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  • Mathematics: Frontiers and Perspectives

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V. I. Arnolʹd
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Mathematics: Frontiers and Perspectives F First Edition

by International Mathematical Union (Author), V. I. Arnold (Editor), M. Atiyah (Editor),
"The twentieth century has transformed mathematics from a cottage industry run by a few semi-amateurs into a worldwide industry run by an army of professionals ... "

--from the Preface by M. Atiyah

This remarkable book is a celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the volume was born as part of the activities observing the World Mathematical Year 2000.

The volume consists of 30 articles written by some of the most influential mathematicians of our time. Authors of 15 contributions were recognized in various years by the IMU as recipients of the Fields Medal, from K. F. Roth (Fields Medalist, 1958) to W. T. Gowers (Fields Medalist, 1998). The articles offer valuable reflections about the amazing mathematical progress we have witnessed in this century and insightful speculations about the possible development of mathematics over the next century.

Some articles formulate important problems, challenging future mathematicians. Others pay explicit homage to the famous set of Hilbert Problems posed one hundred years ago, giving enlightening commentary. Yet other papers offer a deeply personal perspective, allowing singular insight into the minds and hearts of people doing mathematics today.

Mathematics: Frontiers and Perspectives is a unique volume that pertains to a broad mathematical audience of various backgrounds and levels of interest. It offers readers true and unequaled insight into the wonderful world of mathematics at this important juncture: the turn of the millennium.

The work is one of those rare volumes that can be browsed, and if you do simply browse through it, you get a wonderful sense of mathematics today. Yet it also can be intensely studied on a detailed technical level for gaining insight into some of the great problems on which mathematicians are currently working.

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  1. ISBN-10
    0821820702
  2. ISBN-13
    978-0821820704
  3. Edition
    F First Edition
  4. Publisher
    Amer Mathematical Society
  5. Publication date
    January 1, 2000
  6. Language
    English
  7. Dimensions
    7.25 x 1.25 x 10.5 inches
  8. Print length
    459 pages
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Editorial Reviews

From the Publisher

Mathematics: Frontiers and Perspectives - V. Arnold, M. Atiyah, et al.

The mere names of the editors ensure that [the book] is fascinating and exciting ... Several of the 29 authors touch on the nature and/or future of mathematics ... the most interesting essays are those whose authors get out on a limb and dogmatically announce, as saving truth, propositions radically different from common opinion ... Among the authors there are many famous pure mathematicians whose contributions constitute a smorgasbord of delicacies sufficient to satisfy every taste. Do sample them!

--CMS Notes

From the Inside Flap

You can read this book as if listening to a succession of high-powered old school friends who are passing through ... most tell you about the mathematics that animates them ... you get a good sense of what they do, what's difficult about it, and why it matters ... provocative remarks ... vigorous account of much of the Russian school of mathematics ... thought-provoking reflections about mathematical life and language ... The most pleasing feature of this handsome book is the emphasis on the unity of mathematics ... The connections many people here want to make between mathematics and physics, von Neumann algebras and knot theory, number theory and analysis, are not only fresh and vivid, but oddly coherent. They give a sense not only of mathematics undergoing one of its characteristic contractions around a few organising principles, but how productive this reorganisation can be.

--The LMS Newsletter

Product details

  • Publisher ‏ : ‎ Amer Mathematical Society
  • Publication date ‏ : ‎ January 1, 2000
  • Edition ‏ : ‎ F First Edition
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 459 pages
  • ISBN-10 ‏ : ‎ 0821820702
  • ISBN-13 ‏ : ‎ 978-0821820704
  • Item Weight ‏ : ‎ 2.25 pounds
  • Dimensions ‏ : ‎ 7.25 x 1.25 x 10.5 inches
  • Best Sellers Rank: #5,102,219 in Books (See Top 100 in Books)
  • Customer Reviews:

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V. I. Arnolʹd

V. I. Arnolʹd

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Customer reviews

4.1 out of 5 stars
4 global ratings

Top reviews from the United States

  • Peter J. Reynolds
    5.0 out of 5 stars That Hundred Years, and (well), The Next Hundred
    Reviewed in the United States on August 11, 2006
    Format: PaperbackVerified Purchase
    I have perused my new book, and am delighted with it. Technically, I can't get too deeply into the 'Big Five' topics(number, geometry, topology, fractals, and probability), but I am writing in hopes that I could recommend three associated works: Steven Hawking's 'GOD CREATED THE INTEGERS', Benjamin

    Yandell's 'THE HONORS CLASS', and (of course) Morris Klein's

    wonderful 'MATHEMATICS'(The Loss of Certainty). I am sure that

    professional mathematicians are familiar with these works, but

    they might really 'get you in the mood' for Mr. Arnold's book.
    3 people found this helpful
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  • Yan Jiang
    4.0 out of 5 stars Four Stars
    Reviewed in the United States on May 24, 2015
    Format: PaperbackVerified Purchase
    Good!
    Helpful
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  • Bernardo Vargas
    1.0 out of 5 stars Dissapointing.
    Reviewed in the United States on July 18, 2000
    Format: Hardcover
    Judging from the publisher and the editors I expected to get a really outstanding book, but while reading it I got terribly dissapointed.
    This book, with which the International Mathematical Union tried to emulate the famous list of problems proposed by David Hilbert in 1900, together with his description of the state of mathematics those days, totally fails to survey the state of this science in the year 2000 and does even less to present a comprehensive list of important problems in all branches of mathematics that should be solved in the 21st century.
    The editors - all of them highly respected and renowned mathematicians - didn't make a strong effort to collect the opinion of several other high-ranked colleagues; instead they asked their buddies and pupils for contribution. I really would like to read something about the topic from Elias Stein, Steven Krantz, or Serge Lang, to name just a few. Also, the editors could have done something to reach some kind of agreement among the contributors; while some pose some problems of their own interest others claim that even trying to imitate Hilbert is nonsense. Some dissert on the interaction between mathematics and physics (there's even one who claims that mathematics is a part of physics) but almost none pays attention to the newer ineractions between mathematics and other disciplines. It seems that they haven't realized that nowadays most of the motivation for difficult and interesting problems comes from such areas as economics, communications, military and computer science. Its surprising that almost all of the contributors still think that theoretical physics is the main supplier of mathematical problems.
    And the worst: they didn't cover all the branches of mathematics (true, it's a difficult task, but the AMS and the IMU should be capable of doing that). There's nothing said about operator theory, hypercomplex analysis, coding theory, commutative algebra, wavelet analysis, and many other disciplines. Their major lack is applied mathematics, I mean, probability, statistics, reliability, simulation, operations research, etc. Most of the contributors blame Bourbaki for having gone away from the actual sources of mathematical knowledge, but they remain in the Bourbaki setting themselves!
    Conclsion: better spend your money in fine and focused reflections about mathematics and mathematicians, like Hardy's, Polya's, Wiener's, von Neumann's, and even Bourbaki's.
    37 people found this helpful
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