Talk of Math

In a short book about his life, friends, colleagues, and thoughts called A Mathematician’s Apology, the renowned mathematician G. H. Hardy wrote, “It is quite true that most people can do nothing well.” The value of such a reflection in an autobiographical work by one of the great mathematicians of the twentieth century is that it proves to be one of the most helpful of all beginnings for someone trying to learn math. Professor Hardy’s contention was not an attempt to disgrace or criticize anyone. In fact, more than anything else, it was an observation about his own discovery of his love of math.

One of the world’s greatest mathematicians, he did not regard math as something he did particularly well. In fact, he did not really care whether he did it particularly well. He just did it. That he could just do it, without consideration of what others thought or whether what he did he did particularly well allowed him to become a preeminent mathematician.

Most people do not have this perspective when they attempt to advance their study of math. Further, math teaching often promotes the notion that if you are going to do math, then you must do it well. If you do not do it well, then you are advised to find something else to do. The consequences of this approach are somewhat enormous. Consider, for example, that in places like the United States, some experts say that around 90 percent of the population is math illiterate. Granted, that figure might be exaggerated, but even if you lower the figure, the fact is that most people go through their lives and spend almost no time at all doing or learning math.

It is easy to get the impression that being able to do math is something along the lines of a genetically established capability. If you are genetically endowed, it is worth your while to involve yourself in it. Otherwise, you need to find something else to do.

Imagine what it would be like if participating in conversations with friends, relatives, and others was based on such an assumption. You might find your cell phone privileges revoked. You might find yourself barred from cafes, political meetings, school lunchrooms, and churches. You might have to take a test before being allowed to order a sandwich or tell your neighbor good morning.

Such notions are extreme and absurd, but it remains that if you speak with people who have given up on math, you often find such reasoning at work.

Why don’t people allow themselves to just do it, even badly, in the same way that they talk or ride a bicycle? Why isn’t it open for exploration and enjoyment in the same way that conversation is open for exploration and enjoyment? Why is it that it has to be presented in a context in which G. H. Hardy’s observation is completely forgotten?

These are not intended as criticisms. Many math teachers do, indeed, seem to agree with Professor Hardy. On the other hand, many clearly do not. As one student reported after failing introductory calculus, “The teacher told us that the purpose of first-year calculus is to determine who cannot do math.”