Bill Mahavier changed my life. I liked and could learn Mathematics before I met Bill. But in Bill's Calculus class I learned that I could do Mathematics. This changed my life. Today at age 76, having retired from teaching 11 years ago, I am still doing Mathematics with 45 research publications and a research monograph in the 11 years since my 'retirement'. The only difference is that the theorems I proved and the problems I solved in Bill's class had been proven/solved by many people during the previous century whereas the theorems I proved and the problems I solved later are permanent additions to the body of knowledge we call Mathematics.
How did Bill Mahavier teach me to do Mathematics? I learned to do Mathematics from Bill, and later also from John Neuberger, in the same way that I learned to ride a bicycle: I simply did it. They did not interfere with my learning process or stifle my creativity by telling me exactly what to do. Just as my parents picked me up when I fell off the bicycle, they 'picked me up', gently but firmly, when I 'fell off' from my proof and made sure that I clearly understood that I had 'fallen' and encouraged me to keep trying. They never told me exactly what to do but always gave me the impression that they thought I could do it if I worked hard enough. When I eventually succeeded with a challenging problem it was a 'Eureka' moment for me. My Eureka moments then were essentially the same as my Eureka moments are now when I succeed in proving a challenging new theorem.
To avoid a possible misconception that I was an 'elite' student I give a brief synopsis of my background. I came to Chicago at age 16 with my parents, an older sister, and grandmother. We were refugees, citizens of no country i.e. displaced persons - known as 'DPs'. Both of my parents had a sixth grade education in the former Yugoslavia, my mother and sister worked in what later became known as a 'sweatshop', my father was a janitor and my grandmother (who was 65 when we came to Chicago and became a US citizen at age 70) ran the household. At age 16 I had benefited from 7 years of schooling, the first three in Yugoslavia, the other four in Austria. From age 9 to 12 I was in concentration camp Gakowa with no opportunity to go to school. I had no intention of going to school in the US and my parents wanted me to get a job and make money. In Illinois education until age 17 was mandatory. But at age 17 I was strongly motivated to continue my education and my parents, very reluctantly, agreed to let me. So I graduated at age 20 from Chicago Vocational High School and went to Illinois Institute of Technology where I met Bill Mahavier.
Tony Zettl