In Memory of Pieter Hofstra

It is by now a month ago that my first PhD student, Pieter Hofstra, abruptly died. Many people have already expressed their sorrow on the "categories" mailing list; I did not find the words. I could only utter my bewilderment and confusion.

I think I met Pieter somewhere in 1998 when he, although following a master curriculum in Cognitive Artificial Intelligence (this was under responsibility of the Philosophy Department), took some master-level courses with me, I suppose Computability Theory and Category Theory.

He approached me for a master thesis project and because this would formally be a Philosophy thesis, he had two advisors, Albert Visser and me. Two memories from this period, when Pieter consulted each of us in turn: a conjecture I had suggested to Pieter could not possibly be true, which Albert was quick to spot; and Pieter, when discussing a piece of mathematics with me, never needed to take notes. He had some kind of photographic memory.

In 1999, Pieter started a PhD trajectory under my supervision and of course this became a period in which our relationship became more intense. Our lunchtime discussions (in which there were often other participants) could drag on for a long time, and could be about a range of topics. Pieter struck me as a genuine multi-talent:

  1. Pieter was a musician. I was, at the time, seriously studying the piano, but Pieter could have entered the Conservatorium (school for professional music education). He had also performed as entertainment pianist in night clubs, earning money. One of his statements that I remember was: "just as when driving a car, you shouldn't strive for full control every moment". Maybe it is because I never learnt to drive that I never could implement this dictum.
  2. Pieter was an accomplished mountaineer. I had done a lot of alpine trekking, but he would know his way around on a glacier; Toter Mann and similar rope techniques had no secrets for him.
  3. Pieter was an athlete, as we weekly saw during our football matches. He was always the first to be "chosen", when teams were formed.
  4. At the risk of stating the obvious: Pieter was a mathematician. Although he had followed a few master-level courses with me, he had had no formal training in topics that now, being a PhD student in the Math Department, he had to assist teaching in: linear algebra, group theory, complex analysis. It was amazing how effortlessly he gained the necessary background.
And then there was (among the topics discussed at lunchtime) chess, gastronomy, the philosophy of art, politics, religion, phenomenology (it was Pieter who taught me what this is),...

In April 2000 I took Pieter to his first international meeting, the PSSL in Braunschweig. It was his first exposure to Bill Lawvere. Pieter later reminisced that when he asked me about "unity and identity of opposites", I only said: "never question a word by Lawvere". It was during this meeting that he met Eugenia Cheng, who by her account became a lifelong friend. Pieter usually mingled easily.

Of his PhD defence ceremony in 2003 I don't recall much except Pieter's observation that I was more nervous than the candidate, and the fantastic dinner in an exquisite little restaurant outside the city centre (that restaurant stayed in business for only a couple of years; I assume the chef was bought by a competing firm).

In 2006 there were two events in and around Calgary, where Pieter had moved: a special session in the yearly meeting of the Canadian Mathematical Society on Algebraic Set Theory, and a meeting of FMCS in Kananaskis, an outer station of the university of Calgary in the Rocky Mountains. I participated in both events; I stayed with Pieter as a guest for the first week. Pieter was one of the co-organizers of the Kananaskis meeting, which will be forever remembered, not so much for the tutorial in Synthetic Domain Theory that I delivered, but for the encounter of Steve Awodey with a bear. After the meeting, Pieter and his (then still) girlfriend Miyoung took me for an unforgettable ride through the Rockies, up to the Victoria Glacier.

An overview of Pieter's work should appear somewhere else, but I would like to single out one paper of singular importance to me: All Realizability is Relative (Proc.Math.Proc.Cam.Phil.Soc.141 (2006),239-264) which was important to my later students Wouter Stekelenburg, Eric Faber, Tingxiang Zou and Jetze Zoethout. Pieter did a lot of work, often in collaboration with Robin Cockett, on categorical formulations of Computability Theory, but recently he chose another tack in his work with Jonathan Funk on the isotropy group of a topos. And in a paper with Michael Warren he sought to find connections with Homotopy Type theory.

I was deeply moved when, in 2018, he had remembered that I had turned 60 and he organized, together with Benno van den Berg, a PSSL in Amsterdam celebrating my and Thomas Streicher's 60th birthdays. During this meeting he presented me with a bottle of very, very fine Glenmorangie single malt whisky (19 years). I recall that in Kananaskis we had enjoyed a lot of good whisky, but in 2018 I was going without alcohol for a while. And since that "while" has now stretched over more than four years, the bottle is still in its pristine state. And now it is, for me, a token to remember a very precious human being. Whose death at 47 is so unreasonable, so blatantly unjust, that it makes me both mad and sad.

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