Gamma: Exploring Euler's Constant Princeton Science Library: Amazon.co.uk: Freeman Dyson, Julian Havil: Books

Review

[A] wonderful book. . . . Havil's emphasis on historical context and his conversational style make this a pleasure to read. . . . Gamma is a gold mine of irresistible mathematical nuggets. Anyone with a serious interest in maths will find it richly rewarding. -- Ben Longstaff, New Scientist

This book is a joy from start to finish. -- Gerry Leversha, Mathematical Gazette

[Gamma] is not a book about mathematics, but a book of mathematics. . . . [It] is something like a picaresque novel; the hero, Euler's constant g, serves as the unifying motif through a wide range of mathematical adventures. -- Dan Segal, Notices of the American Mathematical Society

The book is enjoyable for many reasons. Here are just two. First, the explanations are not only complete, but they have the right amount of generality. . . . Second, the pleasure Havil has in contemplating this material is infectious. -- Jeremy Gray, MAA Online

It is only fitting that someone should write a book about gamma, or Euler's constant. Havil takes on this task and does an excellent job. -- Choice

This book is accessible to a wide range of readers, and should particularly appeal to those who feel a love for mathematics and are dissuaded by the dryness and formality of text-books, but are also not satisfied by the less rigorous approach of most popular books. Mathematics is presented throughout as something connected to reality. . . . Many readers will find in this book exactly what they have been missing. -- Mohammad Akbar, Plus Magazine

This book is written in an informal, engaging, and often amusing style. The author takes pains to make the mathematics clear. He writes about the mathematical geniuses of the past with reverence and awe. It is especially nice that the mathematical topics are discussed within a historical context. -- Ward R. Stewart, Mathematics Teacher

Product Description

Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery.

In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics.

Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . .. But unlike its more celebrated colleagues p and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction.

Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!).

Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.

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18 of 20 people found the following review helpful

A must have for any maths enthusiast. 17 April 2003

By Andy Richardson

Format:Hardcover

I had heard that this book was coming out and, having read the books by Maor and Nahin, was looking forward to the next 'constant' treatise from PUP; it' s great that the author is English this time! Well done PUP for letting the Brits in (I see that they now have an office in England). The book is (for me) the best yet of the series (if that is what it is) and having read it I can see why Gamma was the topic to be chosen (pi has of course been done several times and so has the Golden Ratio). Havil is a new author and an extremely good one-and he knows his maths. I am just an amateur enthusiast and as such I have learned so much maths from his exposition. The Harmonic Series stuff leading to the Zeta functions was some of the best for me and opened my eyes to the Prime Number Theorem and the Riemann Hypothesis; why has no-one else explained them so clearly and interestingly-and without avoiding the maths? As the author says, some parts need work to understand but it's very rewarding to get to grips with the ideas and particularly with the historical perspective that is woven into the pages. Now I have 3 great books from PUP on mathematical constants on my shelf...I await the fourth..

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15 of 17 people found the following review helpful

Who would have thought!? 27 Jun 2003

By Palle E T Jorgensen

Who would have thought that there can be so much life in a constant? And one with a Greek name! If you have some math interests, I predict that you will get caught up in the thread of events: They are mathematical topics, but are presented like in a novel or a drama. A book that I couldn't put down. The main characters are the harmonic series, the sub-harmonic series, Riemann's Zeta function, its functional equation, its zeros, the Riemann hypothesis(it is worth a million dollars!), the prime number theorem, (..hard stuff! but it somehow seems easy in this book),Bernoulli numbers, Pell's equation, the distribution of prime numbers.... And if you forgot some of your math, you will have it reviewed in the appendices. They are attractive, well written, and to the point.

A Remarkable Compilation of Mathematics 16 May 2003

By Jonathan Trubshaw

The book has just become available in the UK, although it has been on sale in the States for about a month it seems. Havil has filled the gap by writing a book about Euler's constant, Gamma; it was the most obvious number missing from the growing library of 'popular' mathematical explanations. The historical approach of these expositions has great appeal and provides welcome respite from some of the actual mathematics; in the case of this book, there really is a great deal of mathematics too. Fortunately, the explanations are clear and interesting and the whole tone of the work is one of exitement. The author has used the opportunity to cram in as much interesting (and sometimes offbeat) mathematics as he can and as a result the work is pretty much a selective encyclopaedia of some areas of the subject. The reader certainly needs at least a good A level and more than that if the final chapter on the Riemann Hypothesis is to be taken on. Havil's book is nicely complimentary to the other more popular books that have recently been published on this, with the mathematics there in pretty much complete form. In summary this is a quite superbly crafted book with a central important theme and many welcome diversions from it. The author deserves the success that he will no doubt enjoy: bring on his next book!