Much like the bespeckled boy wizard at Hogwarts, I spent my formative days at a school where science and magic were commonplace, the house you were sorted into determined your social circles, and dementors were at the ready to torture our fragile souls. And much like Albus Dumbledore, there were faculty members who were larger than life. We all had our infallible idols: Most had Richard Feynman, but I had Tom Apostol. Anyone who has read J. K. Rowling’s beloved novels knows (spoiler alert!) Professor Dumbledore isn’t as perfect as Harry Potter once thought he was. And anyone who’s read about the Nobel Prize awardee knows Richard Feynman wasn’t perfect either. (Office hours at Strip Clubs? Really??). But what happens to that student who realizes her or his idols aren’t infallible?
Tom Apostol passed away earlier this year. He was a professor of mathematics of Caltech for nearly 40 years, and spent the next 20 years as emeritus writing papers on the history of mathematics and producing videos for Project Mathematics! In fact, there was a memorial service at Caltech recently. Most of us probably know him best for his two volumes simply entitled Calculus.
I began as a freshman at Caltech in 1990, where I was fortunate to place into the sole advanced calculus course taught by Professor Apostol. I remember students coming up to Apostol at the end of class asking for autographs of his books — affectionately known as Tommy I and Tommy II. I wholeheartedly adored Apostol’s lectures. He would walk in a few minutes late with his 3-ring binder, head to the front of the classroom, snap the binder open, and pull out one page at a time that which he would spend the next hour lecturing on. He spoke in a quiet raspy voice, did not interact with the students much, but the exposition was beautiful. The way I lecture to my own students is heavily influenced by the way I was taught calculus even as a freshman.
One little known fact about Apostol was he had an incredible memory. He memorized the names of ALL of his students every year. He even greeted me by name when I started his class in 1990. And when I returned at Caltech as a postdoctoral fellow in 2001 he sent me a personal email welcoming me back to campus! I received two personal welcomes, twenty years apart, without any prompting on my end. I am still in awe of this even now.
But not everything was perfect.
While a freshman, I found out that Apostol worked in Number Theory. In fact he even encouraged us to attend a series of lectures by a former Caltech undergraduate named Harold Stark. I decided to purchase a book by this guy, and I’ve been in love with the subject ever since. That’s when I approached Apostol about doing summer research.
Over the course of a month or so, I visited Apostol’s office at Project Mathematics! to outline ideas I had on finding solutions to a specific class of Diophantine Equations. I had won an award from the mathematics department for a method of finding rational solutions to quadratic forms and I wanted to generalize some of the techniques. I had even looked into funding from the SURF office, so I had arranged everything I needed: funding, a project, and an advisor. All I needed Apostol to do is sign the form.
At the end of class, just when I found out that I had earned a high enough grade to place out of the final exam, I asked Apostol to sign the application for summer research funding. He refused saying he didn’t understand the research project and didn’t feel comfortable working with me on it. Since the deadline was in 2 hours, there was nothing I could do.
My first experience in working with a faculty ended in disaster.
Why do I say all of this? Certainly not to degrade Apostol. But I do tell this cautionary tale to say that our idols are not infallible, and they will disappoint us at times. And that’s okay — because they are human, after all.
I learned two valuable lessons my Freshman year: always have a back-up plan; and the best laid plans of mice and men oft go awry. As I got older, I used these experiences with my idol as positively as possible to help recognize that I’ve probably disappointed my own students over the years. The courses and conversations I had with Apostol made a huge impact on the way I see mathematics even to this day, and these lessons shaped the way I advise my own students. I would like to think these reflections make me a better teacher to some, a decent advisor to most, and perhaps a worthy idol to a few.
Thank you, Tom Apostol. You will be missed.