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Infinite Ascent: A Short History of Mathematics (Modern Library Chronicles) Paperback – January 8, 2008
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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.
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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Berlinski is a genius who can conjure up (for he is a magician with metaphors) new insights, moods and nuances using words as precisely as razor sharp mathematical concepts. Prosaic souls require that the meaning of a Berlinski sentence unfold itself in their minds instantaneously - or else the fault is Berlinski's. They accuse him of ostentation when he displays greater mastery of the English language than they possess. Criticism of his “…using metaphors and similes that serve no evident purpose…” reveals the intellectual poverty of the critic, not any failing of the poet. They resent the effort required to think a new thought forged in a new form, not noticing that their may be enormous intellectual content whose essence could never be reduced to computer input. A strictly either/or mind, a digital consciousness, cannot abide ambiguity.
Berlinski is basically a poet who loves mathematics and science. This is a personal statement that brings more than mere concepts; it brings us new experiences by means of words.
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.
David Berlinski is surely brilliant and erudite (and he clearly wants us to realize that), but he's also a quirky fellow who has never really "fit in" with polite academic society, perhaps not even society in general. Stylistically, this book reflects its author, with Berlinski constantly making all sorts of tangential remarks. Overall, I did find his remarks to invigorate the book and entertain, but they don't add much insight. Moreover, some of his remarks are just plain weird and have no place in the book, especially his perverse sexual remarks (and it's telling that he couldn't resist putting them in the book).
As far as presenting information about mathematics, this book is rather weak. If you don't already know the mathematics, you won't be able to learn it effectively from this book, since Berlinski compromises clarity for cleverness. And if you do already know the mathematics, you'll still have to do some work to fill in the frequent gaps in Berlinski's presentation. I was also a bit disappointed that Berlinski didn't suggest any further reading; as a non-mathematician with a serious interest in mathematics, surely he could have told like-minded readers about some of the books he's personally found helpful?
Overall, I think this book merits 4 stars for entertainment value but only 2 stars for content delivery, so a net 3 stars. With a more honest title like "Comments on Some Milestones of Mathematics," I could have rated this book 4 stars.
Since it's a quick read, I can still recommend this book to the mathematically initiated who are looking for entertainment. But I can't recommend it to readers with limited mathematics background, nor to readers looking for a genuine history of mathematics. Personally, I enjoyed this book, but learned almost nothing.