematics on music.
In terms of scientific developments, Kline provides a lucid explanation of the development of calculus, "grasping the fleeting instant" as he say. He highly praises the work of James Clerk Maxwell in developing electromagnetic theory. Maxwell''s broad theory specifically predicted radio waves, and Kline emphasizes that it was Maxwell''s insistence on EXACT reasoning that was the cause. Rather drolly, he entitles the development of statistics as the "mathematical theory of ignorance." He concludes with three strong chapters on the paradoxes of the infinite, non- Euclidian geometry and the theory of relativity.
Kline does use equations and drawing throughout the book, which should enhance and not detract from the reading experience. None from Maxwell though, which can be a bit difficult. Concerning the role of mathematics, the author concludes with the following: "It is the distillation of highest purity that exact thought has extracted from man''s efforts to understand nature, to impart order to the confusion of events occurring in the physical world, to create beauty, and to satisfy the natural proclivity of the healthy brain to exercise itself." An excellent one volume study of the impact of mathematics on western culture. 5-stars, plus.