Tuesday, November 11, 2014

When Will I Use This?

Douglas Corey—Brigham Young University

The top search engine completions for "when will I use . . ." are all related to school mathematics. Some students ask such questions as a challenge to the teacher, but others sincerely want to know. Like me, you may have a hard time remembering the last time you used multiplication for something other than schoolwork, yet we use multiplication all the time. It is so ingrained in our thought processes that we don't notice it.

When someone asked when I had last used it, I eventually remembered that it was to calculate the area of my raspberry patch. But this example probably wouldn't convince a skeptical student that math is useful. Examples about baseball statistics, recipe conversions, or grocery store price comparisons may also be unconvincing. Why? Because if an application is outside the interest of a student, he or she discounts it. In truth, a teacher doesn't know when a student will use the math being taught (except on the exam). It is fraudulent to pretend otherwise.

Connecting the Dots

Typically we don't know what we don't know. This makes it very difficult to predict what kind of knowledge we will need. It is also very hard to see how we could use knowledge that we don't have.

In Steve Jobs's commencement address at Stanford University, he describes taking a calligraphy class in college. In the class he learned about typography: the technical aspects, the terminology, its history, and the characteristics of a beautiful typeface. This class, which at the time had no practical applications for him, led to his inclusion of multiple typefaces and proportionally spaced fonts in the first Macintosh computer. Jobs said, "You can't connect the dots looking forward; you can only connect them looking backwards. So you have to trust that the dots will somehow connect in your future."

The Eye of the Mind

Knowledge enables us to see what others can't. When one of my sons puts his shirt on inside out and backwards, I think of the symmetry group generated by the actions on his shirt. When I watch the balls on my kids' trampoline roll around, I think about how their paths are modeled by hyperbolic geometry and how the model also governs the path of light through space.

It doesn't go the other way. People don't stand on the trampoline and ask themselves what connection it has to hyperbolic geometry or to Einstein's theory of general relativity. They don't think about abstract algebra when they see a shirt turned inside out. They can't see these connections, so the connections don't exist to them.

Just Look It Up

Students argue that it is a waste of time to memorize formulas, definitions, theorems, and proofs because they can always look up such things. But we look up things only when we know we don't know about them, and we need to know fairly specifically what we don't know in order to search for it.

As an experiment, find a meaningful quote, such as this favorite of mine attributed to Thomas Edison, "We often miss opportunity because it is dressed in overalls and looks like work." Repeat it every morning and evening for two weeks. During this period you'll find that the quote comes to mind as relevant multiple times. Without having memorized it, you would not have stopped and thought, "I wonder if there is a quote by Edison that I could use right now?" You did not know enough to see any connection to Edison's ideas.


No one knows when you will use the math you are learning in your classes. Most knowledge gets applied to situations we never anticipate. It pays to learn all you can about all you can. You will be able to see how you benefit from it only by connecting the dots backwards.

An expanded version of these arguments, which I give to my students, is available at maa.org/mathhorizons/supplemental.htm.

Douglas Corey is an associate professor in the mathematics education department at Brigham Young University. He stays busy with his eight kids, all of whom are girls but seven.

This article was published in the November 2014 issue of Math Horizons.