#### by David E. Rohrlich

I first met Dick Gross in the late summer or early fall of 1976. I had just arrived at Harvard, and Neal Koblitz had initiated some conversations related to CM types of Jacobians of Fermat curves. At an early stage of our collaboration Neal suggested that it would be worthwhile to involve a graduate student named Dick Gross in our discussions. At first I did not know what to make of Dick. I don’t think I had ever met anybody whose actual given name in English was Benedict, and I certainly had not encountered any graduate student whose mathematical intensity seemed quite as frenzied. However an early incident won my gratitude. In a conversation among the three of us I had quoted a fact from the Shimura–Taniyama volume [e1] that seemed important for the matter at hand, but at our next meeting we looked at the quoted passage together, and I was mortified to discover, probably thanks to Dick’s guidance, that I had misquoted it. Worse, I had the impression that in the intervening days Dick had already invested some thinking about the Fermat curves based on the false information I had provided. But Dick seemed embarrassed by my abject apology, and if he felt any annoyance, none was apparent. He swiftly steered the conversation into a more productive direction.

Perhaps this little incident was a harbinger of things to come,
because over the next two years, while he was still a graduate
student and I a postdoc, a role reversal occurred in which
he became
something like a second thesis advisor
to me — not in the sense of
supervising my thesis
but more in the sense of educating
me about the tricks of the trade and the niceties of mathematical
exposition. The things I am referring to here include not only
important insights but also basic habits of mind, even things
as simple as an unremitting awareness that number fields
need not be regarded as subfields of __\( \mathbb{C} \)__. In principle of course
I already had such an awareness, but
it was instructive to observe how in Dick’s case,
this bedrock conviction — not mere awareness — informed his every thought.
In the end
it was my good fortune to witness the genesis of the
Deligne–Gross conjecture:
The order of vanishing of a motivic
__\( L \)__-function
at a central critical
point is independent
of the complex embedding
of the coefficient field of the motive (see
[e2],
Conjecture 2.7(ii), p. 323).
It does not diminish my enormous debt to my thesis advisor
Serge Lang to recognize that
after receiving my degree I was privileged to continue
my graduate school education
under Dick’s tutelage.

After Dick got his degree and I moved on from my postdoc,
we no longer saw each other with the same regularity,
but he continued to be a source of insights and inspiration
at conferences or seminars or
wherever I encountered him. Sometimes I did not appreciate the
significance of his remarks until many years after he made them.
For example,
as I write these reminiscences, I happen to be working
on a little paper involving idele class characters
of a CM field which are trivial on the ideles of the maximal totally real
subfield, and I am reminded of a remark that Dick made to me in the
early 1980s, referring at that time to
an
imaginary quadratic field __\( K \)__: When a character of the type
just mentioned factors through the Galois group of a __\( \mathbb{Z}_p \)__-extension
of __\( K \)__ then the name *anticyclotomic
character* is appropriate,
but in the general case, the classical term *ring class character*
is the correct designation. I did not attach much importance to
Dick’s comment at the time, but I have since come to
realize that this is a case where the history of mathematics,
of which Dick is very conscious, can usefully inform the practice
of mathematics, and what was seemingly just a remark about terminology
has turned out to be intellectually provocative.

I have never adequately acknowledged Dick’s immense influence on me, even in cases like [e4] where a suggestion of his was the catalyst for undertaking a project. But others much wiser than I and a good bit less stingy have managed to find just the right words to express their appreciation. I am thinking, for example, of the acknowledgment at the end of the introduction to the paper [e3] of Rubin and Wiles, who write: “Finally, we thank Gross and Mazur for their helpful suggestions, conscious and otherwise.” Suggestions conscious and otherwise — that says it all. By the way, Deligne’s acknowledgment in loc. cit. is not dissimilar: “Que (ii) soit raisonnable m’a été suggéré par B. Gross.” Deligne’s remark, together with my own firsthand glimpse of the events which preceded it, is the reason that I speak of the “Deligne–Gross conjecture,” even though I have the impression that the epithet has not yet gained the widespread currency that it deserves.

So far I have emphasized Dick’s influence,
but there are two other aspects of his mathematical persona
that I would also like to mention. One is the breadth of
his appreciation of mathematics, which encompasses both the
large and the small, both the sophisticated and the naïve, both
the cutting-edge and the old and familiar.
He calls to mind a linguist who has mastered dozens of
languages but is nonetheless full of admiration when he encounters
somebody who speaks only one foreign language but speaks it
with exceptional gusto. Or perhaps one could compare Dick to
a pianist who tours the concert
halls of the world performing the Emperor Concerto and then
comes home and plays *Für Elise* for an intimate circle.
About four years ago Dick sent me the preprint
[1],
and I was delighted to see
the reappearance of
topics that had once enchanted us both: the Chowla–Selberg formula,
values of the gamma function, periods, and so on. Apparently
they still enchant us. The combination of breadth, depth,
and fidelity to one’s mathematical youth
is one of the traits that I most admire in a mathematician;
it is all too rare, but Dick has it in abundance.

Finally, let me touch on Dick’s capacity for concentration. As essential as it has been to his mathematical career, it is not so much a part of his mathematical persona as it is simply a part of his personality, and it is reflected in all of his endeavors, not just the mathematical ones. In fact it is crystallized for me in a mental snapshot from many years ago of one of Dick’s nonmathematical activities. The Corvallis conference on automorphic forms was held at Oregon State University in Corvallis in the summer of 1977, and at the time there was some grumbling about the lack of recreational amenities available either on campus or in town. But for better or worse, the result was that the participants in the conference had to create their own forms of entertainment. One afternoon I came upon Joe Buhler and Dick juggling bowling pins, tossing them back and forth on the lawn in front of the dormitory which served as our accommodations. I no longer recall how many bowling pins Dick and Joe were able to keep in the air, but the sight was mesmerizing. Even so, the image I retain best is the look of intense concentration on Dick’s face. It was as if juggling were the most important thing in the world to him. The seriousness of his expression allowed for only one interpretation: at that moment, it was.

*David Rohrlich received his PhD from Yale in 1976 and has taught at
Harvard, Rutgers, and the University of Maryland. Since 1990 he has
held the position of professor of mathematics at Boston University.*