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