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Summary: Mathematician Or Not, This Is A Math Book For Everyone!
Review: Absolutely fantastically written. Dunham takes unfamiliar mathematical theorems and makes sense out of the whole works. Plus, he gives detailed (and extremely interesting) accounts of the people and times of certain mathematics. The book has it all, history, humor, interest and most important of all the truth of the universe and the giants who attained those truths. The beauty of it is, you don't even need to be a great mathematician to enjoy and understand this wonderful book.
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Summary: Stunning !
Review: Absolutely one of the most wonderful books i've ever read !In a chronological way, through each chapter, the book covers the background and history of the current chapter's genius, his great theorem and other achievements, including detailed proofs. William Dunham writing style is perfect :)
Amazon's service is really good also, I live in Israel and I recieved the book in less than one week since ordered...
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Summary: Solid Math
Review: Dunham selects several mathematical theorems and discusses their meaning and their proof. The book is arranged chronologically beginning with Hippocrates (Quadrature of the Lune) and follows with Euclid, Archimedes through Newton, Euler up to modern scientists. If the subject was ONLY mathematics he would have succeeded. But I expected more of a historical perspective and review that the merely cursory one presented here. Still, the book was arranged well with many graphs, formulae, pictures and charts.
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Summary: Wonderful book
Review: I came to this book after reading : Uncle Petros and Goldbach's Conjecture , and Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem. Both books were great ,but were lacking the Math itself. This book combines the history of the greatest mathematicians plus enabling the reader to face some of the most beautiful theorems and proofs. It is just a beautiful journey !
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Summary: Quite a Journey
Review: I don't know too many math authors who have consistently written "five-star" books. I had the pleasure of having Dr. Dunham at Muhlenberg (not Muhlendorf!) College for a class on Landmarks of Modern Mathematics. With Dunham's sharp lectures, I hardly needed the book, but with his brilliant book, I hardly needed the lectures. The key, however, is that I wanted both, and couldn't get enough of either. Graduation and reaching the back cover does that... Others have already described what's in the book, but what I must stress is that everything - every single thing - in the book is written in a clear and captivating fashion. You feel like you're sitting right there with the mathematcian under review, solving the problems for the first time with their hints. You wonder if Dunham has a time machine hidden somewhere. What this book adds to the experience is that you get a hint not just about the mathemacians' genius, but also about the personalities of the mathematicians. For example, Cardano is probably one of the humorously psychotic mathematcians that lived. This book is good for anybody who has had half of a high school education all the way up to people who think in numbers. This isn't a "skim over the math" book like those of many of Dunham's contemporaries - and you wouldn't want to do that anyway. Buy it for yourself and then give it to a budding math student - or heck, buy two!
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Summary: An informative an entertaining look at the history of Math.
Review: I studied mathematics in university but never at any great level. I eventually went to law school and I now practice law. I give you this background so that you can appreciate what I know (and don't know about math). When I feel like reading about mathematics I look for a book that can give me a general idea of the math, but that does not get technical (and therfore boring). I also the lives of mathematicians intereting. Dunham's book fits the bill for excellent reading in mathematics. It has just enough meat to it so that I can get insights into various mathematical theories. However he never gets so technical that I fall asleep reading the material. The best parts of the book are the discussions of the various mathematician's and the importance of the mathematical in question. Both form the bulk of the book and are witty and informative. After reading this book, you get the impression that the history of mathematics is filled with a collection of absentminded and colourful men. These parts of the book can be read and enjoyed with absolutely no understanding of the mathematics involved. I would highly recommend this book to anyone who wants to get some basic knowledge of mathematics and its history.
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Summary: Entertaining overview of mathematical history
Review: In "Journey Through Genius," William Dunham has selected twelve of the most famous theorems from throughout the history of mathematics, starting in ancient Greece and proceeding to modern times. He devotes a chapter to each of these theorems. Each chapter begins with background information -- about the mathematician who proved the theorem, the state of mathematics at the time, and any other pertinent mathematical information needed for understanding the proof of the theorem. He then proceeds to present a proof of the theorem, trying to follow closely the original proof, but also making sure to follow modern conventions for mathematical notation, and making sure to present the proof in a way that can easily be understood. Finally, he closes each chapter with additional information of interest regarding the particular theorem and/or mathematician, including other advances in mathematics that followed as a result of the theorem in question.
