| Rochelle Kronzek: Saul, tell us a bit about your background. |
| Saul Stahl: I was born in Belgium during the war (WWII). My brother and I were hidden by our former maid for over two years while my parents avoided capture by keeping on the move. They formed a group of five that included my father's sister. He was the defacto leader of the group. Their goal was to make it to Portugal, which they were not successful in doing. Prior to the war my father was a middleman in the diamond trade. He stashed and sold diamonds during the war to buy the "group of five's" continued freedom as they kept moving to avoid capture. Meanwhile, my brother and I were safe. Ironically, my father had been born in Romania and had been placed in a camp by the Belgian government and liberated by the German government! |
| My family moved to Israel shortly after the war; as soon as Israel became a nation in 1948. My family settled in Natanya. My father resumed his work in the diamond industry, my mother's health was too poor to allow for steady employment, and my brother, sad to say, died when his plane crashed while serving in the Israeli Air Force. |
| Rochelle: Saul, how old were you and what first got you interested in mathematics? |
| Saul Stahl: In the sixth grade I first realized that I wanted to do something with numbers. My home life was tumultuous. My parents fought a lot. Numbers calmed me down. My math teachers in elementary school seemed to be quieter than my parents. That was attractive to me. |
| In high school I took a geometry course that frustrated me greatly. I couldn't figure out what the whole thing was about. I was trying hard as I had committed to myself that mathematics would be my career and future. The breakthrough came when I confronted this exercise: if the bisector of an angle is extended into the vertically opposite angle, then the latter angle is also bisected. I finally got it. I solved the problem but more importantly, I understood the process of how to figure out the answer. That happened to me again in graduate school, in an algebraic topology course. The material was beyond my understanding and, to some extent, still remains so. |
| As often happens, my brother's accident put too much of a strain on the family, and it broke up. My mother and I came to New York in 1958 where we had several close relatives. I did my last year of high school in Brooklyn, New York and then my undergraduate work at Brooklyn College. I started my graduate work in Mathematics at UC Berkeley in 1963. After two years at Berkeley, I went into the Peace Corps for 2 ½ years in Nepal. There I taught mathematics in high school and college. Occasionally, I also taught English (with a Brooklyn accent). |
| After my stint in the Peace Corps, I returned to Berkeley for another year in 1968 before giving up on Mathematics for a while. My father's death had defused my drive and politics at Berkeley proved too distracting. I took a job as a systems engineer at IBM in Endicott, New York and moved back to the East Coast. I worked for IBM for 3 ½ years. I became bored with my career. Around that time, an employee was circulating a difficult geometry problem and I solved it. It was an elegant solution and I realized that I wanted to go back into mathematics study full time. I entered Western Michigan University in 1973 where I completed my PhD in 1975. I taught at Wright State for two years before moving to the University of Kansas where I've been on the faculty for 35 years. |
| Rochelle Kronzek: Who are your heroes in mathematics and why? |
| Saul Stahl: First and foremost there is Archimedes. He was a superb mathematician, physicist and engineer. He is acknowledged as the foremost mathematician of the Greek era, without peer until the arrival of Newton almost two millennia later. He was the first to promulgate physical laws as equations that are still standard fare in today's Physics texts. Finally, as you are aware, he was a famous engineer. Other such heroes were, Newton, Euler, Gauss, Galois, Riemann, Poincaré and many others. |
| Rochelle Kronzek: Why did you decide to be a mathematics teacher? |
| Saul Stahl: At first I never dreamed about inventing new theorems. When I finally wrote my dissertation, research became of paramount importance. With the years this emphasis waned and I slowly reverted to teaching and the writing of textbooks. |
| Rochelle Kronzek: Textbook writing seems to be very important to you. I believe that you have seven textbooks in print on game theory, algebra and several geometry books, including Dover's Geometry from Euclid to Knots, Introduction to Topology and Geometry and The Poincaré Half-Plane: A Gateway to Modern Geometry. Certainly professors are given greater rewards for research and research papers. |
