52 internautes sur 53 ont trouvé ce commentaire utile
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I very much enjoyed this biography (Hoffman calls it "in large part a work of oral history") of the legendary Hungarian mathematician, Paul Erdös. Hoffman's relaxed style with his attention to detail and concrete expression makes it a pleasure to read. You don't need to know any mathematics. Hoffman mentions the math and occasionally goes lightly into it, but for the most part the focus is on the eccentric and loveable mathematician himself and his many friends and collaborators. In fact, the title is somewhat ironic since Erdös was very much a people person, a man who loved and was loved by others. It is only in the case of "romantic" love that Erdös loved only numbers.
By the way, Hoffman does indeed go into Erdös's sex life in a completely tasteful and PG-13 sort of way. He was a man who dearly loved his mother and children but practiced a deep and abiding celibacy all his life. His friends made many jokes about his uneasiness with "bosses" (his pet name for women) and once made a bet with him that he could not go to a burlesque show. He did however, but took off his glasses so he couldn't see anything.
Erdös was a pure mathematician, a child prodigy who fell in love with numbers at an early age and never lost his love while wandering over the entire globe searching for collaborators. He was himself a caricature of the absent-minded professor, a man who asked others to tie his shoes for him, a man who could not drive, who worked nineteen hours at day at mathematics, often calling his friends up at four in the morning to share an insight. He paid no attention to his appearance, cared nothing for literature, the arts, sports, etc., only for his beloved math. He had a way with children and an ability to impose on his friends, often arriving unannounced at their houses and staying for days or weeks at a time. He freely gave away his money to any number of charities, and sometimes to outright strangers on a whim. He cared nothing for worldly goods. He didn't even like applied mathematics, referring to colleagues who had gone that route, as being "dead." Indeed, only children and pure mathematics delighted him.
There's a child-like simplicity to the man that charms us. Hoffman's book reflects this as a kind of fairy tale life lived in delight in spite of all the horror going on in the world. There is a pristine beauty to living one's life so incredibly focused on one thing. In a sense it is like an addiction and in another it is like an all-consuming love. It is the kind of life few of us could ever live (or would want to live), but it is the kind of life we can admire and read about with pleasure.
Hoffman sometimes slips away from Erdös to write about his family and friends, especially about Ronald Graham, Erdös's long-time friend and collaborator, a very interesting man himself, a world class juggler and a practical as well as theoretical mathematician. Hoffman recalls some Hungarian history, some Cold War history, and relates anecdotes from friends and family. He devotes a chapter to Fermat's Last Theorem, Fibonacci numbers, the Prime Number Theorem, etc., and then part of a chapter to the Monty Hall dilemma and the tussle between Parade magazine columnist Marilyn vos Savant and her detractors. There is also a lot of humor, which is appropriate because Erdös liked witticisms and used humor as a way to deal with the world. "Soon I will be cured of the incurable disease of life," he is quoted as saying on page 173. He adds, a little later, still in a sardonic mood, "Television...is something the Russians invented to destroy American education."
There are some photos, a bibliography and an index. Hoffman does not glorify Erdös as much as some would like, but this is an affectionate and balanced, very interesting portrait of a true original and a great mathematical genius.
--Dennis Littrell, author of "The World Is Not as We Think It Is"
112 internautes sur 123 ont trouvé ce commentaire utile
J. G. Gimbel
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This is a disappointing book. Certainly Paul Hoffman should be commended for writing a math book that so many people find lively and informative. Probably it is the only profile of a mathematician that many people will read. But the author makes mistakes of several types. There are what might by typographical errors. For example, on page 252 we find a description of Béla Bolobás who "won Hungary's infamous student math competition..." If the competition is in fact infamous, the reader is never told why.
There are errors of fact. For example, a fainting episode described on pages 244 and 245 as having happened in Boca Raton actually happened in Baton Rouge and was later repeated in Kalamazoo. We learn in this book that Kurt Gödel was an Austrian. This will come as sad news to Czechs and Moravians.
There are less objective examples. For instance Erdös is credited with developing the probabilistic method. While Erdös certainly championed the method and demonstrated its power, it is overreaching to give him all the credit. I would not want to guess as to who first used it, although some attribute it to William Feller. Certainly Tibor Szele used the method in a paper published in 1943. The paper was reviewed by Erdös in Mathematical Reviews. He did not use it until his paper on Ramsey Theory in 1947.
