Top positive review
A sound description of how the irrationals went from the bizarre to routine high school material
on 4 January 2015
When ranking the level of difficulty of a mathematical textbook, the phrase "mathematical maturity" is often used. This refers to that general increase in mathematical ability that one expects students to achieve as they study more and more mathematics. The phrase can also be used to describe the mathematical community as a whole as it develops, assimilates and then refines new concepts until they often reach the level of the routine.
One sees this thread throughout mathematics, in this book the maturity of the mathematical community in discovering, developing and refining the theorems of irrational numbers is covered. Although there is scholarly debate on the severity of the reaction to the initial knowledge of the existence of the irrationals, there is no question that it was significant. Havil does an excellent job in describing this collective mathematical process and spares no equation in the process. He captures the spirit and difficulties as generations of mathematics toiled for hundreds of years in order to develop a sound definition of the irrational numbers as well as the logical mechanisms to work with them.
There is no question that this ongoing process was a major success, I do not remember the precise time in my education where I was first exposed to irrational numbers, but believe that it was in the ninth grade. Now, irrational numbers are routinely discussed, manipulated and occasionally cussed in the high schools, which is certainly the definition of a topic that is "mature." In no way a popular book on mathematics, this book is a sound description of this trek from the "bizarre" to the routine.
Published in Journal of Recreational Mathematics, reprinted with permission