Mathematics: The New Golden Age

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Overview

Mathematics: The New Golden Age offers a glimpse of the extraordinary vistas and bizarre universes opened up by contemporary mathematicians: Hilbert's tenth problem and the four-color theorem, Gaussian integers, chaotic dynamics and the Mandelbrot set, infinite numbers, and strange number systems. Why a "new golden age"? According to Keith Devlin, we are currently witnessing an astronomical amount of mathematical research. Charting the most significant developments that have taken place in mathematics since 1960, Devlin expertly describes these advances for the interested layperson and adroitly summarizes their significance as he leads the reader into the heart of the most interesting mathematical perplexities -- from the biggest known prime number to the Shimura-Taniyama conjecture for Fermat's Last Theorem.

Revised and updated to take into account dramatic developments of the 1980s and 1990s, Mathematics: The New Golden Age includes, in addition to Fermat's Last Theorem, major new sections on knots and topology, and the mathematics of the physical universe.

Devlin portrays mathematics not as a collection of procedures for solving problems, but as a unified part of human culture, as part of mankind's eternal quest to understand ourselves and the world in which we live. Though a genuine science, mathematics has strong artistic elements as well; this creativity is in evidence here as Devlin shows what mathematicians do -- and reveals that it has little to do with numbers and arithmetic. This book brilliantly captures the fascinating new age of mathematics.

Columbia University Press

"Devlin has done a remarkable job describing the profound changes that have taken place. . .in terms that any educated reader can follow."--Herb Wilf, U-Penn

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Editorial Reviews

Mathematical Association of America (of the first ed.)

Excellent.... He presents us with a series of colorful personalities and seminal ideas [and] conveys all of the power, beauty and excitement of mathematics.... Well-written, informative.

Guardian (of the first ed.)

A beautiful, rich book.

New York Review of Books (of the first ed.)

Devlin's choice of material is excellent, and he is to be praised for the clarity and accuracy with which he presents it.

— Martin Gardner

Atlanta Journal-Constitution

Devlin makes the beauty of math apparent, the most esoteric of concepts sing. If more scientists wrote with Devlin's simplicity and feeling, the world would be a much more informed place.

Mathematical Association of America
Excellent.... He presents us with a series of colorful personalities and seminal ideas [and] conveys all of the power, beauty and excitement of mathematics.... Well-written, informative.
Guardian
A beautiful, rich book.
New York Review of Books
Devlin's choice of material is excellent, and he is to be praised for the clarity and accuracy with which he presents it.

— Martin Gardner

New York Review of Books (of the first ed.) - Martin Gardner

Devlin's choice of material is excellent, and he is to be praised for the clarity and accuracy with which he presents it.

Martin Gardner
Devlin´s choice of material is excellent, and he is to be praised for the clarity and accuracy with which he presents it.
Mathematical Association of America
Excellent . . . . He presents us with a series of colorful personalities and seminal ideas [and] conveys all of the power, beauty and excitement of mathematics . . . . Well-written, informative.
Guardian
A beautiful, rich book.
Atlanta Journal-Constitution
Devlin makes the beauty of math apparent, the most esoteric of concepts sing. If more scientists wrote with Devlin's simplicity and feeling, the world would be a much more informed place.
Booknews
Devlin is a mathematician affiliated with St. Mary's College of California, and Stanford U. Center for the Study of Language and Information; he writes extensively and engagingly about mathematics for non-mathematicians. In this work first published in 1988, he charts significant mathematical research beginning in 1960; this revised edition includes developments of the 1980s and 1990s. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780231116398
  • Publisher: Columbia University Press
  • Publication date: 2/15/2001
  • Edition description: Revised and Enlarged Edition
  • Pages: 336
  • Sales rank: 525,062
  • Product dimensions: 5.98 (w) x 9.00 (h) x 0.86 (d)

Meet the Author

Keith  Devlin

Keith Devlin is the Dean of Science at Saint Mary's College of California and a Senior Researcher at Stanford University's Center for the Study of Language and Information. Since 1983, he has been a regular columnist on mathematics and computing for the Guardian newspaper in England, and he is the mathematics commentator on National Public Radio's popular "Weekend Edition" magazine program. He is a Fellow of the American Association for the Advancement of Science and the author of twenty-three books on mathematics and computing, including Life by Numbers and The Language of Mathematics.

