2003 AWM Essay Contest:

Honorable Mention in Grades 6-8 Category

### By Christie Onzol

The word "topology" was anchored in my vocabulary on October 14, 2003 for good. I may have heard it before, but it was an empty designation rather than a meaningful term. For this reason it didn't occur to me that the student I had passed on my way to the Math Department of the California State University, Northridge (CSUN), was holding in his hands two topologically equivalent objects, a coffee cup and a doughnut. At that time, the only association I could see between those two items was that from everyday experience. It manifested itself as always in a proof of Pavlov's Effect. I was going to find out very soon though that such a down to earth picture of the coffee cup and doughnut could be elevated to an entirely different level of perception.

For an average early teenager math represents dry, boring, and endless shuffling of numbers and not much beyond it. Therefore, when I was preparing for my interview with Dr. Magnhild Lien, I struggled with a question on how to talk to a mathematician in order to understand the realm of her expertise without getting into incomprehensible mathematical formulas and convoluted terminology. As it turned out, it was an unnecessary loss of energy.

Professor Lien cheers me up from the very beginning with a drawing of a doughnut, which if properly squeezed, punched, and stretched a couple of times, becomes a coffee cup. "And that's mathematics at work!" she explains. Then on a bit more serious note adds that gluing together, breaking, tearing, and poking holes wouldn't be permitted. Amazing - no numbers, no formulas, just plain words, few strokes of a pen, and some dose of imagination is sufficient to describe the entire branch of mathematics called topology! But as if that wouldn't be remarkable enough, Professor Lien now draws my attention to her earrings. They seem identical from afar. On a closer look however, there's a noticeable difference in a manner the silver wire had been weaved into an artistic rendition of the knot theory. I would have never thought that mathematical theory could be expressed in a form of dangling body ornamentation or be knitted into a warm Norwegian sweater that Dr. Lien made as a utility proof of the study of knots. Knot theory in particular and topology generally are her main professional interests. The ease with which she explains to me this kind of fancy geometry makes one wonder why it is not a top subject in middle school curriculum. It can't be! The picture of topology I'm getting so far is just a polished surface of a complicated and very broad mathematical substance that requires many years of intensive training supported by wide variety of experiences, perhaps just such as Dr. Lien's.

Magnhild Lien was born on the island of Tromoy at the southern tip of Norway, in Arendal, the town once called the "Venice of Scandinavia." Her mother was a homemaker and her father owned a manufacturing business. Her parents supported wholeheartedly scholastic aspirations of their five sons and the only daughter. There must have been some "math-related gene" in the Lien family since four of Dr. Lien's brothers are accomplished engineers, the fifth has a business degree, and the father ran successfully a family business he had inherited from his father. Math wasn't all she loved in school, but she never had any trouble with it. She couldn't! Her older brothers set the standard, and since she had to attend the same schools and learn from the same teachers, there wasn't any question as to her abilities. Schools in Norway are different from those in the United States says Dr. Lien. They require completion of all courses before advancement to the university level and promote greater competitiveness. Magnhild, a mathematician to be, was the first girl on the island of Tromoy to have a Barbie doll and probably the only one in Norway to learn multiplication from a logarithmic table that she got from her brothers with instructions on how to use it. She still has that log table at home as a kind of memorabilia. Her formative years abounded in a wide variety of after school activities, from girl scouts, skiing, orientation running, and Red Cross aid training, to school band, gymnastics, modeling, and chess playing. This broad spectrum of interests had eventually narrowed to a decision of becoming a teacher for the Montessori schools. While attending appropriate courses in Denmark, her interests began shifting toward more general social issues, hence she moved to Canada where she found an employment suitable to her professional pursuits. It turned out shortly not to be a true calling. The local college offered math, chemistry, and English courses and an exciting breadth of new experiences. Mathematics surfaced quickly as a thrilling endeavor for life. No wonder that B.A. degree arrived with a "great distinction", followed by M.S. and Ph.D. from the University of Iowa in almost no time.

Dr. Lien is a very busy woman as the Chair of the Mathematics Department at CSUN, researcher, teacher, participant and organizer of various conferences, programs, seminars, projects, and workshops, lecturer, active member of professional associations and committees, and author of published papers and articles. She maintains though that Poisson's statement, "Life is good for only two things, discovering math and teaching math," is untrue for there's much more to life than that. It is hard to disagree with her in general, but the depth of Dr. Lien's involvement in teaching, and especially promoting a warm environment for women mathematicians, both the students and her faculty staff, is overwhelming. Perhaps it has something to do with this special feminine, semi-artistic touch that underlies the realm of topology?

I felt truly privileged in having the opportunity to interview this extraordinary woman. In 60 minutes she managed to show me mathematics in an absolutely unexpected light. Thanks to her I won't hesitate to say even in Norwegian: "Jeg liker matematikk veldig mye" (I like mathematics very much).

*About the Student: *My name is Christie Onzol. I am a 7th grader at Nobel Middle School in Northridge, California. I also study piano at Pierce College in nearby Woodland Hills. I like all my classes equally. Well, perhaps math and history are just getting about half a step ahead. After school I find pleasure in reading, movies, and playing piano and violin. In the future I would like to research common grounds of math and music, or study quantum physics and medieval history.