But these sorts of problems are mostly minor and have been perhaps corrected in subsequent printings. There is a deeper problem with the structure of the book. Much of the book is based on the author's 1987 article which appeared in The Atlantic Monthly. Discover Magazine also published some of the book. As magazine articles, I thought they worked very well. But the book has a disjointed impressionistic tone that seems distracting. And while Hoffman gathered enough material for two fine magazine articles, he doesn't seem to have enough for a book. So it is diluted with superfluous, albeit interesting, material. These detract from the story. For example, there are discussions of Fermat's Last Theorem and Andrew Wiles contribution. There is a discussion of infinity and set cardinality similar to what would be found in a discrete math textbook published ten years ago (and sadly missing from most textbooks today). Gödel's incompleteness theorem is presented. But donations by Erdös to these things is given little discussion mostly because, I suppose, his contributions to those topics is tangential.
Hoffman has a fascination with Erdös's brilliance, portraying him as an uncanny wizard. There is no denying he had an incredible mind. It's possible that all of the book's anecdotes are true. But still, they seem to miss the target. This is not how Erdös really was. His mind was human. He could interchange maximums and minimums and mix up quantifiers. He sometimes had trouble (as many great minds do) with arithmetic. I recall once asking him about an important theorem he proved with Endre Szemérdi. He didn't recall the result and seemed surprised by its existence. On one occasion he asked me to reproduce a proof he had previously shown me. We went through it twice when he asked to be left alone for half an hour. On my return he said, "I am sorry for being such a stupid old man. Yes, you are right. This proof is correct." No doubt, part of his success rested on natural talent. But much rests on his passion and dedication to mathematics.
But again, I can forgive these problems. My most serious concern is the way this book reduces a kindhearted loveable human to caricature. While Hoffman interviewed many people, including Erdös, Hoffman's account seems to have missed the flesh and blood and left us with a wacko schematic. Nobody will deny that Erdös was a special man with a special personality. He warmly gave so much to so many; especially to young mathematicians and graduate students who would go on to owe much of their careers to his generosity. But portrayed here is something freakish, something best left to carnival sideshows and wax museums. Fascination with his personality seems to be growing; drawn in grotesque proportions. Time Magazine profiled him under the heading "The Oddball's Oddball." His eccentricities are outlined in "Strange Brains and Genius," Clifford Pickover's book on twisted brilliant minds. One wonders how much responsibility Hoffman's writing has in contributing to this persona. The reduction extends even to the title. Paul Erdös did not love only numbers. He loved history, politics, philosophy, science. He loved ideas in just about any area. But most of all, he loved people
34 internautes sur 37 ont trouvé ce commentaire utile
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Paul Erdos' position in number theory of the 20th century is pretty much like Miles Davis' in jazz: in some way or another every important figure in number theory has worked with Erdos, much like every influential jazz musician collaborated with Davis at one point in their respective careers. This may explain the number theorists' obsession with calculating their "Erdos number" (a person is said to have Erdos number one if the person wrote a mathematical paper with Erdos; a person with Erdos number 2 is a person who wrote a paper with a person with Erdos number 1, and so on and so forth. For more information on Erdos number visit oakland.edu/~grossman/erdoshp.html). Erdos was a prolific mathematician. According to the statistics compiled in the site just mentioned, he was the one who authored the most papers in the entire history of mathematics, even surpassing Euler.
The book is a collection of anecdotes related to Erdos. I say "anecdotes" because the book does not follow the usual birth-till-death timeline approach for biographies. Each chapter roughly corresponds to a story surrounding important collaborators of Erdos for a certain type of mathematical problem, not necessarily ordered chronologically. Erdos appears in these anecdotes as a person who cared dearly for his mother (he did not have his own family, not to mentioned he that he died a virgin according to his own words), mathematicians of all sorts regardless of their nationalities, children; as a person who despised anything that confined anyone's freedom, including God, or to put it in his words, SF, the "Supreme Fascist"; as a person who did not even have the ability to operate the most basic things, like operating air conditioners or even slicing a grapefruit with the right side of a knife (according to this book Erdos confessed that the first time he applied butter to bread was when he was in his 20s -- before Erdos' mother took care of him, and henceforth his friends/collaborators did); as a person whose earthly interest was zero (he never had a house -- he lived off at friends/collaborators), who gave everything he earned to any charity organization and every person in need (his entire possession fit into two suitcases); as a person whose love towards mathematics none equaled (he traveled incessantly to give lectures and worked 18 hours daily till he died); as a person who nevertheless feared death.
