When I was in grade school, I remember that I wanted to be an Egyptologist, and I read many books about Egypt. I never imagined that I would become a mathematics professor at a university. I was born in Tucson, Arizona. I grew up in the Spanish speaking part of town. Both of my parents were born in the state of Sonora in Mexico. My father died when I was nine years old, and my mother had to work three jobs to make ends meet. My siblings and I also helped out by working at the family gas station after school, on weekends, and during the summers. Though my family experienced poverty, I came away from it with a sense of pride.
My family valued education, and we were probably the only family in the neighborhood who owned a set of encyclopedias. In the seventh grade, my goal was to read the entire set. In the eighth grade, I read every science fiction book in the teenage section of the library. For a family with little money, reading was inexpensive entertainment. Reading prepared me well for high school and college.
In grade school and high school, I had a supportive group of teachers who believed in me. Though I was a B student in high school, I did terrible in my first semester in college. I earned D’s in chemistry, college algebra, and trigonometry. Rather than give up, I worked extra hard after that. I managed to bring my grades up, and enjoy the many classes that I took in mathematics and physics. I eventually went on to earn a Ph.D. in mathematics.
One thing that I do as a mathematician is study numbers and equations. I separate them into parts and study those pieces. Do you remember when you were learning how to read? You saw bunches of letters on the page, but you had no idea what the different combinations of letters meant. Before you began reading, you broke the words into pieces and learned the alphabet. Once you knew the alphabet, you put the letters back together, learned how the combinations sounded and began reading words. Now you can study all the words in the dictionary! A prime number in mathematics is like a letter in reading. A prime number is a counting number that can only be divided by one and itself, without a remainder. For example 17 is prime because no other number can divide it besides 17 or 1, but 12 is not prime because 12 can be divided by 1, 2, 3, 4, 6, and 12. A mathematician can study all of the counting numbers by studying only the prime numbers. This is because any counting number can be broken down into prime numbers that are multiplied together. For instance, 3828 =2 x 2 x 3 x 11 x 29. One problem that has always fascinated me is called Goldbach’s Conjecture. It says that every even number greater than two is the sum of two prime numbers, for example, 48=17+31. If someone could explain why this curious pattern happens, they would be famous! Experiment for yourself by trying to find sums of two prime numbers for the even numbers 2 100. Keep track of the number of different ways that an even number can be written as the sum of two primes. For example, 48 has 5 such ways: 48 = 5+43= 7+41= 13+37= 17+31= 19+29.
One of the benefits of being a researcher is the opportunity to travel. One of my most interesting lecture tours was a threeweek trip to China in 1988 where I gave lectures in Beijing, Sichuan, and Shanghai.
Video of William Vélez. Dr. Vélez talks about his work, how he became interested in mathematics and what is important to him as a professor.
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