Paul Lockhart opens A Mathematician’s Lament with a musician’s nightmare of a world in which music education is mandatory. But that doesn’t mean singing and playing instruments.

“Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the ‘language of music.’ It is imperative that students become fluent in this language if they are to attain any degree of music competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.”

The musician wakes up in a cold sweat, relieved that it was just a crazy dream. “No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial; no culture could be so cruel to its children as to deprive them of such a natural, satisfying means of human expression. How absurd!”

A painter has a similar nightmare. He finds himself in a classroom where children are filling in the names of color swatches and learning about paint applicators in preparation for getting to paint by numbers. In junior high school, they take Pre-Paint-by-Numbers in preparation for the series of high school courses in Paint-by-Numbers. Because, of course, “Nothing looks better than Advanced Paint-by-Numbers on a high school transcript.” 

The next chapter begins, “The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such.”

There is an astonishing amount of power and truth packed into this 140-page book. If, like me, you feared and resented math in school because it made you feel stupid, perhaps you will understand why Lockhart’s lament almost had me crying by the end of the second chapter. Crying for “what if?” What if I had had even one math teacher in school who had loved mathematics as an art and taught it as such? What if even one of my teachers had given me time to explore the beauty of patterns and have ideas about them? What if, sometime in my twelve years of school, even one teacher had believed, “Being a mathematician is not so much about being clever . . . it’s about being aesthetically sensitive and having refined and exquisite taste”?   

The first part of the book is Lockhart’s “Lamentation,” but he doesn’t leave us with a complaint. Part II is called “Exultation.” He begins this part by likening being a mathematician to being a field biologist. In his analogy, he gives us a picture of studying mathematics as a biologist might study the behavior of hamsters in the Costa Rican jungle. “Let’s not worry about whether there actually are any hamsters in Costa Rica.” Whoever heard of such humor and imagery in math? Certainly not in any of my classes! This I might have understood. 

In “Exultation” Lockhart gives examples of the beauty and simplicity of mathematical patterns, and how to allow students to experience exploring them on their own. 

In his criticism of the way math is taught in our culture, I find a bit of vindication. Maybe I’m not stupid. Maybe I could have learned math if I had been taught by someone who loved math. And though it may be too late for me to learn to love math and feel competent, it’s not too late for me to appreciate Lockhart’s point of view and to spread a bit of his joy in the art when I have contact with young students. 

He ends with:

“And if you are neither student nor teacher, but simply a person living in this world and searching as we all are for love and meaning, I hope I have managed to give you a glimpse of something beautiful and pure, a harmless and joyful activity that has brought untold delight to many people for thousands of years.”

A Mathematician’s Lament is available at Amazon.