## Memories of Al Baernstein

A slight departure from the usual fare of this blog to say something about one of my grad school professors, Al Baernstein, who passed away June 11, 2014.

I began my PhD in mathematics at Washington University in St. Louis in the Fall of 2004. In a PhD program, the first few years are devoted to courses in the major areas of math. At Wash U, this was a full year of algebra, real analysis, complex analysis and geometry followed by a very difficult qualifying exam. Once these are completed, research and progress toward a dissertation can begin. So these years naturally come with a lot of stress. Most of us were used to being able to coast by in undergrad and masters level classes and this would prove to be the most challenging ordeal of my life to that point.

The first day of classes I walked into Al’s complex analysis class not knowing what to expect. I had taken a class in the subject while getting my masters and got an easy A, but I knew this would be a challenge. I already knew my area of specialty would be in finite group theory and all those epsilons and deltas made me uncomfortable. I watched as he painstakingly defined what a complex number was and worked his way through very basic complex analysis (not an oxymoron, non-math friends), and by the end of class thought it was going to be the most boring experience of my life. Boy, was I wrong. I soon learned that he had the same dry sense of humor I did. We covered so much material those two semesters I’m amazed how much it was. Al had taught this course every other year going back to at least the 80s and he had it down to an art. Proofs were usually flawless and major course ideas flowed from one thing to the next. By the end of the year, I couldn’t wait to come to class.

His homework sets were legendary among the graduate students. The first day of class, the syllabus said we were expected to work together in small groups, but to write up solutions individually. This would prove a great challenge as the problems were usually very difficult. Proofs would require some clever idea and the problems that were straightforward still involved lots of nasty computations where you had to be very careful. By second semester, there was a group of five or six of us that would work on every set together. Second semester’s fourth homework assignment was e-mailed to us with the accompanying warning that it was particularly challenging and to get started right away. The hardest homework problem I ever did was from this set and involved the Schwarz-Christoffel theorem. Here’s what the end of it looked like:

Other homework would prove challenging and it was a highlight of my graduate career when Al called a solution I came up with to a particular problem “clever”.

The exams were brutal in this class, too. He would give us a list of theorems to know the proofs for, and while that might sound like it makes things easy, he would give us about 30 theorems and maybe four would be on the test. (One of these was the Riemann Mapping Theorem whose proof is quite long and involved). Plus there were generic problems. What helped out immensely was the fact that he had taught the complex qual so many times that we had about a dozen prior exams to study from. I seem to recall him walking into the exam room and dropping the huge stack of tests on the desk with a loud thunk. Four hours later, I walked out of there knowing I had passed, thanks in large part to his outstanding teaching.

After that first year, my interaction with Al was fairly limited as I had no interest in further pursuing complex analysis. Mostly it was when he would speak at the graduate student seminar, which was always a packed house, not just because of interest in the subject of the talk, but often because we were just waiting to see what he’d say next. His talks always had some interesting aspect of math history in them.

I close with a few specifics I remember about him or his classes:

1. Like any mathematician, he had lots of quirks. He was famous for writing something, then cocking his head sideways while holding the chalk to his lips as if pondering if that was really right or not (it always was). He wore slippers to class every day. I was told this was a gift from a previous class because he was constantly tying his shoes. So he would walk to school from his nearby home, go to his office and put on the slippers for the rest of the day. Also, at least once a day, he would accidentally back into the tall trashcan in the room, almost knocking it over.

2. He would always attribute his theorems and I was incredibly amused one day when he wrote a theorem then put “(me)” after it. I also remember him once mentioning a post-doc at Wash U that improved a constant bound by some ridiculously small value like 10^-332.

3. When I was at Wash U, the math department building only had one classroom to itself. The rest were shared by the whole school, so we would frequently walk into class and find the desks in a circle from the previous English class, (the blackboard usually pristine). One day, the blackboard had one word written on it: META-DISCOURSE. Al walked into class as the previous instructor was leaving and he asked, “What is meta-discourse?” She said it’s when you talk about discourse. He cocked his head to the side, took the chalk, and wrote a META- in front of it and asked if that’s what we’re doing now. The other teacher left the room when we started talking about the inverse limit of this sequence.

I’d welcome comments below with similar stories from those who knew him.

Rest in peace, Al. You were one of the best.

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