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Journey through Genius: The Great Theorems of Mathematics Paperback – August 1, 1991
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Los Angeles Times
“It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.”
— Isaac Asimov
“Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments.”
—Ivars Peterson, author of The Mathematical Tourist
Top Customer Reviews
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.Read more ›
I am a layman with a computer science degree, and a layman's understanding of mathematics, so I am no expert! But I loved this book.
I found Dunham's description of Archimedes' life and his reasoning for finding the area of a circle and volume of a cylinder to be (almost!) riveting.
Dunham's decription of Cantor and his reasoning regarding the cardinality of infinite sets was fascinating to me. But most of all, I loved his chapter on Leonhard Euler. Having in high school been fascinated by Euler's derivation of e^(i*PI) = -1, I was even more amazed at the scope of this man's genius, and Dunham's description of his life.
The chapter on Isaac Newton is an especially good one as well.
Dunham smartly weaves these important theorems of mathematics into the history of mathematics, making this book even more understandable, and, dare I say it, actually entertaining!
This book is a gem, and for anyone interested in mathematics, it is not to be missed.
The order of presentation is chronological. Early on we see great admiration for Euclid and his "Elements" as two of Euclid's theorems appear on the list, a proof of the Pythagorean theorem and the proof that there are infinitely many primes. Euler and Cantor are also honored with two theorems included among the collection.
However there is more to Dunham's presentation than just the proofs. We find other related results by these masters and other great mathematicians that were their contemporaries. He shows reverence for Newton. Gauss and Weierstrass and others are mentioned but none of their theorems are highlighted.
It is not his intention to slight these great mathematicians. Rather, Dunham's criteria seems to be to present the theorems that have simple and elegant proofs but often surprising results. His coverage of Cantor is particularly good. It seems that he is most knowledgeable about Cantor's mathematics of transfinite numbers and the related axiomatic set theory.
For a detailed description of the chapters in this work, look at the detailed review by Shard here at Amazon. I found this book to be well written and authoritative and learned a few things about Euler and number theory that I hadn't known from my undergraduate and graduate training in mathematics. Yet I did not give the book five stars.
There are a couple of omissions that I find reduce it to a four star rating. My main objection is the slighting of Evariste Galois.Read more ›
Most Recent Customer Reviews
I wrote an extra credit paper on this book for a proof-based class at my university. The book was very clear and concise, considering that proofs are not my strongsuit. Read morePublished 3 months ago by Savannah C.
I found the biography of the mathematicians and history of the times fascinating. I followed with interest the proofs of the theorems. Read morePublished 4 months ago by Neil Karl
From the title I didn't expect what I got. This is a great book about the history of mathematics.Published 4 months ago by J. Patrick Dolan III
As a novice recreational mathematician, I found this book very pleasurable. Similar to a textbook, but with more backstory and more fun. Read morePublished 6 months ago by Timothy
Great book. Not an easy read for me, as I have been out of school for over 50 years. However, I have a nice sense of accomplishment, because I am, with effort, able to understand... Read morePublished 7 months ago by Reader from San Jose
Great book. I did buy used but it was more of fair condition then good. Cover was bent in a few places.Published 7 months ago by Katelynn