Richard Arens
My first teaching job took me to UCLA in the fall of 1967, a few years after
the release of the film Mary Poppins. One of the supporting actors in the
cast was the venerable British comedian Ed Wynn, who played the role of
Mary Poppins’s Uncle Albert. At the time I arrived at UCLA, one of the
senior members of the mathematics department was Richard Arens, who
bore a striking physical resemblance to Ed Wynn—he had a bald head
with a fringe of hair surrounding it, and an air of perpetual amusement.
In the course of my work, I had occasion to read several papers that
Arens had written. These papers were a treat—they contained interesting
and unexpected results, almost invariably proved in an interesting and
unexpected way (many results in mathematics are proved by techniques
so well known that a few lines into the proof you can say to yourself some-
thing like “Cantor diagonal proof ”—this was used to show that the set of
all infinitely long names cannot be matched one-to-one with the positive
integers—and skip to the next section).
At one stage in his impressive career, Arens decided that what was
needed was for a mathematician to look at quantum mechanics. He did
so for a number of years. I talked to him about it, and he said that he had
studied it intensively, and had basically gotten nowhere. I suspect that
“nowhere” for Richard Arens was a lot further than it might be for others,
but nonetheless it indicates the depth and complexity that appears in
quantum mechanics.
Any Questions?
For a number of years, I was the graduate adviser in the Mathematics
Department at CSULB. One of my jobs was to keep tabs on our teaching
associates, the graduate students we supported by having them teach
lower-level classes. At the start of each year, I gave a short talk on what I
considered generally good advice for teaching. One of the issues con-
cerned how to handle perplexing questions. I told them that every so
often a student would ask them a question that they couldn’t answer off
the top of their head. It’s happened to me, and I’m sure to practically
every other math teacher as well. I told them that in that case, they
should say, “That’s a very interesting question. Let me think about it
and get back to you on it.” In doing this, they have paid respect, both to
the questioner and the question, and have kept faith with what is one of
the essential missions of a teacher—to answer questions as well as pos-
sible. Sometimes the correct answer to a question requires work, and itAll Things Great and Small 43