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Clever math book's insights add up

Hey there, time traveller!
This article was published 13/6/2014 (1139 days ago), so information in it may no longer be current.

Once every generation, it seems, there is a crisis in math pedagogy. The debates over how math is taught have their source in some variation of the rift between the roles of rote learning (such as memorizing the multiplication tables) versus teaching primarily the comprehension of conceptual matters of math.

This muddle over some version of a "new math" plays out against an important psycho-social backdrop; namely, that only a small percentage of humans have a strong and positive affinity toward math of any kind. The rest of the race embodies a deep antipathy: from those with a math anxiety, through those whose eyes glaze over if anything even hinting at numbers arises, to those who will not even pick up a book if it contains an equation.

No wonder commercials for math-teaching tools must resort to parading kids screaming, "We love math!" to an otherwise apathetic audience.

Jordan Ellenberg, a widely published math professor at the University of Wisconsin-Madison, has no compulsions about putting math in his book. Indeed, he unabashedly wallows in it, for the book is chock full of numbers, tables, diagrams, and those dreaded equations.

The hook for the possibly reticent reader is that the book is not about math as mathematics alone, but rather about applied math, the mathematical stuff that underlies real and diverse things in the world, such as the stock market, lotteries, political polls and elections, and the efficacy of drugs.

Well-written in an informal chatty style, it purports to explain math to those not trained in math or not enamoured with numbers. And it delivers, but beware: don't be fooled by the relaxed atmosphere.

Many a reader will need to stop, reread and maybe even make some notes on many of the topics in order to understand completely his arguments. For example, the long section on betting in lotteries will surely lose many novices as Ellenberg plows through probability theory and the shenanigans of what the bettors do.

Nonetheless, overall the book is clever, witty (when was the last time you laughed out loud at a math book?), and crammed with fascinating stories ranging across science, baseball, psychology, art, theology, criminology, medicine, warfare and more.

There are many highlights: an important explanation of various ways in which percentages can fool you; an exposition on the statistical errors in the alleged secret codes in the Bible; an elaboration of the critical distinction, often missed, between correlation and causation; a fascinating discussion of how to spot purposeful misinformation put forth by politicians manipulating statistics.

The catchy title entails a profound idea expounded by 20th-century philosopher Karl Popper -- that science progresses by falsifying previous hypotheses rather than proving new ones. Newton replaced Aristotle, but Newton was replaced by Einstein, and so forth. Science moves forward by correcting its mistakes.

Mathematics, for Ellenberg, plays a similar role by finding errors in reasoning, and thus correcting an argument so that it is "not wrong." It is a noble goal, and one that right-minded folks should embrace, although to get there we must pass through the pesky mathematics that repels most of us.

Let's hope, however, that those screaming "We love math!" kids and their children will grow up to read books like this.


David Topper is senior scholar in history at the University of Winnipeg. His next book, Idolatry and Infinity: Of Art, Math, & God, will be published this summer by Brown Walker Press.


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