4 of 4 people found the following review helpful
Great Popular Math Book,
This review is from: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (Paperback)
Georg Friedrich Bernhard Riemann is one of the most significant and influential mathematicians of all time. He has singlehandedly created whole new branches of mathematics (such as differential geometry) and has made seminal contributions to several others. Unfortunately, Riemann's life was cut short at the age of thirty-nine, and we can only speculate on how much more he could have given us had he lived longer.
One of the areas of mathematics that Riemann made a major contribution in is the analytic number theory. Analytic number theory is one of the most fascinating chimeras in all of mathematics. It combines two at the first glance completely unrelated fields: analysis, which deals with continuity, and number theory, which works with the discrete countable numbers. Prime numbers in particular are the most discrete numbers of them all, and from the very early on people have been fascinated with their properties and distribution amongst other numbers. In one of his many papers Riemann made a conjecture about the exact form of this distribution, and this conjecture has become known as the Riemann Hypothesis. As of this writing this hypothesis remains unproved, and attempts to shed some light on it are among the most important areas of the contemporary mathematical research.
Writing about mathematics for the general audience is a major challenge. In most sciences it is possible to appreciate the objects that are studied even though one does not understand any of the research tools or conceptual frameworks that are being used. Black holes and genetic engineering have become parts of the general culture. To paraphrase a statement attributed to Euclid, there really isn't any royal road to mathematics. Having that in mind, one ought to applaud John Derbyshire and his valiant attempt to bring the Riemann Hypothesis to as wide of an audience as possible. Roughly speaking, the book alternates between chapters that deal with mathematics and those that deal with mathematicians. Mathematics is ultimately a human invention and learning about remarkable individuals who have built it to what we have today is a fascinating story in its own right. The math chapters of this book can prove a bit challenging. It is probably impossible to explain Riemann Hypothesis in anywhere nearly accurate way without employing calculus and complex numbers. However, if you are comfortable with these two concepts then John Derbyshire's explanation will be the gentlest yet the most comprehensive one that you will come across. Short of opening a math textbook you will not find a batter explanation of what Riemann Hypothesis is all about.
This is an eminently well written book. John Derbyshire combines good, smooth-flowing prose with historical insights that help the reader navigate through the maze of modern mathematics. He exhibits a deep appreciation for his subject, and this book conveys much of this enthusiasm. "Prime Obsession" is easily one of my favorite popular mathematics books.