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The Mathematician's Brain: A Personal Tour Through the Essentials of Mathematics and Some of the Great Minds Behind Them First Edition Edition

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David Ruelle (Author)
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David Ruelle (Author)
3.8 out of 5 stars 6 customer reviews
ISBN-13: 978-0691129822
ISBN-10: 0691129827
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Product Details

  • Hardcover: 176 pages
  • Publisher: Princeton University Press; First Edition edition (August 5, 2007)
  • Language: English
  • ISBN-10: 0691129827
  • ISBN-13: 978-0691129822
  • Product Dimensions: 0.8 x 5.8 x 9.2 inches
  • Shipping Weight: 14.4 ounces (View shipping rates and policies)
  • Average Customer Review: 3.8 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #1,197,933 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

13 of 15 people found the following review helpful
good insights from a real mathematician; needs more editing
By Nim Sudo on December 4, 2007
Format: Hardcover
The author, who is a very distinguished mathematician, gives his personal view on how mathematicians think. It is welcome to have books like this written by real mathematicians, as opposed to philosophers who doesn't know that much math. While professional mathematicians might not learn much, students of mathematics can get some very nice insights into how mathematics and mathematicians work.

Unfortunately, some parts of the book that discuss specific mathematics (as opposed to what mathematics is like in general) are not clearly written and should have been edited better. For example, it shakes the confidence of the reader when early on, the pythagorean theorem is stated incorrectly, and then on the next page a statement is asserted to follow from the pythagorean theorem, when it actually follows from the converse of the pythagorean theorem. Most readers of the book will probably know this anyway so it doesn't matter, but later, descriptions of more advanced mathematical concepts are sometimes so brief that they would probably be incomprehensible to someone who does not already know them, and puzzling to someone who does.

Disclosure: I only skimmed this in the bookstore because I didn't feel like paying 20 cents per page for it. I hope that an inexpensive paperback edition will appear, with corrections.
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8 of 9 people found the following review helpful
Limited but intriguing
By physics student on December 6, 2007
Format: Hardcover
In this small book the author (a distinguished professor of mathematical physics) touches on what mathematicians do, how they do it, how they think and feel about it, and how they relate to the world at large. On such a quick tour there are bound to be some mysterious turns and bumps on the road. More than necessary occur in this book: advanced topics are frequently introduced with unhelpful advice for the novice such as "Just go through it rapidly." Nevertheless I enjoyed learning a new bits of math (now I can define algebraic geometry) and stories of mathematicians. What kept me going was the author's skeptical attitude toward the mathematical establishment of which he is a part, and his genuine compassion for colleagues whose genius can so easily turn to madness.
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3 of 3 people found the following review helpful
A book to treasure
By Irfan A. Alvi VINE VOICE on December 30, 2009
Format: Hardcover Verified Purchase
I sense that David Ruelle wrote this book as a labor of love, and I feel priveleged to have been able to read it (as with his wonderful book Chance and Chaos). He provides a fairly penetrating and sophisticated treatment of the nature of mathematics and what it's like to be a research mathematician. His writing style is informal and friendly without sacrificing clarity, precision, and elegance. He doesn't shy away from including some real and nontrivial mathematics (for demonstration purposes), but the book isn't overly technical and he puts the harder stuff in the endnotes. If you've at least dabbled in higher mathematics and have some rudimentary familiarity with set theory, abstract algebra, topology, number theory, Turing machines, etc., you should be able to handle the book (and love it); without that background, it may be tough going.

Perhaps the best way to describe the content of the book is to summarize some of the key points:

(1) A goal of mathematical deduction is to derive nontrivial and interesting results (particularly mathematical theories), not just any or all results which follow from the axioms. Mathematics makes progress because new theorems are built on prior theorems. As it has developed, mathematics has generally become more difficult, though breakthroughs sometimes allow the solution of many problems to be greatly simplified.Read more ›
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