Professor Max Mintz – In Memoriam

To tell a story about Professor Max Mintz, let me begin with a math problem: Take graph paper and draw x and y-axes. Grab a fidget spinner, tape a pen to it, set it on the graph paper somewhere above the x-axis, and spin it. As the pen spins, consider how the imaginary line along the pen intersects the x-axis. For each half revolution, the intersection will start far away, zoom toward the center, slow down as it gets just below the spinner, and then pick up speed as it zooms off again.

If you plot the time that the intersection spends on the x-axis, you will end up with a beautiful curve that looks a lot like the “normal” distribution. However, it is not. Anyone who has taken Professor Max Mintz’s “Decision Making Under Uncertainty” course will know to cringe as I reveal that the curve is the evil monster called the “Cauchy distribution”. 

As students of Penn’s General Robotics and Sensory Perception (GRASP) lab, we would frequently need to measure the world around our robots to do path planning, pick up objects, and coordinate tasks. Professor Mintz gleefully and enthusiastically warned us that if we take samples of something that follows the Cauchy distribution, the average of our samples will never converge and the variance would be undefined. It "is a distribution that will eat you for breakfast!" With a sly grin, he taught us that as we create our robotic systems, we should always be prepared for fun edge cases and crazy error conditions.

I had the honor of having Professor Mintz as both a teacher and a member of my thesis committee. He was always generous with his time, his intellect, and his joy of mathematics.

This past semester, my 19-year-old daughter took “Intro to Statistics” and asked for my help with P-value problems. As I looked at her textbook I was immediately transported back 25 years to Mintz’s course and I cheerfully exclaimed, “this assumes you are dealing with normal random variables, let me tell you about the Cauchy distribution!” Of course, my daughter rolled her eyes because I was lecturing again.

Professor Mintz instilled in us a fascination, not only with the beauty of mathematics, but also the exciting challenges and quirks that it reveals. I believe that through those of us blessed to have spent time with him, the positive reverberations of his work will, like the Cauchy distribution, are unbounded.

Thank you Professor Mintz!