Innumeracy is both a brilliant book by John Allen Paulos and the term (coined by Paulos) for the mathematical equivalent of illiteracy. The book makes a compelling argument for innumeracy being as dire a problem as illiteracy, presents a scathing indictment of the cultural conditions that encourage innumeracy in our culture, and offers a primer in basic numeracy with amusing and engaging examples. Totally excellent.

The main concept of innumeracy is the inability to comprehend orders of magnitude -- to not be able to select the approximate population of the earth when presented with these choices:
1. 6,000
2. 6,000,000
3. 6,000,000,000
4. 6,000,000,000,000
I did a little teaching and grading in grad school, and it was sad to see the innumerate engineering students not only come up with an answer that was 5 orders of magnitude off, but to not realize that there was something horribly, utterly wrong with it. It's not the initial error that's bad (I have come up with such horribly wrong answers myself at times -- I remember my senior group project where we, at first pass, came up with a tower 5 miles tall instead of 25 feet due to a unit conversion error -- but we, all of us, immediately recognized the answer as ridiculous and went back to find our error) but the inability to notice how impossible the number is bad -- and that's innumeracy.

Part of the innumeracy problem is that with the prevalent use of calculators and computers today, people aren't taught to do any proper sort of estimation. Estimation is pointless to the innumerate, since they can't answer the question at the start of this writeup, so they will never think to learn it themselves either.

There are a lot of books I've read multiple times, but very few non-fiction books make that list. Usually they're more referency than read-straight-through books, and all too often consist largely of filler. John Allen Paulos somehow avoids these traps (for the most part) in his excellent book, Innumeracy: Mathematical Illiteracy and its Consequences.

Innumeracy, as mentioned by previous writeups, is the mathematical analog to illiteracy. It consists not only of the inability to handle very large (and very small) numbers, but also a profound misunderstanding of probability. There are most certainly other inabilities one would consider aspects of innumeracy, but these are the two Paulos finds most widespread and troublesome.

Paulos points out that innumeracy is not only socially acceptable (unlike illiteracy), but actually something people will even brag about. It's trendy to be bad at math. Similarly, your bank probably brags that you're a person to them, not just a number, and then, as Paulos glibly comments, proceeds to screw up your transaction.

Paulos litters the book with examples to illustrate his points. The original Rubix Cube packaging noted that the cube had over three billion combinations. True enough, but the actual number is close to forty quintillion. When asked to estimate how fast human hair grows in miles per hour, one student insisted that hair just doesn't grow in miles per hour.

Those examples may seem trivial--yes, people should know better, but what harm is there? So what if people can't grasp the idea of measuring human hair growth in miles per hour? Paulos delves into some major problems that are largely a consequence of innumeracy. Take, for example, pseudosciences. Consider how many dreams you have, and how many are about your life (probably most). It's pretty likely that people will have predictive dreams due to coincidence. Astrology relies on coincidences. Bad statistics turn up in the courtroom. People say they don't bike to work because they could be hit by a car, and then they fall over dead of a heart attack or stroke.

These issues are not entirely innumeracy--there are numerous cognitive biases involved in our general stupidity, but the ability to apply math allows us to detect when we're being stupid and perhaps opt instead to be rational. Paulos' book is not an essay on how to do this, but is an enjoyable read exploring common innumerate errors in American society.

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