After a decade of teaching mathematics, I think I have developed a gracious response to statements like, "Math? I was never good at that," or "I was good at math in elementary school, but when I got to algebra, that was it for me," or even "I always hated math." While attempting to conceal my inner agony, I usually announce, "Well, everyone has their strengths and weaknesses." However, when I do occasionally probe to determine the cause of their disillusioned or hostile disposition toward a subject I adore, I commonly discover that most people view the discipline quite differently than I do. Consider the mathematician's perspective:
"Mathematics, rightly viewed, possesses not only truth but supreme beauty—a beauty cold and austere, like that of sculpture." - Bertrand Russell
"The mathematician's patterns, like the painter's or the poet's, must be beautiful." - G. H. Hardy
"It is impossible to be a mathematician without being a poet in soul." - Sophia Kovalevskaya
"To speak freely of mathematics ... I call it the most beautiful profession in the world ..." - Blaise Pascal
"At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world." - Bertrand Russell
Most people rarely think of mathematics as "beautiful" or something "as dazzling as first love." However, this is how I see mathematics. It is how I want my students to see mathematics. Contrary to popular opinion, we, as believers, should expect mathematics to be beautiful, intriguing, and awe inspiring. It is a reflection of the order, complexity, and beauty of the God we serve. Mathematics should be studied for what it is instead of being peddled as a set of rules to be followed and exercises to be completed.
Mary Beth Ruskai, a mathematics professor at Tufts University, says, "We cannot hope that many children will learn mathematics unless we find a way to share our enjoyment and show them its beauty as well as its utility:' Ruskai recognizes the importance of understanding both the utility and the beauty of mathematics. However, most efforts to convince students they should learn mathematics are based on its utility. Popular slogans include "Do Math and You Can Do Anything” (National Council of Teachers of Mathematics) and "Math is Power" (The Ad Council). A fashionable poster in many high school math classrooms is titled "When am I ever going to use this?" The poster cross-references jobs with mathematical topics. Understanding and experiencing the uses for mathematics is important. However, the utility argument has been insufficient in elevating students’ interest in and love for mathematics.
The utility argument helps the student to see that math should be studied for the student's sake. However, students would be much more inclined to study, understand, and even love mathematics if it were studied for math's sake. Alfred Posamentier, Professor of Mathematics Education at the City College of New York, wrote the following in a 2002 New York Times article:
The point is to make math intrinsically interesting to children. We should not have to sell mathematics by pointing to its usefulness in other subject areas, which, of course, is real. Love for math will not come about by trying to convince a child that it happens to be a handy tool for life; it grows when a good teacher can draw out a child's curiosity about how numbers and mathematical principles work. The very high percentage of adults who are unashamed to say that they are bad with math is a good indication of how maligned the subject is and how very little we were taught in school about the enchantment of numbers (Posamentier 25).
If everyone considered and experienced the "enchantment of numbers" and the beauty intrinsic to mathematics, people would be more inclined to confess their fascination with prime numbers, discuss coding techniques used for internet security, or argue over probabilities involved in daily life. People nobly say they enjoy seeing a Monet, listening to Bach, or reading Shakespeare. Similarly, the enlightened mathematics student should be enamored by Gauss' insight into arithmetic series, enjoy playing with Fermat's theorems in elementary number theory, and appreciate the beauty of the Mandelbrot fractal.
I invite you to investigate the beautiful, captivating, and enchanting world of mathematics. It is not a world of fluff but of substantial and provocative insights. Mathematics is not the drudgery that you may have suffered. See mathematics from my point of view. Investigate the heart of mathematics with a good book such as Journey through Genius: The Great Theorems of Mathematics or The Mathematical Universe by William Dunham, Math Charmers: Tantalizing Tidbits for the Mind by Alfred Posamentier, Zero: The Biography of a Dangerous Idea by Charles Seife, or The Art of the Infinite: The Pleasures of Mathematics by Robert Kaplan and Ellen Kaplan.
If you prefer, participate in an enlightening course in mathematical thinking. In the fall 2007 semester, PBU will be adding a course to the Arts & Sciences Core Requirements entitled Mathematical Thinking. The textbook supporting this course is The Heart of Mathematics: An Invitation to Effective Thinking by Edward Burger and Michael Starbird. Experience a preview at http://www.heartofmath.com/.
In this course, students will investigate encryption and prime numbers, number patterns found in nature, smaller and larger infinities, contortions of space, chaos and fractals, randomness and probabilities in daily life, deception and statistics, risk taking, and voting schemes among a number of other interesting and understandable topics. Furthermore, most of these topics demand integration into other subject areas, into real-life scenarios, and, most importantly, into addressing significant worldview questions: Did God create a chaotic universe? Is there true randomness? What does it mean to be infinite? What is acceptable risk? Is mathematical knowledge objective? Did God design a mathematical standard for beauty?
In the forward of The Heart of Mathematics, the authors state, "We hope you discover the beauty and fascination of mathematics" and, "We want you to discover what mathematics really is and to become a fan. However, if you are not intrigued by the romance of the subject, that's fine, too, because at least you will have a firmer understanding of what it is you are judging" (Burger & Starbird xi). Study mathematics for its artistic beauty, powerful intrigue, and elegant "romance." However, beware. You might succumb to its allure and "become a fan."
"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful." - Henri Poincare
Burger, Edward B. and Michael Starbird. The Heart of Mathematics: An lnvitation to Effective Thinking, 2nd Ed. Everyville, CA: Key College Publishing, 2005.
Dunham. William. Journey through Genius: The Great -Theorems of Mathematics. New York: Wiley, 1990.
Dunham, William. The Mathematical Universe. New York:Wiley, 1994.
Famous Mathematics Quotes. Oklahoma State University. 9 January 2007. https://wwwanath.okstate.edu/—wli/teach/fing.html
Kaplan, Robert and Ellen Kaplan. The Art of the Infinite: The Pleasures of Mathematics. Oxford: Oxford University Press, 2003.
Mathematical Quotations Server. Furman University. 9 January 2007. https://math.furinamedu/—mwoodard/data.litivil
Posamentier, Alfred S. Math Charmers: Tantalizing Tidbits for the Mind. Amherst, NY: Prometheus. 2003.
Quotations About Mathematics and Education. John Handley High School. 9 January 2007. https://www.pen.k12.va.us/Div/Winchester/jhhs/math/quotes.html
Quotations Page. www.quotationspage.com. 9 January 2007. https://www.quotationspage.corn/quote/2685.1thnl
Seife, Chards. Zero: The Biography of a Dangerous Idea. New York: Penguin, 2000.
Jason VanBilliard, Ed.D., is an Assistant Professor and Chair of the Department of Secondary Education in PBU's School of Education. He may be reached at: firstname.lastname@example.org.
PBU Today, Spring 2007, p. 7-8