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Sto caricando le informazioni... Infinite Ascent: A Short History of Mathematicsdi David Berlinski
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Iscriviti per consentire a LibraryThing di scoprire se ti piacerà questo libro. Attualmente non vi sono conversazioni su questo libro. A 4 for content...a 2 for usefulness... This book has bouts of brilliance but was short on usefulness. I found myself time and again asking what the point of this book was. I wasn't sure if Berlinski was happy that math has taken the turns that it did or if he is waiting for the next mathematical revolution. I'm not sure that I would recommend this book to anyone because I don't know what type of person would find it remotely intriguing. nessuna recensione | aggiungi una recensione
Appartiene alle Collane Editoriali
In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton's Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure. Berlinski focuses on the ten most important breakthroughs in mathematical historyand the men behind them. Here are Pythagoras, intoxicated by the mystical significance of numbers; Euclid, who gave the world the very idea of a proof; Leibniz and Newton, co-discoverers of the calculus; Cantor, master of the infinite; and Godel, who in one magnificent proof placed everything in doubt. The elaboration of mathematical knowledge has meant nothing less than the unfolding of human consciousness itself. With his unmatched ability to make abstract ideas concrete and approachable, Berlinski both tells an engrossing tale and introduces us to the full power of what surely ranks as one of the greatest of all human endeavors. Non sono state trovate descrizioni di biblioteche |
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Google Books — Sto caricando le informazioni... GeneriSistema Decimale Melvil (DDC)510.9Natural sciences and mathematics Mathematics General Mathematics Biography And HistoryClassificazione LCVotoMedia:
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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. 14); "[Exponential functions] mount up inexorably, one reason that they are often used to represent doubling processes in biology, as when undergraduates divide uncontrollably within a Petri dish." (p. 71). Huh?
_Infinite Ascent_ has few formulas or other concrete mathematical details, and what there is is often wrong. The formulas for the solutions to quartic equations of quadratic type are botched (p. 93), roots of equations are confused with zeros of functions (p. 80), inscribed rectangles are described while circumscribed rectangles are drawn (p. 56), and g12*du1*du2 is misidentified as a formula for the infinitesimal distance between the points u1 and u2 (p. 120). The sections on logic are the ones Berlinski handles most competently, but even that has been covered better by many others.
Berlinski thinks that Weierstrass's definition of limit is "infinitely wearisome" (p. 145) and is "promptly forgotten" by mathematicians after they have learned it. I think most analysts would disagree strongly with his opinion, and would classify the definition of limit among those things they couldn't forget if they wanted to. (That Berlinski himself very well might have forgotten it is suggested by his unconventional decision to use the letter delta to represent a *large* index (p. 61) in his definition of the limit of a sequence.)
Berlinski opines that the Fundamental Theorem of Calculus (connecting differentiation to definite integration) is something that "no one at all would expect". On the contrary, I consider it to be eminently plausible. Berlinski also describes the classic math book _Counterexamples in Analysis_ as consisting of "a series of misleading proofs supporting theorems that are not theorems." _Counterexamples in Analysis_ actually contains nothing of the sort. Rather than containing fallacious "proofs" of non-theorems, it contains exactly what its title says it does: Counterexamples (i.e., examples that show why the hypotheses of (true) theorems are necessary and why stronger conclusions are unwarranted). ( )