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Infinite Ascent: A Short History of Mathematics (Modern Library Chronicles) Paperback – January 8, 2008

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Editorial Reviews

From Publishers Weekly

No one knows for sure when mathematics went from being a functional system for keeping track of sheep to a philosophical system that transcended the objects it counted, but as well-known science writer Berlinski (Tour of the Calculus) tells readers, around 500 B.C. Pythagoras elevated mathematics into a religion. It has kept its near-mystical status ever since. (Even students instructed in its arcane languages can only gape at how numbers dictated where missing elementary particles like positrons and quarks were to be found.). Readers may have heard of the short-lived Évariste Galois, killed in a duel over a woman, but here they will come to understand his importance to group theory, his thoughts scribbled down the night before his death. Non-Euclidean geometry led to Einstein's universe, and Berlinski introduces us to the German scientists who opened the door to multiverses: Gauss, Cantor and Riemann. Finally, we encounter Kurt Gödel, who threw the acolytes of mathematics into a panic with his incompleteness theorem. Readers will need to remember some of their high school math to benefit from Berlinski's discussions of calculus and complex numbers, but his engaging style should attract many readers, science buffs and generalists alike to this excellent entry in Modern Library's Chronicles series. (On sale Sept. 6)
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved. --This text refers to the Hardcover edition.

From Booklist

Mathematicians are people, too, and come in all types: mystics such as Pythagoras, misanthropes like Newton. Along with Euclid, Descartes, Leibniz, Euler, Gauss, Galois, Riemann, Cantor, and Godel, they animate Berlinski's lively history of the least popular school subject. Yet even solid-C survivors of geometry can recall math's rhapsodic allure in a problem solved or a window opened on some cosmic truth, such as Euclid's axiom that through a point off a line, there passes only one line parallel to the other line. Alas, as Berlinski archly elaborates, this self-evident idea bugged centuries of mathematicians doubtful about its validity, as have many things in math ever since Pythagoras freaked out about irrational numbers. Berlinski has a light but incisive style by which he conveys the inner turmoil and triumph, or tragedy in the case of 20-year-old Evariste Galois, who invented group theory the night before he was killed in an 1832 duel, an invention marking the greatest discoveries in mathematical history. Subtly instilling the interconnectedness of the specific concepts, Berlinski releases math from its textbook script and restores its majestic drama. Gilbert Taylor
Copyright © American Library Association. All rights reserved --This text refers to the Hardcover edition.
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Product Details

  • Series: Modern Library Chronicles
  • Paperback: 224 pages
  • Publisher: Modern Library; Reprint edition (January 8, 2008)
  • Language: English
  • ISBN-10: 0812978714
  • ISBN-13: 978-0812978711
  • Product Dimensions: 5.2 x 0.5 x 8 inches
  • Shipping Weight: 5.6 ounces (View shipping rates and policies)
  • Average Customer Review: 3.0 out of 5 stars  See all reviews (25 customer reviews)
  • Amazon Best Sellers Rank: #1,235,172 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

75 of 86 people found the following review helpful By Christopher Grant on October 31, 2005
Format: Hardcover Verified Purchase
At the time that I ordered this book, I had a natural inclination to be sympathetic with its author, since his reputation indicated that he and I had similar views about politics and the philosophy of science. That only increased my disappointment when this ended up being one of the least enlightening and most annoying books I've ever encountered. If Berlinski is as talented as I'd been led to believe, it's hard not to interpret _Infinite Ascent_ as either some sort of practical joke or a rush job to fulfill a contract.

In _Infinite Ascent_, Berlinski has a tendency to wax grandiloquent, using metaphors and similes that serve no evident purpose and are sometimes downright bizarre, as when, for example, he likens sets and their elements to the male anatomy (p. 129). Following this up one page later with Berlinski's fantasy about schoolgirls with "their starched shirt fronts covering their gently heaving bosoms" (p. 130) does nothing to ameliorate concern about the author's tendency to get distracted.

