#### by Nolan R. Wallach

During my years at Rutgers, I had on many occasions attended or spoken
at seminars at Princeton. I was aware of Dick but had no interaction
with him. In fact, the main thing that I remember about him from that
time was that he tutored a
movie star on how to give a mathematics
lecture. Because of him Jill Clayburgh gave a passable lecture on the
snake lemma in the 1990 movie *It’s my turn*.

Dick’s wife, Jill
Mesirov, spent the academic year 1993–1994 at CCR La Jolla (a branch
of a private corporation whose main client was NSA). Dick decided to
go on leave from Harvard to UCSD with the plan of working with
Harold Stark.
Fortunately for me, he and
Dipendra Prasad
had recently
discovered the Gross–Prasad conjecture about the restriction of
unitary representations of orthogonal groups to symmetric orthogonal
subgroups. They had derived the conjecture as a consequence of part of
the Langlands program. Thus, in addition to the beauty of the implied
formulas, the conjectures had a serious role to play in number theory.
Dick came to my office with a question about the first nontrivial
special case of the conjecture for real orthogonal groups. I was
immediately taken with the problem and started working on it. Since
Harold was the chair of the UCSD
Department of Mathematics he had almost
no time to do mathematics. After a short time Dick and I were working
full-time together. I have had deep collaborations with many of the
best mathematicians of the twentieth century, but I treasure that year
of work as the one that I enjoyed the most. In addition to working
with Dick on attempting to prove his conjecture in a special case I
was his de facto mentor on the so called “real case” (or as a number
theorist would say the “infinite prime”). Like many number-theorists
Dick was conversant with the so called
__\( p \)__-adic case (“finite
primes”). I had two other great mathematicians who had asked me to
explain some aspect or representation theory to them:
Harish-Chandra,
who asked about the recent work (at the time) on applications of
homological algebra to representation theory,
and
Pierre Deligne
who
asked for an explanation of Langlands’ proof of the Langlands quotient
theorem. In my first meeting with Harish-Chandra I started with a
definition of an injective module. Harish-Chandra stopped me and said,
“When I first came to the institute I gave a lecture on class field
theory.” He then gave me a lecture on class field theory and asked me
to return in a week. A week later I started as before and he
interrupted me with “I will never understand homological algebra” and
he
indicated that there was no point to continuing the lessons. In
Deligne’s case it was the
opposite: he grasped everything rapidly and
even found an error in Langlands’ proof of one of his main lemmas.
Dick was like Deligne:
teaching him forced me to have a deeper
understanding of my own work. During that year Wiles’ first proof of
Fermat’s Last Theorem was submitted. Somehow, Dick got a copy of it.
One time when I stopped in his office, he looked up from the
manuscript, pointed at it and said, “There’s a black hole in the
paper.” We all now know what that was. Another time, he was doing a
calculation with pencil and paper that involved immense numbers. I
asked how he could be sure that his calculations were
correct. He
said, “I’m a number theorist”.

Our collaboration led to three papers. Two of them [1], [2] were beautifully written by Dick about how the geometry of the quaternionic real forms and the corresponding twistor spaces effected the structure of unitary representations related to the quaternionic discrete series. The third gave the solution to the initial problem that Dick posed when he arrived at UCSD [3].

The third paper was written two years after we did our work. This delay was caused by two major medical events in our lives. During the year after his visit to UCSD Dick was forced to have a major operation to repair part of his abdomen that was damaged by radiation therapy when he was a child. The next year, it was my turn to have invasive surgery. The day before I was to go under the scalpel I received a call from Dick giving me advice about my upcoming surgery. This included, “Don’t be brave, take the morphine”.

We both recovered from our surgeries. Most
of our later interactions before he moved to UCSD involved seeing him
on visits to Southern California or in emails. One email involved a
question about generalized Whittaker models for holomorphic discrete
series. When I answered his query, he then let me know
what he
really needed: the same question for quaternionic discrete series for
__\( G_2 \)__. This was much more difficult and led to my paper on the models for
quaternionic and holomorphic discrete series. Dick’s ideas, in this
direction, led to his work with
Wee Teck Gan
and
Gordan Savin.
Dick
spent another year as a visitor at UCSD in 2007. During that year he
was deeply immersed in work with Wee Teck (a professor at UCSD at the
time) and Dipendra (on leave to UCSD). So, I had little chance to work
with him.

During his 60th birthday conference, in addition to a picture with his former students, Dick set up for a picture of his teachers to be taken with him. It was my great honor to be included in that distinguished group.

We wrote our most recent paper in 2011 [4]. He showed me his ingenious method of using the Weyl dimension formula to calculate the Hilbert polynomials of homogeneous projective varieties. I showed him how his idea could be modified to also calculate the Hilbert series. Many graduate students have thanked me for that paper since it freed them from the standard (horrible) calculations of the Hilbert polynomials of Grassmannians.

In 2016, Dick and Jill moved to
San Diego. Jill was appointed to
a high administrative position in
the UCSD Medical School in 2015 (she is now an
Associate Vice Chancellor of the
Medical School) and Dick
eventually
became a regular (1/2 time) member
of the
mathematics department. As an emeritus faculty member who had
just given up his office, I was assigned to one of the offices for four
or five emeriti. Dick was kind enough to let me be his officemate.
Unfortunately, during his tenure at UCSD we have had little chance for
interaction. One reason is that the problems that
led to our
surgeries in the
1990s recurred. In August of 2017 I had major
heart surgery. The day after the surgery I was walking around the
halls of the hospital using a wheelchair to hold myself up and pulling
an oxygen tank when I saw Dick. He came with a book for me — *Barbarian
Days*, a Pulitzer Prize-winning book about surfing. The pandemic kept
me from visiting Dick during his latest hospitalization. Instead, I
sent him a book, *Noise*, by Kahneman et al. Dick wrote to thank me
with, “Right now I am thinking slowly” (this was an indication that he
had read Kahneman’s previous book *Thinking Fast and Slow*). I wrote
back: “Thinking slow for you is like others thinking fast.” By which I
meant, even when Dick thinks slowly, in the sense of Kahneman, he does
it fast.

*Nolan Wallach is a Professor Emeritus of Mathematics at the University of
California, San Diego. He has done research in Riemannian geometry,
algebraic geometry, representation theory, analysis combinatorics, and
quantum information.*