Customer Reviews

Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning

5 star:		(13)
4 star:		(3)
3 star:		(1)
2 star:		(1)
1 star:		(1)

 

 

Now here is a fine weekend escape - a delightful book to be read with one's feet up and an ice cold beverage all the while contemplating the wonders of numbers. Mostly about the integers, there are such mathematical adventures as 2, 3, and 4 dimensional magic squares, numbers so huge they require special notation and easily dwarf the number of atoms in the known universe, fractal number sequences, Mozart numbers, and lots of other fun things in the 125 chapters. My favorite numbers are the Schizophrenic numbers (Chapter 93) which when evaluated to 500 digits reveal patterns of seemingly random digits alternating with chains of repetitions of identical digits. The book is especially entertaining for the connections shown between some of these numbers and music, art, science, and other areas of mathematics.

For additional enjoyment the Further Exploring section offers additional background including references to books and web sites and also some challenges to readers - a few of which even include a cash prize. And, best of all Wonders of Numbers is written in plain English and accompanied by splendid graphics, lively anecdotes, and a generous supply of epigraphs. A fun way to while away a weekend.

Pickover's latest book is wonderful! I specialise in teaching very able mathematics students and have used Clifford A. Pickover's books and web site with great success. The students really respond to his sense of humour.

Wonders of Numbers is exactly the sort of material which stimulates the bright kids (and their teachers!), and gets them thinking in depth long after the class has finished. It takes them beyond the idea of just "getting sums right" to the concept that mathematics is a glorious plaything.

Many of the chapters include computer related themes (fractals, programming) so students can see that mathematics is an evolving subject, not something which was all discovered long ago.

The constant inclusion of interesting people, the humour in the writing, the validity of the topics mathematically, the strange sidelines and the general sense of fun, ensures I have another gem to extend the students beyond the regular curriculum. The chapters are just the right size to initiate a topic and motivate the students to pursue it. It is lovely to have material to use which doesn't just lead to a correct answer and end to the problem, but leads them to take it further and further.

Wonderful!

Narrated by the outstanding and eccentric mathematician Dr. Francis Google, this book is a collection of unusual mathematics problems, from those involving very large numbers to those defined by applying operations. For example, the Leviathan number (10^666)! is used to demonstrate that it is not necessary to compute a number to learn some of the properties that it has. Sets of numbers such as apocalyptic numbers, those that involve 666, the number of the beast, appear several times. One of my favorites are the Schizophrenic numbers, defined by the formula f(n) = 10 * f(n-1)+n, f(0) = 0, which is a set of integers demonstrating a simple pattern. However, the action starts when the square roots of the numbers are taken. These roots exhibit an unusual, repeated pattern in their digits.
Some incidents of mathematical history that are interesting trivia are also used. The number 365, 365, 365, 365, 365, 365 is supposedly the largest number that was ever squared in the head of a human. Other segments were based on surveys, where people answered questions such as, "Which would have had the greatest impact on the world as we know it today: `If Albert Einstein had lived another twenty years with a clear mind?', `If mathematician Srinivasa Ramanujan had lived another twenty years with a clear mind?", If Steven Hawking was not afflicted with Lou Gehrig's disease?'." A ranking of the top eight female mathematicians of all time, a listing of the five greatest scandals in mathematics history, the ten most important unsolved mathematical problems, the ten most influential mathematicians of all time, the ten most influential mathematicians alive today and the ten most difficult areas of mathematics to understand provide additional intellectual fodder.
Every time I read a Pickover book, the number of ideas used as the seeds to generate the text astounds me. He always seems able to come up with new twists on old problems and sometimes new problems that set your brain moving in circular motions as you try to comprehend the consequences of the statements and attempt to follow the logical consequences of the transformations. While some of the best books keep you reading from page to page without stopping, others cause you to read a little, process a lot and then read some more. That is what this book did to me, and I am sure that it will do the same to you.

Published in the recreational mathematics e-mail newsletter, reprinted with permission.

Pickover fans will buy and enjoy this book - his 26th by my rough count.

But if you aren't a fan, if you've tasted and returned to the kitchen previous titles by Mr. Pickover, you might still enjoy this fascinating buffet.

And those are 5 hard-earned stars in my rating! I was well past starting to think that the best parts of Pickover's books were the always-intriguing titles. I had started a number of these in the past, but usually ended up skimming or setting them aside. None that I have read would have earned more than 3 stars. Until now!

"Wonders of Numbers" is, somehow, different. It still has some of his quirky lists ("The Unabomber's 10 Most Mathematical Technical Papers", "A Ranking of the 5 Strangest Mathematicians Who Ever Lived"). It still has the intriguing titles - each of 125 "chapters" carries one, ranging from "The Pipes of Papua" to "Anchovy Marriage Test". The pieces still seem to jump all over the place. Most of these things didn't grab me in past Pickover titles. Here, they all fit together and work nicely.

