Book Review: The Math Book by Clifford A. Pickover

The Math Book, by Clifford A. Pickover, is a chronological compilation of 250 of the greatest milestones in the history of mathematics involving the greatest mathematicians. To get a glimpse at the vast time frame Pickover covers he starts at c. 150 million B.C. which is when the discovery that ants can "count" their steps came about and concludes with Max Tegmark's Mathematical Universe Hypothesis of 2007. Each mathematical turning point that is described in this book is portrayed in just a one page entry with a corresponding visual that might help with the understanding of the mathematical achievement. Not only were there several theorems and innovations depicted, numerous mathematicians, logicians, philosophers, and scientists were featured. In some instances I would read two or three entries in a row with the same person mentioned, which I found to be amazing.

All of the entries were intriguing, and of course milestones like the Fundamental Theorem of Algebra, the Pythagorean Theorem, and works from Archimedes and Aristotle we included, but I compiled, though hard to pick so few, some of my personal favorites to share:

• Ant Odometer (c. 150 million B.C., pg 18): The Cataglyphis forits, a Saharan desert ant, is able to travel tremendous distances and return to original starting point with a direct path. Light from the sky isn't  the only thing that helps their orientation for travel but this ant seems to have an internal "pedometer" that counts their steps for measuring distances. A few German and Swiss scientists allowed these ants to reach their destination and then would either amputate their legs or add stilts to their legs. The researchers noticed that when the legs were shortened the ants didn't quite reach their starting point and when the legs were lengthened the ants went too far past their starting point.

• Quipu (c. 3000 B.C, page 28): A quipu was a device used by ancient Incas for storing numbers in the form of strings and knots. The Incas lack of writing left them to record everything by a logical-numbering system on these quipus. Speculation suggests that these information systems contained construction plans, dance patterns, and records of human and material resources. One application of the quipu that I found most interesting and a bit gruesome was that it was used as a death calculator.  The chords represented roads and the knots referred to the sacrificed victims. The quipu dismisses the idea that mathematics prospers after writing is developed. Here is an example of a quipu:
  
  

• Rope Around the Earth Puzzle (1702, pg 162): This particular puzzle intrigued me because of its seemingly external complexity but rather simple solution. The question posed is: If you have a rope that wraps around the equator of a sphere the size of Earth, how much longer would you have to make the rope so that it is one foot off the ground all away around the equator? It seems this problem would be much more difficult than the what the answer is, which is 2*pi.  

• Gödel's Theorem (1931, pg 362): Kurt Gödel was a brilliant logician that had quite a few people in disbelief or conflict. His theorem pretty much dwindles down to that mathematics is "incomplete." I included this as one of my favorites because when I was left speechless, or I guess my mind was speechless!

• Mathematical Universe Hypothesis (2007, pg 516): Max Tegmark came up with the hypothesis that "our physical reality is a mathematical structure and that our universe is not just described by mathematics - it is mathematics." Tegmark believes that we discover mathematical structures rather than invent them. One of greatest debates about mathematics is whether it is invented or discovered and Tegmark sheds some light on this. 

Though The Math Book is a relatively quick read, there is a lot of information to take away from it. If mathematics is even in the slight bit of interest to you, I would recommend this book. Some parts of math can be pretty dense and hard to grasp, but Pickover does an excellent job of condensing the crucial information of each milestone in to a one page entry in a manner that is more easily understood. As a bonus the visuals are just as appealing as the milestones! 



Photo from: http://www.nationalgeographic.com/inca/inca_culture_3.html