The book's format may have been just right for describing Erdos, whose life perhaps had no other way of being described of other than through mathematical problems. However for 1) the lack of information re. Erdos' "real" accomplishments (omitted most likely for general accessibility), 2) the author's occasional deviation from Erdos (for e.g. an entire chapter devoted to Fermat's last theorem which almost has nothing to do with Erdos; retelling of the most "popular" paradoxes of mathematics) which I felt catering to commercialism, I do not feel that the book depicted Erdos' life the best. The book is at best an entertaining read of one of the most interesting and influential mathematicians of the past century.
17 internautes sur 19 ont trouvé ce commentaire utile
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I knew Paul Erdos since I was a small child. I consider that this book, and, even more, the blurb about it, misrepresent him quite seriously. According to the book, Hoffman did not know Erdos well personally; and his portrayal of him in the book is simultaneously oversimplified, confused and inaccurate. I am giving the book two stars rather than one, because at least it is better and more accurate than the blurb about it.
Erdos is portrayed as narrowly obsessed with mathematics, to the point of almost being a freak. He is described in the blurb as having none of the normal interests in sex, companionship, art or even food. While I don't usually describe the personal characterstics of my friends and acquaintances in a public review, Erdos has for some reason become so much of a topic for public discussion that I feel that I should respond to some of the wilder remarks. It is true that Erdos was celibate, but he had a very great liking for companionship, and friendships were important to him..
He disliked being alone, and mostly managed to avoid being alone. He had a very large number of friends, to whom he was very warm and caring and extremely generous. Yes, he could be a tiring guest, but he gave far more than he ever took, and far more than most people ever do. He gave absolutely unstintingly of his time, mathematical ideas, money (whenever he had any) and influence (whenever he had any). He always made very special efforts not only to visit and help his friends when ill or in difficulties, but to do the same with the friends and relations of his friends. Not all his friends were mathematicians. Notably, he was extremely fond of children. He carried out his desire for companionship into his professional life, where he carried out a great deal of his work in collaboration with others, and had more collaborators than any other scientist of whom I have ever heard. As regards food, he had a great appreciation of good food, and would for example, sometimes reciprocate his hosts by taking them to good restaurants. While he did not have a special interest in art, he was very fond of nature, and also had strong interests in languages, history and politics. He was certainly not a "Man Who Loved Only Numbers". He was indeed obsessed with mathematics; but this was his least unusual characteristic. Many people pursue interests and careers obsessively; Erdos differed from others in being infinitely more creative and successful in his chosen pursuit than most others; in the extent to which he combined this obsession with an intelligent interest in other subjects; and in pursuing creative mathematics into old age.
The book and the blurb about it, also make me uneasy in my professional capacity as a developmental and cognitive psychologist who studies individual differences in cognition. While few people are as outstandingly talented in any direction as Erdos in mathematics, many people - a far larger number than had at one time been thought - are uneven in their abilities. It is both scientifically inaccurate, and a potential source of distress to the individuals concerned, to assume that such unevennesses are solely a matter of attention and focus. Thus, the implication that Erdos' physical clumsiness and difficulties with certain practical activities were due solely to a narrow focus on mathematics is both unfair to Erdos personally and a disservice to the many less eminent people who are physically clumsy or have other specific cognitive or motor difficulties.
If anyone is interested in reading a good biography of Erdos, I would strongly recommend them to read Schecter's "My Brain Is Open" - much better than this ... book.
19 internautes sur 22 ont trouvé ce commentaire utile
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Paul Erdos, a giant of twnetieth century mathematics, takes center stage in this biography which discusses the extent of both his brilliance and eccentricities. This is a man who made up his own language, roamed the world to discuss mathematical theory, befriended and frustrated his hosts and collabortators, and in is universally remembered as a loving genius. The book itself is a series of vignettes about Erdos's life woven together with explanations of numberous mathematical problems and theories, as well as stories of other math legends. It is very inclusive of the Erdos's predecessors as well as contemporaries, and shows the evolution of mathematics, within the larger context of a biography.
I loved this book, mainly because of Erdos, who was a wonderful character. I was a poor math student in school, but Hoffman's descriptions made these incredibly complex ideas that Erdos played with understandable and interesting. Also, I learned a lot about the field of mathematics, mathematicians, and about passion. These men and women devote their lives to theorems that may never have any real appication, but they do it because of a love for the subject. It was facsinating and inspiring throughout, and a wonderful book for those who want a good story, great characters, and an understandable lesson in math.