Editor's note: Dr. William Vélez will be lending his expertise in a MiSciNet column for administrators beginning January 2004 and alternating every other month. The focus will be on the recruitment and retention of minority students.

I was born in Tucson, Arizona, in 1947 and grew up in the warm embrace of the Spanish-speaking part of town. Both of my parents, Emilio Garcia Vélez and Julia Yslas Vélez, were born in the state of Sonora, Mexico. After they were married, they lived in both Mexico and the U.S. By the time they started having children, they had settled in Tucson, and all of my siblings and I were born in the U.S.

My father was a mechanic and had his own garage and gasoline station. I was pumping gas and fixing flat tires by the time I was eight. My father died when I was nine years old, and of course, this created great hardship for my mother. She worked three jobs and managed to keep things together. I want to emphasize that the hardship fell upon my mother and not me. Everyone in the neighborhood struggled to make ends meet, so being poor was not unique to our family. My mother created a home full of warmth and care, so I don't remember suffering terribly through poverty. I remember the loving family that surrounded us, the wonderful Mexican music and movies that were part of our lives, and the concern that my mother had for those around us. After my father died, my mother went into politics and was vice mayor of South Tucson for 14 years.

An Inauspicious Beginning

I began my undergraduate studies at the nearby University of Arizona in 1964, just after high school. I was an immediate and pronounced failure. I started as an engineering major and enrolled in calculus. Halfway through that semester I realized that engineering was not for me. Within 4 weeks I had to drop calculus. I simply could not understand anything the calculus instructor was saying. This is fairly typical behavior for students, and universities have created a safety net to address it: They allow students to drop back to a prerequisite course, and this is what I did.

I dropped back to college algebra and trigonometry, but I still did poorly. I earned nine (yes nine) units of D's that semester. However, the next semester, I did the oddest thing--I enrolled in calculus again. I did this on my own. There was no one to advise me. If I'd had an adviser, I would have been discouraged from continuing on with mathematics, for my own good. Students get this kind of advice routinely in colleges and universities around the country, but this guidance keeps many students from realizing their full potential. It is difficult to gauge a student's inner strength and desire to succeed.

My failure that first semester injured my pride, and I just could not bear it. There was just no way I could believe that I was incapable of understanding calculus, or any other subject, for that matter. I had no idea what I was going to do. No one in my family had ever taken calculus, much less used it professionally. At the time, I didn't know why anyone would want to study calculus, but I knew that I would understand it. To me, this was now a family matter. I represented my family at the university, and the sense of pride and self-worth that had been instilled in me as a child would not allow me to accept these failures.

I enrolled in calculus my second semester and also changed my study habits to include a more focused attitude on my academic subjects. It shouldn't be a great surprise to learn that attending class, doing the homework, attending office hours, and seeking help when you are confused is a formula that will lead to better understanding and therefore better grades. I did better in all of my classes that semester, and in particular, I earned a C in calculus. Not a great performance, but I was able to take the next step.

I began my second year in college by taking calculus and physics. The more I studied mathematics, the more I was struck by its utility--the way it seemed to model physical situations so naturally. I found it amazing that mathematics could predict the future. By the end of my sophomore year in college, I had decided that I was going to pursue a Ph.D. in either mathematics or physics. In my junior year I realized that graduating with a degree in physics would require taking a year of physics lab. Since no experiment of mine had ever turned out correctly, I recognized that I could not go that route. In 1968 I received my B.S. degree with a major in mathematics and a minor in physics. I spent the next two years in the Navy, and I returned to earn my master's degree (1972) and my Ph.D. (1975) in mathematics at the University of Arizona. My full résumé can be seen on my Web page.

Knowledge, Skills, and Confidence

That decision to take calculus changed my life. Mathematics gave me the knowledge, skills, and confidence to choose a much different path in life from the rest of my family's. Pursuing a Ph.D. also gave me another set of skills. It taught me how to communicate my technical ideas, how to write down my results, and how to plan and carry out a research agenda. More importantly, it gave me something worth so much more: the freedom to pursue my own ideas.

No one, by looking at my record after that first year, could possibly believe that I would go on and earn a Ph.D. in mathematics or that I would create new mathematics and direct Ph.D. dissertations. Who would believe that I would become a full professor of mathematics at a research university and work at national laboratories, applying my mathematical knowledge to address problems in military communication systems? Who would believe I would earn patents along the way and also work at the National Science Foundation, making decisions on who would receive research grants in the fields of algebra and number theory? Who could believe it?

My position as professor of mathematics is not a job--it is an adventure. I find great joy in helping students understand complex mathematical ideas and seeing these students move on to successful careers. I couldn't tell you what I will be doing next year. I can tell you that whatever it is, it will have been my own choice and that I will be enjoying it. I hope the educational decisions you make will provide more opportunities and open doors never before imagined. Continue to believe in yourself.

Dr. William Y. Vélez is University Distinguished Professor and Professor of Mathematics at the University of Arizona. He may be reached at velez@math.arizona.edu.