This book wants to illustrate how mathematics has grown. New results were only possible thanks to what was done before. A step forward is only possible with the right person at the right time in the right place. The mathematicians are of course the instruments that make this progress possible, and yet these are humans, an aspect that is sometimes forgotten when his or her name is just an abstract name specifying some theorem of transform. This is what the authors have tried to illustrate when compiling this book.

The book starts with a general, relatively short (only 35 pages), introduction to mathematics and how it evolved from numbers and counting, over astronomy, algebra, calculus, to what we now know as mathematical science. But evolution does not stop there. It is still evolving under the influence of computers and computer science whose history of algorithms is interwoven with the history of mathematics.

The major part of the book is an encyclopedic collection of names of mathematicians and computer scientists (the distinction is often minimal and fuzzy) with a short biography and their main achievements. They are listed in chronological order from 3374 BC till approximately 2000. Each name gets a mention varying from a few lines (e.g. Hölder, Laguerre) to a some six pages (e.g. Pythagoras, Gauss). Clearly the time line is more densely populated towards the 20th century. It is also obvious that, even though many names are in the list, there is a chance that your favorite mathematical hero does not appear or does not get the attention he or she deserves. It is too easy to give critique and to find examples of people missing. You might also find much more information about mathematicians on the well known MacTutor history of mathematics website. Even though for the longer entries of this book, there is some overlap with the corresponding online biography (if it exists), it is also complementary, since there are details to be found in the book that are not online and vice versa. The main advantage of this book however is that it is concise and that it is not only restricted to pure mathematicians since also more applied, numerical, and computer oriented people are included. Although, given the more recent history of computer science and computational aspects, the majority of the entries are of course mathematical.

What is included and what is not is a choice the authors had to make. Usually a minimal entry contains the year and place of birth (if known), a sketch of the career and what the person is remembered for. For the longer descriptions, also some details on the person's character and private life is given. The authors hope that this will shed some light on the way the person was thinking and how he (there are not many she's) came to his results. Where appropriate the person is placed in relation to his contemporaries and possibly between predecessors and successors. But all this remains very brief and to the point as you may expect in a one-volume encyclopedia.

The book has an extensive name index as well as a subject index. These are clearly essential instruments for a book like this. I had a problem though of finding Ada Lovelace. She is a daughter of Lord Byron, and is generally considered to be the first computer programmer. She was married to Lord King, Count of Lovelace and hence became known as Ada (Countess of) Lovelace. You should know that you have to look for her under the "C" of Countess and not under the "L" of Lovelace. Her father George Gordon Byron (Lord Byron) is listed as "Byron, L.". (No problem here since he is under the "B" of Byron where he should be, but the "L." is apt to discussion.) Knowing this, I could also spot an "Earl" and a "Duke". So it may require some imagination to find who you are looking for. Fortunately these are exceptions. The name used is what the authors consider the most widespread. For example Marie Słodowska Curie is listed as "Curie, Madame", while "Madame" is not really her first name. For some reason, the name of Galois is spelled Galöis, no explanation given. I could not find this spelling anywhere else.

One may wonder it it is still a good idea to bring this kind of encyclopedia on paper, while a dynamic database might be a more appropriate format in this time of e-libraries. I believe that for the time being, there is room for this version of the book. It contains all the information in one volume, not available elsewhere in this form. So it certainly deserves a place in a mathematics library. For those who explore the world from behind their computer, they can use the pdf version in which they can search electronically if they prefer that instead of paging through a hard copy book.