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Chargement... Infinite ascent : a short history of mathematics (édition 2005)par David Berlinski
Information sur l'oeuvreUne brève histoire des maths par David Berlinski
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Inscrivez-vous à LibraryThing pour découvrir si vous aimerez ce livre Actuellement, il n'y a pas de discussions au sujet de ce livre. 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. aucune critique | ajouter une critique
Appartient à la série éditoriale
Tout ce que vous avez toujours voulu savoir sur les plus grands math?maticiens de l'Histoire Descartes, Euclide, Leibniz, Newton... Cinq ans apr?s l'incroyable succ?s de La Vie r?v?e des Maths, David Berlinski, le c?l?bre math?maticien philosophe, revient avec un nouveau volume tout aussi captivant. Au fil d'anecdotes historiques, il passe en revue la vie et l' uvre des plus grands math?maticiens. Son style accessible et amus? plonge le lecteur dans l'aventure envo?tante et inattendue des math?matiques. Sous sa plume, th?or?mes, axiomes, fonctions et d?monstrations n'ont plus de secrets. Berlinski r?ussit avec cet ouvrage l'?quation impossible entre les chiffres et les lettres. David Berlinski invite le lecteur ? d?couvrir les th?ories math?matiques au fil des si?cles. A PROPOS DE L'AUTEUR Philosophe et math?maticien, David Berlinski est n? ? New York en 1942. Il a ?t? professeur ? Columbia, Stanford et Rutgers. Il vit aujourd'hui ? Paris o il se consacre exclusivement ? l'?criture. Il est l'auteur de nombreux romans et essais parmi lesquels figurent le Don de Newton et la Vie d'Albert Einstein (Simon & Schuster, 2001) et Une petite histoire des math?matiques (Random House, 2001). EXTRAIT L'histoire des math?matiques commence en 532 av. J.-C., ann?e de naissance du math?maticien grec Pythagore. Fuyant son ?le natale de Samos pour ?chapper au tyran Polycrate, Pythagore voyagea en ?gypte o, comme tant de jeunes Grecs impressionnables, il ± apprit des ?gyptiens le nombre et la mesure [et] fut stup?fait de la sagesse des pr?tres... Par la suite, il s'installa dans le Sud de l'Italie, se mit ? enseigner et attira rapidement des disciples. On dispose de tr?s peu d'informations directes sur sa vie, si ce n'est que ses contemporains le tenaient pour admirable. Aucun de ses ?crits n'a ?t? retrouv? ; mais il a ?chapp? ? l'oubli, pr?serv? par l'ambre de divers t?moignages litt?raires. L'admission dans la secte pythagoricienne reposait naturellement sur les comp?tences math?matiques. L'observation du secret ?tait de mise, et les f?ves, bannies du r?gime alimentaire. Les nouveaux membres devaient garder le silence pendant plusieurs ann?es, politique qu'aujourd'hui encore de nombreux enseignants trouveront exemplaire, et ?taient cens?s mettre ce laps de temps ? profit pour m?diter et r?fl?chir. Aucune description trouvée dans une bibliothèque |
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Google Books — Chargement... GenresClassification décimale de Melvil (CDD)510.9Natural sciences and mathematics Mathematics General Mathematics Biography And HistoryClassification de la Bibliothèque du CongrèsÉvaluationMoyenne:
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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). ( )