BALTIMORE — EACH time I hear someone say, “Do the math,” I grit my teeth. Invariably a reference to something mundane like addition or multiplication, the phrase reinforces how little awareness there is about the breadth and scope of the subject, how so many people identify mathematics with just one element: arithmetic. Imagine, if you will, using, “Do the lit” as an exhortation to spell correctly.

As a mathematician, I can attest that my field is really about ideas above anything else. Ideas that inform our existence, that permeate our universe and beyond, that can surprise and enthrall. Perhaps the most intriguing of these is the way infinity is harnessed to deal with the finite, in everything from fractals to calculus. Just reflect on the infinite range of decimal numbers — a wonder product offered by mathematics to satisfy any measurement need, down to an arbitrary number of digits.

Despite what most people suppose, many profound mathematical ideas don’t require advanced skills to appreciate. One can develop a fairly good understanding of the power and elegance of calculus, say, without actually being able to use it to solve scientific or engineering problems.

Think of it this way: you can appreciate art without acquiring the ability to paint, or enjoy a symphony without being able to read music. Math also deserves to be enjoyed for its own sake, without being constantly subjected to the question, “When will I use this?”