When Stephen Colbert introduced the word truthiness on his show, he told us to trust our guts.

That’s where the truth comes from, ladies and gentlemen: in the gut. Do you know that you have more nerve endings in your stomach than in your head? Look it up. Now somebody’s going to say, I did look that up, and it’s wrong. Well, mister, that’s cause you looked it up in a book. Next time, try looking it up in your gut.

Truthiness, chosen as the Word of the Year in 2005 by the American Dialect Society, is the quality of certain kinds of baloney that seem true. Technically:

Truthiness, n, the quality of stating concepts or facts one wishes or believes to be true, rather than concepts or facts known to be true.

Colbert’s coinage recognize that for some unscrupulous actors, seeming true is good enough. The genius of truthiness is that it pinpointed how people take advantage of a lack of skepticism. When something seems true, we tend to take it at face value. As soon as it passes the gut check, we take it as a given.

There’s one kind of truthiness that’s particularly subtle and malevolent, and that’s the kind where mathematics gets involved. Author Charles Seife just wrote a book about it, and coined the word to describe it. The book is called Proofiness: the Dark Arts of Mathematical Deception.

Proofiness refers to a particularly devious kind of truthiness: the use (and misuse) of mathematics to give bull the illusion of truth. What makes proofiness so terrible is that numbers glow with truth. Introduce a number into a statement and it just seems truer. (It can be up to 7.3 times as truthy!)

Charles Seife wrote Zero, a decent but not exceptional pop math book. Proofiness is better, and more important. In fact, I could imagine it being the backbone of a (required?) high school class. Seife even raids science, hitting sexy articles from Nature and exposing their errors deducing patterns from noise, an error he terms randumbness. (Seife coins many such terms throughout the book—Potemkin numbers when they’re made up, causuistry for the confusion of cause and correlation, and many more. Normally, I bridle at this kind of cutesyness, and I did here a little, I have to say. In his defense, it was sometimes nice to have terms for some of the specific types of proofiness he discussed.)

Seife’s best chapters have to do with how risk is managed—culminating in a discussion of the financial meltdown that led to the Great Recession, how systematic bias affects polls, and, perhaps most damnably, how faulty probability lead to (probably) wrong outcomes in court. Along the way, he hits some pretty subtle mathematical ideas, and I have to say, he handles them very smoothly. You get a little probability and statistics, a little bit of reading graphs, on proper measurement, estimation, and disestimation—one of my favorite of his coined terms, and an intuitive picture of how gerrymandering works. But more gripping than the strictly mathematical parts is the sense of outrage. You read it and think, I remember when they said that Hummers were more fuel efficient than Priuses. Why didn’t I notice that they made up the numbers? (Advertisers argued that Hummers would last a lot longer, pulling numbers pretty much out of nowhere.) You’ve got to be pretty sophisticated, and pretty vigilant, not to have been taken in by these techniques.

And that’s the point, and the reason the book is important. The issues Seife covers–advertising, our economy, propaganda, science, justice, journalism—are critical to our functioning democracy. We need to understand math, it turns out, to protect ourselves from being manipulated by it. As Seife ends his book,

Mathematical sophistication is the only antidote to proofiness, and our degree of knowledge will determine whether we succumb to proofiness or fight against it. It’s more than mere rhetoric; our democracy may well rise or fall by the numbers.

This book is one of the best articulations of the need for a baseline of mathematical facility in an educated citizenry, and a primer on what kinds of mathematics are most important for everyone to know (calculus, no; statistics, yes). Put it on your summer reading list. And even better, let’s see high school classes that deal with these topics sprouting up soon.

[Note: it’s almost inevitable that some of Seife’s arguments were problematic themselves, especially since he makes a colossal effort to remain evenhanded when it comes to political issues; for every conservative example of proofiness, he tries to find a liberal one to match it. One of these, a nitpicky jab at Gore’s Inconvenient Truth (which Seife takes issue with only on certain details, not in the main) was taken apart here.]