Mathematics and Morality

Want to do the right thing? Do the math

   Andrew Fiala

Originally published 2012-08-25

As kids tune up their calculators and complain about their math homework, let’s consider the moral value of mathematics. It is widely known that American students struggle with math and are being outperformed by kids in other countries. In response, President Obama plans to contribute $1 billion to support expert math and science teachers.

Is this a wise investment? Why do we put children through the math wringer: hammering them with algebra, geometry, trigonometry and calculus? At least one pundit has claimed that all of this is cruel and unnecessary.

In a recent essay in The New York Times, Andrew Hacker — a professor at the City University of New York — questioned the need for advanced mathematics. Hacker claimed, “Algebra is an onerous stumbling block for all kinds of students.” He argued that the solution was to change our emphasis on higher mathematics, focusing less on algebra and more on applied quantitative skills.

While I smiled at Hacker’s claim that “poets and philosophers” do not really need to do calculus, I suspect that higher mathematics remains useful. This is not because we use algebra or trigonometry in daily life, but because training in mathematics, like training in music or a foreign language, helps us hone our mental skills. Most adults don’t play the French horn they practiced in middle school, or speak the French they learned in high school. But we are better for having studied these things. Mathematics, like music, is a new language. To learn it, you have to apply abstract rules, think creatively, problem solve, and practice and persevere.

Morality seems to require the same ability to apply abstract rules that we associate with mathematics. Morality involves problem solving, as we come to see how the rules ought to be applied in a variety of complex cases. Of course, ethics involves more than following rules. Moral acuity also involves an emotional and empathetic element. It is a bit more like music in this regard. But as in music, creative and emotional responses must be grounded in a basic understanding of the principles and rules of the art.

The ancient Greeks thought that there was a connection between mathematics (and music) and morality. Plato’s school — the Academy in Athens — was said to have a sign on the door that read, “Let no one ignorant of geometry enter.” The path to enlightenment, for Plato, was prepared by mathematical insight. Mathematics provides rigorous discipline for the mind, which leads to higher wisdom.

There is a parallel between the orderly procedures of mathematical reasoning and the orderliness of a virtuous life. The Greeks thought that a good life was properly proportioned, with each part in its place. Aristotle taught that virtue was a “golden mean,” the middle or average amount: not too much, not too little. He defined justice as giving “equal to equals.” In order to distribute things fairly, you need to understand math.

There is also an analogy between mathematical and moral knowledge. Everyone agrees that 2+2=4. You don’t have to test this claim against the world. Rather, it is true for everyone, at all times, known with certainty. Plato thought moral knowledge was like that: universal and innate.

Unfortunately, people often disagree about morality. Some people don’t eat meat; others do. Some get abortions; others don’t. And so on. Moral principles appear to be quite different from mathematical truths, insofar as people vigorously debate them, even killing one another over them. This leads some people to skepticism about morality. It might be that there are no universally valid moral principles.

But someone like Plato might respond by saying that just as we can make mistakes in “doing the math,” we can also make mistakes in “doing morality.” Disagreement does not prove there is no right answer. If a child adds 2 and 2 and ends up with 5, we don’t give up on mathematics. Instead, we teach him or her how to do it right. And when children have good teachers and do their homework, their math skills improve.

Morality may be similar. We need good teachers who correct our mistakes and teach us how to do better. And, of course, we all need to keep practicing our instruments and doing our homework.