(Don't Be) "Bad at Math"

Nothing in life is to be feared. It is only to be understood.

— Marie Curie

Equations are just the boring part of mathematics.

— Stephen Hawking

Let's start with a multiple-choice question.

Question: Imagine that you're at a party, and you've just struck up a conversation with a dynamic, successful businesswoman. Which of the following are you most likely to hear her say during the course of your conversation?

Answer choices:

a. "I really don't know how to read very well."

b. "I can't write a grammatically correct sentence."

c. "I'm awful at dealing with people."

d. "I've never been able to think logically."

e. "I'm bad at math."

We all know that the answer is E, because we've heard it so many times. Not just from businesswomen and businessmen, but from actors and athletes, construction workers and sales clerks, and sometimes even teachers and CEOs. Somehow, we have come to live in a society in which many otherwise successful people not only have a problem with mathematics but are unafraid to admit it. In fact, it's sometimes stated almost as a point of pride, with little hint of embarrassment.

It doesn't take a lot of thought to realize that this creates major problems. Mathematics underlies nearly everything in modern society, from the daily financial decisions that all of us must make to the way in which we understand and approach global issues of the economy, politics, and science. We cannot possibly hope to act wisely if we don't have the ability to think critically about mathematical ideas.

This fact takes us immediately to one of the main themes of this book. Look again at our opening multiple-choice question. It would be difficult to imagine the successful businesswoman admitting to any of choices A through D, even if they were true, because all would be considered marks of ignorance and shame. I hope to convince you that choice E should be equally unacceptable. Through numerous examples, I will show you ways in which being "bad at math" is exacting a high toll on individuals, on our nation, and on our world. Along the way, I'll try to offer insights into how we can learn to make better decisions about mathematically based issues. I hope the book will thereby be of use to everyone, but it's especially directed at those of you who might currently think of yourselves as "bad at math." With luck, by the time you finish reading, you'll have a very different perspective both on the importance of mathematics and on your own ability to understand it.

Of course, I can't turn you into a mathematician in a couple hundred pages, and a quick scan of the book should relieve you of any fear that I'm expecting you to repeat the kinds of equation solving that you may remember from past math classes. Instead, this book contains a type of math that you actually need for life in the modern world, but which you probably were never taught before.

Best of all, this is a type of mathematics that anyone can learn. You don't have to be a whiz at calculations, or know how to solve calculus equations. You don't need to remember the quadratic formula, or most of the other facts that you were expected to memorize in high school algebra. All you need to do is open your mind to new ways of thinking that will enable you to reason as clearly with numbers and ideas of mathematics as you do without them.

The Math Recession

For our first example, let's consider the recent Great Recession, which left millions of people unemployed, stripped millions of others of much of their life savings, and pushed the global financial system so close to collapse that governments came in with hundreds of billions of dollars in bailout funds. The clear trigger for the recession was the popping of the real estate bubble, which ignited a mortgage crisis. But what created the bubble that popped? I believe a large part of the answer can be traced to poor mathematical thinking.

Take a look at Figure 1, which shows one way of looking at home prices during the past few decades. The bump starting in 2001 represents the housing price bubble. Let's use some quantitative reasoning to see why it should have been obvious that the bubble was not sustainable.

Here's how to think about it. As its title indicates, the graph shows the ratio of the average (median) home price to the average income. For example, if the average household income were $50,000 per year, then a ratio of 3.0 would mean that the average home price was three times the average income, or $150,000. The graph shows that the average ratio for the three decades prior to the start of the bubble was actually about 3.2, which means someone with an income of $50,000 typically purchased a house costing about $160,000 (which you find by multiplying 3.2 by $50,000).

Now look at what happened during the housing bubble. After increasing modestly in the 1990s, the ratio began shooting upward in 2001, reaching a peak of about 4.7 in 2005. This was nearly a 50% increase from the historical average of 3.2, which means that relative to income, the average home was about 50% more expensive in 2005 than it was before the bubble. In other words, a family that previously would have bought a house costing $160,000 was instead buying one that cost nearly $240,000.

With homes so much more expensive relative to income, families had to spend a higher percentage of their income on them. In general, a family can spend a higher percentage of its income on housing only if some combination of the following three things happens: (1) its income increases; (2) it cuts expenses in other areas; or (3) it borrows more money. Other statistics showed clearly that average income was not rising significantly, and that while homeowners gained some benefit from relatively low mortgage interest rates, overall consumer spending actually increased. We are therefore left with the third possibility: that the housing bubble was fueled primarily by borrowing. With little prospect that incomes would rise dramatically in the future, it was inevitable that this borrowing would be unaffordable and that loan defaults and foreclosures would follow. The only way to restore equilibrium to the system was for home prices to fall dramatically.

Lest you think that this is a case of hindsight being 20/20, keep in mind that these kinds of data were available throughout the growth of the bubble. Anyone willing to think about it should therefore have known that the bubble would inevitably pop, and, indeed, you can find many articles from the time that pointed out this obvious fact. So how did everyone else manage to miss it?

Although it's tempting to blame the problem on a failure of "the system," it was ultimately the result of millions of...