"Figured out" not figured out; figures not out

(Letter to the Boston Globe, sent August 24, 2009)

Penrose triangle

Mark Feeney ("Figured out", Boston Sunday Globe, Aug 23, p. C10) writes, "Intellectually opaque, the practice of mathematics is visually null. It can be understood...but that doesn't mean it can be seen...Sets of numerals and symbols on a board...that's about it for mathematics made visible."

Penrose tiling

Feeney is not even close. Pictures bring mathematics to life. As a teacher and as a tutor, I rarely let a lesson go by without visualizations.

Some of of the best-known visualizations come from mathematicians mentioned in the article. Sir Roger Penrose is noted for the Penrose triangle, a simple 3-dimensional figure that cannot exist in our world, and for Penrose tiling. Benoît Mandelbrot is known for the Mandelbrot set.

Mandelbrot set

One contributor to the infamous "math anxiety" is the misapprehension that math is "intellectually opaque." Visualizations help us to see it more clearly. I hope the curious reader will spend a few minutes with a search engine to see how beautiful and awe-inspiring mathematics can be.

Jon Dreyer

Jon Dreyer • Math tutorComputer Science tutorwww.mathtutorlexington.com
781-696-2614 • 81 Baker Ave, Lexington MA 02421-6228 • email

I have no special talent. I am only passionately curious. —Albert Einstein