One of Berlinski's running themes is the use of "..." in mathematics to represent the continuation of a pattern. He likes to joke about this so much that he starts inserting these dots in his formulas needlessly, just to get to comment on them. For example, instead of just writing down the (extremely short) formula for subtracting complex numbers (p. 69), he leaves an ellipsis and then states that "the crutch of three dots [covers] the transmogrification of a plus to a minus sign and nothing more."

Some of Berlinski's comments are real head-stratchers: "[The Elements] is very clear, succint as a knife blade. And like every good textbook, it is incomprehensible." (p.
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33 of 40 people found the following review helpful By A. Ali on November 10, 2005
Format: Hardcover
It's difficult to determine whom this book is addressed to. A lay reader will come out none the wiser after reading the chapters on complex numbers and groups. Just dressing up powerful general ideas in vague, mystifying, and allusive prose serves no purpose. For instance (p.81) he refers to the heart-breaking charm of complex analysis. Yeah, so? These statements don't edify a lay reader. The same can be said for the discussion of Lie groups (pp. 100-101).

A mathematician on the other hand, will find the book redundant, and annoying -- both for its inaccuracies and general, loose vagueness.
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9 of 11 people found the following review helpful By John Anderson on May 27, 2007
Format: Hardcover
Just for the record, Paul Dirac was British, not French as asserted by Berlinski on page 8. Dirac was born in Bristol and held the Lucasian Chair of Mathematics at Cambridge and built the mathematical foundation for quantum electrodynamics. Dirac has been written about extensively. It is amazing that a book that purports to be "a short history of mathematics" doesn't have anyone checking facts, proof reading, or editing. One loses interest after encountering a major flub so early in the book.
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20 of 27 people found the following review helpful By Flying Scot on December 1, 2005
Format: Hardcover Verified Purchase
I've never come across such a work or author before. This author is plainly venting his passive-aggressive tendencies in this less than enlightening work. It took me until page 108 to finally figure what he's up to.

There he puts Euclid's axioms in such a format as to be quite deliberately obscure. Then two pages later he suddenly jumps to measuring angles in radians, though he's never done it before and makes no statement that he's doing so. If you are not already ahead of him, you are lost. So it goes with the rest of the book. Meanwhile Berlinski stands to the side saying, "What did I do? What did I do? Oh, well, perhaps you should read something simpler if you cannot follow me."

Berlinski is plainly a person of wit and intelligence. Alas, he's allowed another side of his persona to pop up here.
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7 of 9 people found the following review helpful By The Concise Critic: on December 28, 2009
Format: Paperback Verified Purchase
"The sum total of what a man knows is vanishingly small. What seems in the end more important is that one should pursue knowledge." Bertrand Russell

Discussed mostly are mathematical things which will always be beyond me. But, to my credit, I keep trying to understand them. To David Berlinski's credit he keeps trying to explain them. (Yes, he can be obtuse--but can anyone make some of this stuff clear? . .Yes, he can be flippant. . .Yes, he can be arrogant. . .) (He can be refreshing and funny, too!) But instead of finding fault with any of the presentation, I would rather praise him for bringing me some insight and for bringing me somewhat closer to understanding. He ends this book with a reference to the tingle that mathematicians sometimes sense. That, perhaps, is how Berlinski should be judged; and there are times this book tingles.
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9 of 12 people found the following review helpful By Ricky Hunter on October 17, 2005
Format: Hardcover
A dazzling series has taken a bit of a misstep in Infinite Ascent, A Short History of Mathematics by David Berlinski. Like others in the series it is short but, unlike the rest, it does not make its subject very readable for anyone not already well-versed in the topic, which is a primary joy of this series of books on such varied topics. Granted, this is one of the more difficult areas to cover in such a short span of pages and, at times, the author does dramatically bring out the passion of the subject and the various historical figures throughout the book in an entertaining fashion, he just as often overwhelms the general reader with difficult information lacking an understandable context and, what is far worse, makes the situation wholly untenable by interjecting rather lame humour reflecting his own social and political issues and not being in any way helpful in illuminating an already complex subject. A rather tough and joyless read with occasional flashes of heart when a character from the past such as Galois or Gobel enters the story. Definately not a book for the casual reader.
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