Mathematics: The New Golden Age

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Mathematics:
The New Golden Age

by
Keith Devlin

general information | our review | links | about the author

Title:	Mathematics: The New Golden Age
Author:	Keith Devlin
Genre:	Mathematics
Written:	1999
Length:	309 pages
Availability:	Mathematics: The New Golden Age - US
	Mathematics: The New Golden Age - UK
	Mathematics: The New Golden Age - Canada

This is a (fairly extensive) revision of the first edition, published in 1988.
The (British) Penguin and the (American) Columbia University Press editions apparently differ slightly. This review refers to the Columbia University Press edition.

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Our Assessment:

B : interesting survey of contemporary mathematics and recent advances and discoveries

See our review for fuller assessment.

The complete review's Review:

Keith Devlin's objective in this book is to convey:

... to the interested layperson some of the most significant developments that have taken place in mathematics in recent times.

       Restricting himself to advances since 1960 that have "merited attention in the world's press" he still manages to offer a broad overview of a variety of areas of mathematics. The eleven chapters in the book deal with mathematical problems much in the news -- chaos theory and Fermat's Last Theorem -- as well as others, from topology to that old standby, the four-colour problem.
       It is an interesting mix, touching upon a broad range of mathematics, from prime numbers (and their use in creating secret codes) to group theory to algorithms. Devlin also manages to tie the various areas together, showing the often surprising connections that exist in mathematics.
       Most of the chapters are built around specific examples, mathematical problems that were recently solved. Fermat's Theorem is the best known of these, but others, such as Hilbert's Tenth Problem, the four-colour conjecture, and the classification of finite simple groups are also discussed. In setting up these problems and describing the historical backgrounds to them -- as well as the many mistakes made in trying to solve them (often by illustrious mathematicians) -- Devlin manages to provide a broad picture of these areas of mathematics. Of particular note, as he mentions several times, is how modern computational ability has facilitated discovery in certain areas -- indeed, how it has fundamentally changed the nature of mathematical proof in certain areas (an advance that brings its own difficulties with it).
       Devlin is particularly good at showing the change in mathematics and how mathematics is done. By contrasting the original approaches to mathematical problems and questions with modern ones he provides good insight into the practise of mathematics in this day and age.
       The examples are complex ones, and Devlin generally only outlines the approaches taken, the solutions themselves being far too advanced (and detailed and long) for any book such as this one. Nevertheless, he tries (generally successfully) to explain the main points and discoveries which allowed for the solution of the problems. The mathematics Devlin employs is fairly basic and he explains the formulae he uses quite well; nevertheless, it does require some patience and effort for the non-mathematician to follow. Only the completely innumerate will be stumped by much of it -- it is not an elementary text. For those subjects that can be illustrated in pictures (the four map problem and topology (and knots !) in particular) there are also many useful illustrations.
       It is hard to convey mathematics clearly, especially when dealing with arcana that is almost completely inaccessible to anyone but a specialist. Devlin offers the gist of many of these problems and areas of interest, a simplified version that gives a good general idea of the maths involved without getting bogged down and lost in the specifics. He presents the topics well, and this volume is a useful survey of recent mathematical advances. It also provides a good general picture of the contemporary state of mathematics.
       In his title Devlin suggests ours is a "new golden age" of mathematics. Certainly, these past decades have been rich and fruitful, with a large number of stunning achievements. Devlin's examples show that these are exciting times to be involved with mathematics -- and that it is well worth knowing what is being done in the field. A good, relatively accessible survey, relating many interesting episodes from mathematics, this volume can certainly be recommended to those interested in mathematics and the history of mathematics.

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Links:

Mathematics: The New Golden Age:

Columbia University Press publicity page

Keith Devlin:

Faculty page
Devlin's Angle archive

Other Books under Review that might be of interest:

Imre Lakatos' classic Proofs and Refutations
Deborah J. Bennett looks at Randomness
Stephen M. Stigler tosses Statistics on the Table

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About the Author:

British-born mathematician Keith Devlin is 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. A prolific author he has published some two dozen books, as well as writing for The Guardian and regularly writing the column Devlin's Angle on the MAA site.

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