| Saul Stahl: As early as in high school I thought about writing expository books. I remember fantasizing about doing an honors project explaining how to approach construction problems in geometry. I hope that I've developed a unique and interesting approach in my writing style and my explanations of mathematical theories. I'm very interested in the history and evolution of mathematics and I lean heavily on them in my books to explain mathematical principles. As Poincaré put it: the teaching of mathematics should be informed by its history. |
| Rochelle Kronzek: Would you give us an example or two of how you explain things using historic theorems? |
| Saul Stahl: Sure. It is commonplace amongst mathematicians that Galois resolved the question of solvability of equations by radicals in 1832, and that he invented Group theory for that purpose. On the other hand, history of mathematics texts attribute to Abel the (negative) solution of the special case of the quintic equation in 1829. Well, if Galois did not invent Group theory until 1832, then what algebraic tools did Abel use? So I actually went to the KU library, located Abel's article and realized that the last couple of pages were devoted to a "lost proposition" on permutations. Lost in the sense that it is a rare algebraist who has heard of it, even though they agree that it is interesting. Anyway, the "lost" proposition and its proof provided me with a new framework for an evolutionary exposition of modern algebra. |
| Rochelle Kronzek: Can you give me some examples of discrete mathematics? |
| Saul Stahl: Certainly. I was contacted once here in Kansas by a volleyball coach from Wichita who faced the following scheduling problem for a volleyball tournament: Given 15 teams and 5 courts, how should he group and regroup the teams over seven days so that every two teams would meet in exactly one court to play a mini-tournament of 3 games. Imagine my surprise when I realized that his problem is actually just superficially different from the classic Kirkman's schoolgirl problem posed in 1850: Fifteen young ladies in a school walk out three abreast for seven days in succession - it is required to arrange them daily so that no two shall walk twice abreast. |
| During my stay in Ohio I was called by the manager of a local pizza store who wanted to know in how many ways a pizza could be made using seven different ingredients. The answer is 256 different pizza combinations. With 10 ingredients, there are 1024 different potential combinations. |
| Rochelle Kronzek: You teach so many different mathematics courses and have produced a spectrum of different textbooks. Which topics do you enjoy most? |
| Saul Stahl: Discrete Geometry is one. I'm very interested in the number of ways that a graph or network can be represented on a surface. One of my favorite theorems is the Classification of Covering Projections which are supposed to describe the ways that surfaces map into each other. |
| Rochelle Kronzek: What are your outside hobbies and interests? |
| Saul Stahl: I'm passionate about dancing. I started studying ballet late (at 35 years old) and actually performed with a downtown dance theatre here in Lawrence. I became interested in ballet after seeing Gene Kelly in a movie, Take Me Out to the Ballgame. |
| I also do folk dancing. I'm still folk dancing and I'm a member of an Argentine Tango club in downtown Lawrence. |
| I'm also very interested in languages. I speak English and Hebrew fluently. At some time or other of my life I was also fairly fluent in French, Nepalese, Yiddish, and modern Greek; I had two years of Russian in college and various one or two semesters in hieroglyphics, Chinese, Arabic, and German. Currently I am studying Spanish. |
| Rochelle Kronzek: Do you have any family of your own? |
| Saul Stahl: I have two daughters and a son. My youngest has just graduated from high school. I am also happily married. |
| Rochelle Kronzek: What comes next? |
| Saul Stahl: I plan to phase out of teaching during the next three years but I'm actively continuing with my textbook revisions. I have revised two of my books recently and I'm in the midst of revising my algebra book. |
| Rochelle Kronzek: Thank you for spending some time with me Saul. In closing, please chose a favorite chapter from your Dover edition of Geometry from Euclid to Knots to share with our readers. |
| Saul Stahl: I suggest that you use pp. 1-19. |
| Click here to download this sample. |
