One of Gian-Carlo Rota's virtues lay in the fact that he was welcoming not just to a few intimates, but to a large community of mathematicians. In that sense, there is nothing ``special'' about the following recollections, however precious I find them. Any of his students and very many who were not will recognize their experiences here.

My first memories of Rota are from my first semester in graduate school. He
was teaching and I was taking 18.315, officially titled ``Introduction to
Combinatorial Theory.'' Rota was running this as what he called a ``Hollywood''
course, with pretty results and enough overlap between lectures to keep his
audience from getting lost even if we hadn't carefully studied the previous
lecture. The Rota trademarks were all there: digressions on apparently
tangential subjects that he thought important for a young mathematician to know;
the dollar bill for a student to fetch a can of Coke; and the problems,
seemingly tossed of the top of his head and collected by a designated student
(Dan Port as I recall) to be written down and become the homework in the course.
I recall working late at night on them, by myself and with other students. I
recall some, like ``find a symmetric chain decomposition of the n-cube'' that I
couldn't solve at all. I remember the exercises that started, ``state correctly
and prove...'' I don't recall at the time whether I thought this was a symptom
of laziness on Rota's part. Perhaps I did. In retrospect, I think it was a
service to his students; the ones who worked the exercise needed to do the kind
of experimentation so important in research and so rarely taught to students.
The ones who didn't got to see the idea unobscured by technical detail. It was
this focus on structure rather than detail that most attracted me. I loved
seeing mathematics fitting together into a broad picture. He gave me papers to
read constantly, and I appreciated Julia Yang's advice that ``you don't have
read *all* of them.'' But one of the first papers I *do* remember
reading was Rota's paper with Joni on coalgebras and bialgebras in
combinatorics; I still remember the excitement I had seeing children's puzzles
put into an algebraic framework. It was the ability to ask ``Why?'' in
mathematics and actually get a solid answer that first attracted me to math. It
was Rota's attention to answering that ``Why?'' in as deep a way as possible
that convinced me to be a combinatorialist.

I remember Rota's characteristic generosity: The research problems he shared
freely, not just with his graduate students, but with anyone he talked to or
taught; the dinners out at *good* restaurants, not just after my thesis
defense or those of friends (I pocketed matchbooks from these as souvenirs) but
also the dinners and champagne to which he treated grad. students and postdocs
even on no particular occasion. I was introduced to La Groceria this way, and to
the Chinese restaurant across the street which I only remember as the ``May
Flower'' because that was how, at Gian-Carlo's prompting, Rosa Huang translated
the name. I first had risotto at Gian-Carlo's apartment, the evening after my
orals. As I recall the dish was chosen because Sara Billey wanted Gian-Carlo to
teach her how to cook it. I certainly recall the lox with capers and lemon that
preceded the risotto-the ingredients all fruits of a trip across the street to
Barsamian's. Gian-Carlo was generous as well with his time. I remember traveling
to his apartment in Harvard square to talk about my work even when he wasn't
going to be at MIT. I remember telling him about results in my thesis, drawing
tableaux on the slightly rickety easel he had up in his living room. And I
remember a weekend spent at his apartment, mostly sitting at the Macintosh in
his bedroom redrafting my first paper; when I'd shown him my first draft of our
work, he'd asked ``are you *trying* to hide your techniques from your
readers?'' By the time that weekend was over, the techniques, and the paper were
clear.

I saw him last this past summer (1998). He was traveling as usual, but then so was I. I remember him in Genoa, carrying on a mini-seminar with Lascoux and a bare handful of others, in French. I remember talking to him at length in Cambridge and walking with him from MIT to Barsamian's before I continued on to Harvard Square. I remember his taking an entire conference out to dinner in Cortona and I remember listening, in a gorgeously frescoed room in a medieval-style villa in Cortona, to one of Gian-Carlo's enthusiastic and elegant talks. When he reached the end of the talk and started on what he saw as the important open problems, I picked up my pen and started writing. Someone leaned over and whispered, ``He's just given you your homework...''.

In that sense, he's given me quite a lot of ``homework'' during this last decade. And I've found over this last week that I keep wanting to share certain results with him. Not the brand new discoveries, though I hope he'd be pleased with those, but the simple proofs that suddenly make a theory easier to grasp. I'm going to miss his inspiration, his charm, and his humanity. I won't be alone.

--Brian D. Taylor, Detroit, Michigan, April 1999

File translated from T

On 8 Jan 2000, 02:10.