The overall result of putting together each of these individual chapters is that the book as a whole serves as an excellent introduction to mathematical history, with most of the important people and events in mathematical history discussed. I found it to be a very entertaining book, one that is written with the layman in mind, rather than the mathematical expert. In fact, all that is needed in order to follow the proofs and other mathematical presentations in this book is a solid grounding in high school algebra and geometry (knowledge of calculus is not required).
This book may not have a very wide appeal, but for someone like myself who has always liked math, this is a very enjoyable book. I found it very satisfying to follow the logic of each of the proofs, and I learned some things about mathematical history that I didn't know even after taking several college-level math classes. I didn't find the book to be particularly challenging, but I think that the author's intention was to get the reader to appreciate the aesthetic "beauty" of each of the proofs, rather than to present an intellectual challenge. I would recommend this book for anyone with a strong interest in mathematics.
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Summary: A Mathematical Tour de Force!
Review: Mathematical truths possess a beauty quite unlike any other work known to man, and the ability to appreciate that beauty should not be limited to expert mathematicians. In the preface to his book, Journey Through Genius, William Dunham notes that there are books on the great works of art, literature, and music, but that discussions on the mathematical ``classics'' are scarce. His excellent, thoroughly enjoyable, and articulate book fills that void. Most importantly, the book is written for the layperson, requiring only a familiarity with high school geometry and algebra. A simple elucidation of the greatest mathematical discoveries would be interesting in its own right, but this book goes far beyond that. It also presents fascinating glimpses into the lives of the mathematicians themselves and the cultures in which they worked. For example, we discover that academic positions during the Renaissance were not guaranteed by tenure, but were rather bolstered by successes in public, intellectual ``duels''. As a result, mathematicians kept their discoveries secret, sometimes revealing them only on their deathbeds. We also learn of the ongoing sibling rivalry between the mathematical brothers Jakob and Johann Bernoulli. And we feel sympathy for Georg Cantor, whose counter-intuitive results were widely criticized, driving him to several bouts of mental illness. What emerges overall is an engrossing patchwork presentation of the history of mathematics and of humanity in general. The book is divided into 12 chapters, each describing and proving a ``great'' theorem. These theorems have been chosen to represent discoveries spanning both time (with the notable exception of the first through 16th centuries) and a diverse range of mathematical disciplines. Each chapter sets the historical scene for a great theorem to be proven, and gives short biographies of the mathematicians contributing to its discovery. Moreover, each chapter presents (and proves) many other results, and each concludes with an enlightening epilogue section. These epilogues usually discuss later developments regarding the theorem, and often relate the result to other theorems in the book. The journey begins in the 4th century B.C. with the ancient Greeks. They pondered the problem of quadrature, that is, the use of only a straight-edge and compass to construct a square having the same area of some given figure. The ultimate goal of the Greeks was to ``square'' the circle. Dunham shows us how to easily ``square'' figures such as rectangles, triangles, and arbitrary polygons composed entirely of straight line segments. He concludes with Hippocrates' theorem that a figure composed of curved lines---namely, the lune---can be squared. This gave the Greeks a false hope that the circle could be squared also; later mathematicians showed that the task is impossible. A full two chapters are devoted to Euclid and his famous work, The Elements. The first chapter focuses on Euclid's contributions to geometry, culminating in his proof of the Pythagorean Theorem and its converse. The emphasis here is on Euclid's method, and the epilogue delves into a discussion of non-Euclidean geometry. The second chapter on Euclid describes his lesser-known results in number theory, that branch of mathematics dealing with properties of whole numbers. Euclid used an ingenious argument to show that there are an infinite number of prime numbers, those numbers divisible only by one and themselves. We are next introduced to the brilliant mathematician and engineer Archimedes, who is probably best known for discovering the law of buoyancy. Although