Columbia University Press

Biography

Odds are, John Grisham doesn’t get interview questions like this: "If you could meet any mathematician, who would it be?"

But author Keith Devlin does, this time from Discover magazine as part of a January 2001 article coinciding with the publication of his book The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. His answer may go a long way toward explaining why he has managed to make the world of numbers not only understandable but also enjoyable to a segment of the population that can’t balance a checkbook without a net -- or backup from MIT.

“Isaac Newton,” Devlin told the inquiring minds at Discover. “He was a quarrelsome, egotistical person, but he also invented calculus. He did it, by the way, when he was a student at Cambridge. The Great Plague was going on, so the university was closed, and young Newton found himself without studies to do. Most 20-year-olds would think, ‘Whoopee! I’ll just have a good time.’ Newton went home and invented calculus.”

It is this same kind of passion for mathematics that has enabled Devlin, now the executive director of the Center for the Study of Language and Information at Stanford University, to persuade readers that arithmetic, geometry and calculus can be a bracing addition to the stack on the bedside table. In The Math Gene, he explains the “innate sense of number” that lives inside the human mind and how the development of mathematical thinking is closely bound to the development of language. In Goodbye, Descartes: The End of Logic and the Search for a New Cosmology of the Mind, he argues against the possibility of artificial intelligence, saying that computers are simply logic machines that cannot replicate the rational thought and communication that are part of human smarts. In his newest book, The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time, he explains a historic competition announced by a Cambridge, Massachusetts foundation in 2000: Anyone who could solve any one of seven of the most perplexing math problems of the current age would win $1 million.

In a 1999 review, the Economist noted that “Devlin succeeds both in giving us a glimpse of the internal beauty of the subject and in demonstrating its usefulness in the external world. The Language of Mathematics is lucidly written and richly illustrated, and remains accessible and enthusiastic throughout.”

On NPR’s Weekend Edition, where he has become a regular guest, Devlin is referred to simply as “The Math Guy,” or as host Scott Simon once put it “our white knight of the world of mathematics.”

And, going back to that provocative subtitle in The Math Gene, just how is math like gossip? “Mathematicians deal with a collection of objects -- numbers, triangles, groups, fields -- and ask questions like: ‘What is the relationship between Objects X and Y?. If X does this to Y, what will Y do back to X?’” he told Discover. “It's got plot, it's got characters, it's got relationships between them, and it's got life and emotion and passion and love and hate, a bit of everything you can find in a soap opera. On the other hand, a soap opera isn't going to get you to the moon and back. Mathematics can.”

Just don’t forget to carry the 1.

Good To Know

Devlin was the coauthor of the television special A Mathematical Mystery Tour, broadcast as part of the Nova series in 1984.

He once offered as proof of the human brain’s intuitive math skills the ability to judge speed and distance while driving and the ability to add up bowling scores.

Devlin once managed to explain the mathematical difference between a knot and a tangle to National Public Radio’s listeners.

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    1. Hometown:
      Palo Alto, California
    1. Date of Birth:
      March 16, 1947
    2. Place of Birth:
      Hull, England
    1. Education:
      B.S., King's College, London, 1968; Ph.D., University of Bristol, 1971

Table of Contents

1. Prime Numbers, Factoring, and Secret Codes2. Sets, Infinity, and the Undecidable3. Number Systems and the Class Number Problem4. Beauty from Chaos5. Simple Groups6. Hilbert's Tenth Problem7. The Four-Color Problem8. Hard Problems About Complex Numbers9. Knots, Topology, and the Universe10. Fermat's Last Theorem11. The Efficiency of Algorithms

Columbia University Press

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