# Arnold Ross Lectures, 2001

The AMS partnered with the St. Louis Science Center on April 3 to present the twelfth in this series of lectures for talented high school mathematics students. Over 125 students and teachers came to hear this year's invited speakers, Mary Ellen Rudin (University of Wisconsin) and John H. Conway (Princeton University).

Professors Rudin and Conway circulated freely among the students and teachers as they arrived, introducing themselves and chatting. One busload came all the way from Breese, Illinois, two hours away! Conway, in his inimitable style, entertained all and challenged some with his sleight of hand using ropes and metal braids.

Prof. Deborah Tepper Haimo (Planning Committee Chair) provided the welcoming remarks and introduced the speakers. Mary Ellen Rudin's talk was entitled **What is Topology**. Her abstract in the program posed, "Since one needs background in algebra and analysis to seriously study topology, students often want an answer to the question of what topology really is. It is strangely difficult to answer, in part because in reality it is many things and becomes even more things as mathematics expands. I answer at least clearly enough to see why it is hard to answer." With the aid of transparencies, she explained that topological space has points and limits and that topological space can be any size and in multiple dimensions. In one clever drawing she showed how "a donut is the same as a coffee cup"! She outlined the many specialties within topology, and emphasized that one needs calculus and analysis to use and understand topology.

Conway's **Tangles, Bangles and Knots** program abstract asked "How can you understand the shape of a knot, or prove that it is really knotted? What makes one knot different from another? I describe some ways in which elementary arithmetic can help. Be prepared to dance!" His "lecture" involved lots of drawings, "what if" and "why would this be" questions, explanations and audience participation. The students were entertained, engaged and enthusiastic.

The **Arnold Ross Lectures** illustrate recent developments in mathematical research, stimulate interest in mathematics beyond the traditional classroom, and show the tremendous opportunities for careers in mathematics--as teachers and as researchers in government, industry, and university programs.

The **St. Louis Science Center** serves as a bridge between scientist and layperson, encouraging an understanding of ecology and the environment, humanity, technology and the space sciences and how each interrelates. By fostering an active interest in science and mathematics, the Science Center prepares people to make decisions that may shape the future and meet society's needs for scientific literacy.