he was the mind behind the practical inventions forming the ``one-man army'' that long kept the Romans from conquering Syracuse, Archimedes was happiest doing abstract mathematics. His ``great theorem'' concerns the value Pi, defined to be the ratio of a circle's circumference to its diameter, and his discovery that it also plays a role in the formula for a circle's area. Archimedes also gave the first means of computing Pi to arbitrary precision. The book revisits this topic in its discussion of Isaac Newton's invention of the calculus. The middle ages brought a blight to mathematics and to human innovation in general. The journey continues at the dawn of the Renaissance with the tale of Gerolamo Cardano, a flamboyant and idiosyncratic Italian mathematician. Cardano is known for his discovery of the closed-form solution to the cubic equation A x^3 + B x^2 + C x + D = 0. This is perhaps the most enjoyable story in the book, filled as it is with intrigue, secrecy, tragedy, and brilliant ingenuity. Later chapters deal with results in algebra, number theory, and set theory, including the rather surprising discovery by the Bernoulli brothers that the infinite sum 1/2 + 1/3 + 1/4 + ... diverges. Also highlighted is the genius of Leonhard Euler and his amazing result that the similarly appearing infinite sum 1/1 + 1/4 + 1/9 + 1/16 + ..., the sum of the reciprocals of squares, converges to the improbable value (Pi^2) / 6. Another chapter highlights results from number theory by Euler and Carl Freidrich Gauss. The book concludes with two astounding results by Georg Cantor demonstrating the infinite hierarchy of orders of infinity. The presentation of material throughout the book is consistently clear. Not only is the book well-organized and well-written, but it also contains scores of illuminating figures. Some of these figures are even taken directly from the original publications. To preserve the historical objective of the presentation, Dunham has stayed as closely as possible to the original notation and proofs. His effort pays off handsomely: the historic flavor of the descriptions goes a long way toward conveying the intuition contributing to each discovery. Overall, Journey Through Genius is an excellent survey of truly great and beautiful discoveries in mathematics. The theorems it discusses are indeed ``great'': they are all ground-breaking and surprising, without having complicated proofs. Moreover, the book's fascinating presentation of historical nuances shows the human side of the story, and it helps us to appreciate the true genius of the mathematicians involved. One cannot help but feel a sense of awe for both the mathematicians and the discoveries themselves. I highly recommend this immensely rewarding book....
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Summary: Sublime beauty
Review: Rarely is it properly appreciated that mathematics is one of the arts, and --- like all the other arts --- has created monuments of surpassing beauty through the centuries. Dunham does a wonderful job in this whirlwind tour of the past two thousand years of mathematics. He presents math as a story of triumph after triumph. Each chapter highlights one "great" theorem, and in every chapter he makes clear the context of the theorem by discussing preceding work, the life of the mathematician who proved the theorem, and the applications it opened up. He is masterful at mentioning tidbits in historical context that will be logically necessary to understand a few chapters further. No advanced knowledge of math is necessary, but I will caution: one must be at least reasonably fluent in both geometry and second year algebra in order to get the most out of this book. The more rusty one's algebra skills are, the more burdensome the proofs will be. For someone comfortable with that level of math, the book is breathtaking in the panoply of intellectual vistas it opens up. For anyone doing any kind of work in any technical field, I simply cannot recommend this book highly enough.
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Summary: a math history you can play with
Review: This book is an important read for a layman trying to get a better grasp on the actual historical building blocks of math. Because Dunham goes through the actual problems and solutions of great mathemeticians the book moves beyond a simple narrative. A deceptively relevant book for anyone trying to understand intellectual history. Its nice to finally see the beauty of what the dullards back in math class were trying to teach us. The reviewers are right that the personalities of some of the mathemeticians do come alive here. But that has been done elsewhere (in more detail as well). The discovery and refinement of mathematics is a central component of civilization, and this is a wonderful way to see its actual historical footings.
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