Rating: 
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...
Rating:
Summary: Fascinating blend of history and mathematics
Review: As a high school math teacher, I found Dunham's book perfectfor filling what is sadly lacking in math textbooks--the idea thatreal people have contributed to the progress of mathematics. Dunham makes it clear that mathematics is not simply calculation, but an exciting journey of discovery. I have included the book in my Advanced Mathematics courses for several years now, and my students always name it as one of the best parts of the class. The other day, one of my calc students corrected an underclassman's pronunciation of Euler, commenting, "he was great enough that we should pronounce his name correctly." Journey Through Genius is where he encountered Euler's greatness.
Rating: 
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.
Rating:
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 !
Rating:
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.
Rating:
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....
Rating:
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.
Rating:
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.
Rating:
Summary: Brilliant book. Belongs on the top shelf.
Review: Some books, such as Ball's and Beiler's seem to have sparked a life-long love of mathematics in practically everyone who reads them. "Journey Through Genius" should be another such book. In the Preface, the author comments that it is common practice to teach appreciation for art through a study of the great masterpieces. Art history students study not only the great works, but also the lives of the great artists, and it is hard to imagine how one could learn the subject any other way. Why then do we neglect to teach the Great Theorems of mathematics, and the lives of their creators? Dunham sets out to do just this, and succeeds beyond all expectations. Each chapter consists of a biography of the main character interwoven with an exposition of one of the Great Theorems. Also included are enough additional theorems and proofs to support each of the main topics so that Dunham essentially moves from the origins of mathematical proof to modern axiomatic set theory with no prerequisites. Admittedly it will help if the reader has taken a couple of high school algebra classes, but if not, it should not be a barrier to appreciating the book. Each chapter concludes with an epilogue that traces the evolution of the central ideas forward in time through the history of mathematics, placing each theorem in context. The journey begins with Hippocrates of Chios who demonstrated how to construct a square with area equal to a particular curved shape called a Lune. This "Quadrature of the Lune" is believed to be the earliest proof in mathematics, and in Dunham's capable hands, we see it for the gem of mathematics that it is. The epilogue discusses the infamous problem of "squaring the circle", which mathematicians tried to solve for over 2000 years before Lindeman proved that it is impossible. In chapters 2 and 3 we get a healthy dose of Euclid. Dunham briefly covers all 13 books of "The Elements", discussing the general contents and importance of each. He selects several propositions directly from Euclid and proves them in full using Euclid's arguments paraphrased in modern language. The diagrams are excellent, and very helpful in understanding the proofs. If you've ever tried to read Euclid in a direct translation, you should truly appreciate Dunham's exposition: the mathematics is at once elementary, intricate, and beautiful, but Dunham is vastly easier to read than Euclid. The Great Theorems of these chapters are Euclid's proof of the Pythagorean theorem and The Infinitude of Primes, which rests at the heart of modern number theory. Dunham obviously loves Euclid, and his enthusiasm is infectious. After reading this, it is easy to see why "The Elements" is the second most analyzed text in history (after The Bible). Archimedes is the subject of chapter 4, and he was a true Greek Hero. Even if most of the stories of Archimedes' life are apocryphal, they still make very interesting reading. However the core of the chapter is the Great Theorem, Archimedes' Determination of Circular Area. His method anticipated the integral calculus by some 1800 years, and also introduced the world to the wonderful and ubiquitous number pi. The epilogue traces attempts to approximate pi all the way up to the incomparable Indian mathematician of the 20th century, Ramanujan. Chapter 5 concerns Heron's formula for the area of a triangle. The proof is extremely convoluted and intricate, with a great surprise ending. It is well worth the effort to follow it through to the end. Chapter 6 is about Cardano's solution to the general cubic equation of algebra. Cardono is certainly one of the strangest characters in the history of mathematics, and Dunham does a great job telling the story. The epilogue discusses the problem of solving the general quintic or higher degree equation, and Neils Abel's shocking 1824 proof that such a solution is impossible. Sir Isaac Newton is the topic of chapter 7. Rather than go into the calculus deeply, Dunham gives us Newton's Binomial Theorem, which he didn't really prove, but nevertheless showed how it could be put to great use in the Great Theorem of this chapter, namely the approximation of pi. Chapter 8 breezes through the Bernoulli brothers' proof that the Harmonic Series does not converge, with lots of very interesting historical biography thrown in for good measure. Chapters 9 and 10 discuss the incredible genius of Leonard Euler, who contributed very significant results to virtually every field of mathematics, and seems to have been a decent human being to boot. Chapter 10, "A Sampler of Euler's Number Theory", is my favorite in the book. A large portion of his work in number theory came from proving (or disproving) propositions due to Fermat, which were passed on to him by his friend Goldbach. This chapter gives complete proofs of several of these wonderful theorems including Fermat's Little Theorem, all of which lead up to the gem of the chapter. Taken as a whole it is the kind of number theory detective work that has lured so many people into the field over the years. Chapter 10 is a mathematical tour de force. The last 2 chapters handle Cantor's work in the "transfinite realm", and should certainly serve to expand the mind of any reader. By the time you finish, you'll have an idea about the twentieth century crisis in mathematics, and its resolution, and what sorts of concepts are capable of making modern mathematicians squirm in their seats. Dunham does a beautiful job of demonstrating Cantor's proof of the non-denumerability of the continuum. At this altitude of intellectual mountain-climbing the air is thin, but it is well worth the climb! In brief, "Journey Through Genius" might almost be considered a genius work of mathematical exposition. I can think of few authors more capable of conveying the excitement and beauty of mathematics, as well as an appreciation for the sheer enormity of the achievements of the human mind and spirit.
Rating:
Summary: Biography, history, mathematical theory rolled into one
Review: There is a reason all the reviewers for this book have given it 5 stars. It is simply a wonderful book. This is the kind of book that would make almost anybody learn to love mathematics. Although I myself have always liked mathematics, I can heartily recommend this book to anybody with just a passing interest in the subject. Some of the theorems that are discussed could be somewhat involved. However, those who are not interested in the details can skip them without compromising their enjoyment of the book. William Dunham seamlessly weaves a story of these wonderful mathematical geniuses, the times they lived in, their motivations and last but not least, their theorems. A great mathematical epic unfolds as you move from one era to another and from one genius to another. The author's love for the subject is obvious and a lot of it is bound to rub off on you too. Recommended without reservations.
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