DAVID WELLS has written extensively on problems and popular mathematics, and many of his titles are available in Penguin. He is involved in education through writing and research, and lives in this country.
No recreational mathematician should be without it2000/12/11
In the foreword to G.H. Hardy's book A Mathematician's Apology, C.P. Snow tells an anecdote about Hardy and his collaborator Srinavasa Ramanujan. Hardy, perhaps the greatest number theorist of 20th century, took a taxi from London to the hospital at Putney where Ramanujan was dying of tuberculosis, Hardy noticed its number, 1729. Always inept about introducing a conversation, he entered the room where Ramanujan was lying in bed and, with scarcely a hello, blurted out his opinion about the taxi-cab number. It was, he declared, "rather a dull number," adding that he hoped that wasn't a bad omen. "No, Hardy! No, Hardy," said Ramanujan, "it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways." Usually it takes a great deal of insight as well as considerable mathematical training to discover a yet unknown properties of some number. Only recognizing the beauty of a number pattern is much easier, though, especially with a friendly book like this one on hand. Wells, a long-time mathematics popularizer, has collected over 1000 numbers he considers interesting. Each of them is given a short explanation, often accompanied with a bibliographic reference. Celebrities among the numbers, like i, e or Pi, are given a more comprehensive treatment. Included are also several sequences, like Fibonacci's, Mersenne's, Fermat's, Carmichael's or Kaprekar's, each accompanied with its explanation. So are cyclic, amicable, untouchable or lucky numbers, and many more sequences you probably didn't know about. While Wells' dictionary certainly gives the impression of a well-researched work, the list of numbers is by no means exhaustive. Anyone familiar with chaos theory will notice the absence of Feigenbaum constant; prime hunters would probably be interested in discussion on Woodall primes, Sophie-Germain primes, or Proth primes. But they are better off with Paulo Ribenboim's book on primes, anyway, while Wells' book, with its easily understandable explanations and accessible price is probably more suited for the "recreational mathematics" audience.
Googolplex good reasons why read this book!1999/4/30
Loaded with information, light-hearted and extremely well written! The book is so enjoyable that whenever you get near it you feel like grabbing it and find the vices and virtues of yet another number. And between one number and the next, one meets an entire gallery of mathematicians, mathematical terms, unsolved problems, great achievements and colossal mistakes... It's a jewel of a book - I strongly reccomend it.
Great for Middle and High School Students2000/6/16
Gary the blues man
A great supplemental tool for teachers! I had terrific fun with my 6th grade math students when reading them certain passages in this book. Many of the topics covered, such as factorials, hexidecimals, triangular numbers, pi, primes, etc. are not generally covered in the middle school very well or at all, and this book serves as a great launching tool for discussions that kids enjoy and think about long after class is over. Also, many topics go in depth and will challenge even the best high school math students and take them in many directions that traditional math education does not.
For me, this is a dream book: I can read it on the bus to work (with the necessary ear-plugs inserted to filter out cellphone conversations) and marvel at the succinct, witty and colorful entries & all that they convey about the magic of numbers. I recommend it to anyone who loves mathematics and who occasionally gives rein to the impulse to tell other people all about the amazingly weird thing one just discovered about a certain number ...
I wanted to dock this half a star. I also wanted to seek out David Wells and shake him down, because ... a number of entries mention a function, phi(n) (this is not "the golden ratio," by the way, although that phi is also discussed in this book). I had no idea what this function was or entailed, so checked in the index, according to which the function is defined under the entry for the number 30. I repaired to the entry for the number 30 and found ... no such definition. Aiee! I looked again. And again. Could not find it. There _is_ an anomalous blank line in the paragraph under the heading '30' ... perhaps it was there and somehow got dropped (and never re-inserted) in a reprinting? I don't know.
I eventually looked the function up in other books, and it IS interesting ... but what happened to Well's entry?
Eventually I will have read through the entire book and, if it is in there somewhere, I will find it -- and come back here to update this review (either that or someone will point out to me where it is).
UPDATE 11.2.12: Of course I found it -- it is defined, along with a number of other functions / things, in the Glossary at the front of the book.
I should also add that the Kindle edition should be avoided. My experience with Kindle + mathematical content has been woeful.
Wonderful starting point to a lifetime of investigations1998/6/6
This book gives a summary of every interesting number known. A great way to find areas of maths to explore further and use as a stimulus to teaching. Check out his other Penguin Dictionaries, too - they make a great set.