Benson Farb, Professor in Mathematics and the CollegeBy Steve Koppes
When Benson Farb and Shmuel Weinberger, Professors in Mathematics and the College, developed a new course called Geometric Literacy in 1999, they jokingly advertised that it would meet for a full 30 years.
The course was appropriately ambitious for an award-winning teacher. Farb is a 2002 recipient of a Faculty Award for Excellence in Graduate Teaching.
We had said this course will cover what every good geometer should know, Farb said. Thinking about it, that could take 30 years, and actually it would take forever since the area is currently expanding faster than one can teach it.
The course, consisting of three-to-four-week modules on important topics in the area, is meant to give an uncommon breadth of knowledge to graduate students studying geometry, topology, group theory and dynamical systems.
Judging from the enthusiastic student feedback the department has received, the course offering seems to be quite successful. Since implementing this course, the number of graduate students in this area has risen dramatically, Farb said.
Six graduate students are currently conducting research under his supervision. He encouraged them to talk math with each other, which led them to meet weekly in a student seminar during the 1999-2000 academic year. Farb usually met with the students, but sometimes they got together on their own. One of his students, Dan Margalit, nicknamed the meetings Farbeques.
We took turns giving talks to one another, either describing papers we had read, or our own research, said Ashley Ahlin, who will complete her Ph.D. in mathematics this quarter. I suppose that we called it the Farbeque because of the grilling we sometimes got, with Benson questioning us until we had made everything absolutely clear. Ahlin noted that the Farbeque was a friendly moniker. It was meant to convey the rigor of the sessions, not harshness.
I try to meet frequently with my students, and try to always let them know that I care about what they are doing and how they are progressing, Farb said. I try to share my own experiences and struggles with them.
And three of them may have taken a lesson from his teaching style. Ph.D. students Angela Barnhill, Margalit and Kevin Wortman have garnered three of the five Mathematics Department prizes for undergraduate teaching by graduate students.
Farb, who specializes in the interaction between geometry, topology and group theory, considers himself a pure mathematician.
Newton called pure mathematics the queen of the sciences, said Farb, who recently returned from a visiting professorship at the University of Bourgogne in Dijon, France. Pure mathematicians, like poets, are guided by the beauty of ideas; our goal is simply the furthering of human knowledge. Amazingly, though, nature seems to follow the rules imposed by mathematics, and so mathematics is fundamental for understanding everything from the basic workings of DNA to the structure of the universe.
But Farb also is something of a pure teacher, in that he derives satisfaction from sharing knowledge at all levels, from graduate students to the Universitys SESAME (Seminars for Elementary Specialists And Mathematics Educators) program for elementary school teachers.
I believe there are high-content, fascinating problems that can excite and can be understood by children, Farb said. A favorite I often ask is: why do mirrors reflect left/right but not up/down? How does a mirror know the difference?
Although the question has inspired much debate in his classes for teachers, the issue has never been fully resolved in class. But ever the teacher, he offered yet another intriguing phenomenon: Look at your reflection in the mouth of a spoon. Now look at your reflection in the other side. Its cool what happens.