Oddly enough, I think the appeal of this volume might be its eclecticism. Pickover is not trying to create a whole story as he has in some earlier books ("Time: A Traveler's Guide", "Surfing through Hyperspace"). The unifying center of this book is, simply, mathematics and the myriad ways it exposes its wonders to us. I'm guessing that the reason I haven't put this one down is my own fascination with mathematics itself. The broader the scope the better - and none takes a wider view than Clifford Pickover. The book has something for everyone - but it will also draw you in to other pieces you thought you weren't interested in. Martin Gardner meets Conway & Guy ! A nice combo.

An amazing amalgam of mathematical treats! Each chapter is super short. Fun for readers of wide abilities. Here are some of my favorite topics: Ackermann's function, Maria Agnesi, Alien snow, Amicable numbers, Apocalyptic numbers, Audioactive decay, Bible code, Catalan numbers, Cellular automata, Doughnut loops, Paul Erdos, Fractals, Sophie Germain, Goldbach Conjecture, Hexamorphic numbers, Obsessive-compulsive disorder, Palindromes, Roger Penrose, Poincare Conjecture, Srinivasa Ramanujan, Scandals, Self-similarity, Transcendentals, ... and more.

I really enjoyed this book. There's a tremendous number of interesting questions raised, many of them currently unanswered. Not a huge amount of depth on any particular question but each chapter has it's own "alter ego" at the back in the "further investigations" part of the book with answers (when they're known) and resources to take off on your own. The book actually becomes most interesting when you're not reading it - when you've set it aside and started thinking about the interesting ideas on your own. Most of these problems are simple enough to comprehend that you can immediately start making new little discoveries on your own if you're even a little mathematical. Very "Martin Gardner"ish in that sense, and in my book there's no higher compliment to pay to a book than to compare it to Gardner's classics. So if you have a mathematical bone in your body and you want to exercise it this is a great book to use as a springboard into really interesting and big ideas.

This latest book of Pickover's never ceases to amaze me. There are 100s of puzzles, some playful, some very deep. The numerous illustrations make this book a delight. My favorite chapters were those on how to create caverns using simple rules, Faberge egg synthesis, Gaussian frothlike bubbles produce by fractals, and Spidery Math. I also liked some of the unusual surveys. Something for everyone! The range of problems is so extraordinary that I think even middle school students would like many parts of this book -- yet the book will also appeal to seasoned mathematicians and grad students. The publisher has some of the computer code on a web page, but you don't need a computer to have fun with this book.

The book has a walloping 125 short chapters divided into 4 main sections titled: 1) "Fun Puzzles and Quick Thoughts," 2) "Quirky Questions, Lists, and Surveys," 3) "Fiendishly Difficult Digital Delights," and 4) "The Peruvian Collection." Sample chapter titles: "Attack of the Amateurs" (describes how amateurs have made progress in math), "The Fractal Society" (games played on fractal playing boards), "Einstein, Ramanujan, Hawking" (some thought-provoking questions), "A Ranking of the Five Saddest Mathematical Scandals" (hard to guess), "The Spring of Khosrow Carpet" (recipes for creating Persian carpets), "Schizophrenic Numbers" (weird stuff!), and "The Emerald Gambit" (fun puzzle).

Buy the book and feed your head (or your kid's head).

This book contains a delightful collection of mathematical puzzles in the tradition of Martin Gardner. There are Klingon Paths, Hexagonal Cats, Messages from the Stars, and Doughnut Loops. If you liked the puzzles in Pickover's "Alien IQ Test", you will like the puzzles in this book.

The book is not all numbers. There are historical anecdotes and stories about mathematicians told by the author's alter-ego, Dr. Googol. Are all mathematicians insane? The answer is not clear. However, the author describes the five strangest. Did you know that Pythagoras believed that it was sinful to eat beans?

There are a number of interesting top ten lists. As one who thinks that the proper role of mathematics is to solve the problems of the physical world, I was happy to note that Dr. Googol chose equations of physics for six of the ten most important mathematical expressions, e.g. Gauss' law and Newton's law of gravitation. Dr. Googol must have some physicist friends.

This is just one in a series of wonderful books that Dr. Pickover has written. I also recommend "The Science of Aliens, or Time: A Traveler's Guide", and his new book "A Passion for Mathematics".

The best collection of math topics! Each chapter is less than 5 pages and you can jump right to any of them and have fun: check "Who is the Number King", or "Hailstone Numbers", or "Hexagonal cats", or many many others. Written in "recreational" style with numerous curios facts and ideas this book provides hours of entertainment!

You don't need to be an advanced mathematician to enjoy and benefit from this book. I think the ideal reader is someone who is interested in numbers and likes to think about things in logical and interesting ways.

While I found this book a lot of fun (even at my age), I think it would be ideal for a high-school student who had developed some facility with numbers and was busy developing their thinking patterns. This book would help them learn to think in new ways and probably give them some new paths to explore.

It isn't just interesting problems, although there are many very interesting things to solve. There are fascinating lists and explanations that can spur continued investigation and even provoke development through disagreement!

The "answers" in the back provide explanations that are also written as a springboard for further investigation.

Good stuff! Four stars only because it is so specialized. But if you like this topic it is a five star book.