Innumeracy: Mathematical Illiteracy and Its Consequences [Paperback]

If you are feeling cowed about your math ability, take heart! Most of the concepts here you can handle. For example, can you multiply two numbers together? You can answer "yes" to my question if you can do so with a calculator. If so, you can appreciate almost all of the examples in the book.

Professor Paulos has a mind that works differently and more inquisitively from mine, but I enjoyed learning how his thoughts. He thinks about topics like how long it would take dump trucks to excavate Mount Fuji, how many times a deck of cards need to be shuffled to become random, and what the Earned Run Average is for a pitcher who lasts one-third inning and gives up 5 runs. I realized that if I thought about more things like this, I would develop new perspectives on the world.

He makes a helpful attempt to create solutions so that more people can appreciate the world in a quantitative sense. These include using exponents to indicate the size of numbers (such as the Richter Scale does for earthquake strength), refocusing secondary math education to practical applications rather than teaching calculus earlier and earlier, having talented mathematicians teach younger people, and disciplining those who communicate in public to check the mathematical accuracy of what they say.

What do we lose if we don't? Well, those who don't learn a little math will end up in careers that pay a lot less. Social resources will be misapplied to problems that are less serious (obscure diseases and terrorism get a lot more attention to reducing accidental deaths among young people, which is a greater danger). We will make bad resource decisions in our own lives (such as by playing the lottery without realizing that 50% of the money is not paid out to anyone buying a ticket).

I also appreciated how few people can use mathematics in creative ways, to solve problems. For instance, in our professional practice we developed a new way to forecast certain forms of investment behavior. Over 20 years of doing this work, I have never found anyone who could make a single useful suggestion for how to improve the mathematics of our approach, despite having had conversations with dozens of people with advanced math and statistics degrees who would get benefit from an improved approach. I suspect from this experience that there's a higher level of mathematical thinking that Professor Paulos did not explain in his book that we would all benefit from learning. Where do we start? I can hardly wait to learn!

Writers generally put the motivation statement at the front of the book, but this occurs at the back. His anger does indeed fuel part of his need to write, and is one of the reasons why he succeeds but not fully. A moments reflection reveals that many books, of all types, are not motivated by anger at all. I am sure that in a calm moment he would appreciate the economy of the refutation 'NOT' appended to the first sentence of his statement. The question it raises is, can he justify his anger as righteous and thereby redeem it, like a mathematical cleansing of the temple? Or do we read the book with respect for his position and experience, but gingerly, lest we disturb a dog best left sleeping?

I like this book for the human-ness of its strengths and weaknesses. Published in 1988, it is fresh and contemporary, of course the math can never date, but his applications and examples have not dated either. As an experienced and passionate teacher of mathematics the professor has some valuable insights into the art and science of maths teaching. 'Math anxiety' and the 'extreme intellectual lethargy which affects a small but growing number of students' all concern him, as they do me. (My own small experiences in this area as a tutor and in the classroom echo his. He might also add the 'trained ability to concentrate' as a fundament of doing math - and perhaps all intellection.) He badly wants us all to gain an instinctive sense of number and master its huge array of applications in sorting the wheat from the chaff in life's great information silo. The cheap, slap-happy and sensationalist reporting of the media, astrology, quackery, pseudoscience, and the jiggery-pokery-statistics of governments all come under his sharp scrutiny. His sense of humour, wit, and selection of amusing quotations leaven the text throughout.

Some embedded gems: sections such as those on combinatorial co-efficients (how the lottery works), and binomial probability (how to test for ESP) are good, but they really are a little too brief, and use examples which are more difficult than need be. These repay careful re-reading and require expansion with one's own pencil and paper - which enforced exercise is not his intent in writing. As he himself notes, he has a weakness for being overly concise when writing, his symbolic math habits being so strong. As an author, he should try to avoid statements like 'this part can be ignored, as indeed can the whole book'...counsels of despair! And he also promises not to lecture us or patronise us in this book, as he is aware of the temptation to do so in this type of work: mostly he succeeds. For something lighter you could try 'Why Do Buses Come In Threes?' by Eastaway & Wyndham. For something a little more rigorous try 'How to Solve It' by Polya, or 'Reasoning with Statistics' by Williams & Monge'. Keith Devlin's 'The Maths Gene' is good for some psychology of math.