Gamma: Exploring Euler's Constant (Princeton Science Library)

An excellent mathematical book! It's actuality less about Euler's Gamma constant than about logarithmic functions and related. Prime Numbers and their relation to Riemann's Zeta Function and the Li Function are covered and constitute a significant portion of the book. Much of this territory parallels mathematical portion of John Derbyshire's "Prime Obsession"; another excellent book! Havil does not delve much into the personalities behind the mathematics, as Derbyshire does. Havil's approach is also more mathematical; at a minimum the reader should have a good familiarity with Calculus. For a math hobbyist, the book gives lots of hints that can be used for calculating by computer esoteric functions such as the prime counting function Pi(n). Other topics are covered as well, for example Benford's law which posits that the first significant digit of numbers seen in everyday life -- such as street addresses -- are counter-intuitively not uniformly distributed but instead distributed -- you guessed it -- in a way related to logarithms. Really a wide ranging discourse on everything logarithmic, Euler's Gamma being one of them! A great read for the mathematically inclined!

I am a fan of Havil. And rate this book highly, but I just ordered a print edition because this kindle edition has math too tiny to read without zooming each individual entry -- which is a pain. It appears to me that whoever created the kindle edition never checked his work. I'm surprised that the author hasn't insisted on a fix. I'd complain to amazon, but I've misplaced Bezo's email address.

Like all of Havil's many mathematics books this one is excellent. It is presented at a level that is very high, however, by which I mean that he assumes a pretty thorough grounding in Calculus and Differential Equations -- a better one, evidently, than I acquired, albeit it 40 years ago, as an undergraduate Mathematics major at the U. of Chicago. I wish the book had more graphics and examples to clarify the most difficult concepts, as well as a fuller explanation why knowing about gamma and its associated functions allows one to do important things, both with respect to other mathematics and with respect to problems that arise in the everyday world

I have always found Euler's constant interesting because I would like to be able to say that it is one of the 3 great transcendental numbers along with pi and e. The number e is what Kurt Mahler called an S number; perhaps pi and Euler's constant also are. My interest started about 1968 and I was soon led to the gamma and Riemann zeta functions. I am pleased to see that Havil confirms the path I followed.This is a very interesting book about a relatively unpublicized development of calculus. Admittedly this book requires good skills in mathematics, but let's be candid: a good understanding of mathematics calls for experience in working things out.Now I must express a disappointment. I bought the book at least in part because I wanted to know the history of attempts at proving (or disproving) the transcendence of Euler's constant. I have found almost nothing. There is a copious history of attempts at proving Fermat's last theorem. Perhaps Euler's constant has just not attracted so very much effort. I do not know of any financial reward that has been offered for Euler's constant. Hilbert in 1900 did not specify this number in his seventh problem. I have not seen this problem emphasized as one for the 21st century.For some years I thought of questions that might lead to a proof or disproof of transcendence. How long is the shortest proof that Euler's constant is transcendental or not? Can the question be answered in finitely many steps? Is there a number related to Euler's constant in the way that e is related to pi? I did not find these questions mentioned in this book.It is my hope that some high school student (or even grade school student) will read this book and, perhaps after some 40 years, become the Andrew Wiles of Euler's constant.

I was hoping to find a book that went further into the rabbit hole of the gamma constant than most books. It pops up in many places, but why? Here, Havil goes further than I expected, and is easy to follow. He also remains entertaining while doing so.And it is always interesting to end up with my favorite subject, the Riemann Hypothesis. My friends sometimes tease me for reading books on math and the Riemann Hypothesis (boring!), but they noticed my enthusiasm for this one.

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.

This is an extremely well written book. Havil's exposition ties together much historical mathematics - Naperian logarithms, harmonic series, series expansions for pi, Euler's contributions, etc - and presents the topics in a detailed, coherent, and lucid manner. I very much like the way Havil leads the reader in a clear fashion into the Riemann Hypothesis and related topics. This book strikes a nice balance between a text book and some of the current nicely written but rather elementary expositions of mathematical topics. I will scan the Amazon web pages for future texts by this author.

I'm only a few chapters into the book, so this should not be considered a review of the contents, but I do want to note that the typeface is extremely small in the paperback edition. If you have trouble reading small type, as I do, reading this book will cause severe eyestrain.

Although I say "accessible" , be warned this is a book for someone with say single subject A level maths, and one needs a pen & paper to work through it: the book is not a popularization, but a serious attempt to explain number theory , Gamma, and in the end the Riemann Hypothesis, to a wider audience.From introductory calculus, the integral of 1/x is the natural logarithm of x. Imagining the graph of 1/x divided into strips of width one, the graph is bounded above and below by these strips 1/n : Gamma is the limiting number, as n gets larger, of the difference (log(n)- (1+1/2+1/3+...+1/n)). It's about 0.577,, No one knows whether it is the solution of an equation or is not, like pi or e.The book successfully answers the question "just what is it about the the complex zeros of the Riemann zeta function that makes them relevant for the distribution of prime numbers and the Prime Number Theorem?"Hence in some sense this book could be regarded as a follow on to John Derbyshire's book Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in MathematicsPrime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

A brilliant book and one you'll return to again and again!Highly recommended for anyone with an interest in maths, an impressive and illuminating work.

well written book on the Gamma Function

Freeman Dyson is not a co-author, he merely wrote the foreword.I think the attribution on Amazon's website is therefore misleading.

Very nice and informative reading on Euler'constant gamma but has also much material on logarithms, the harmonic series and zeta functions. As the author makes clear at the begining, you really need pencil and paper sometimes. The last two chapters on the Prime Number Theorem and Riemann Hypothesis, respectively, are particularly harder than the rest of the book. In general, the book fails sometimes at not giving explicit references for various informations but the really curious reader can find these elsewhere as he decides to go deeper.