In Memory of Anne Troelstra

It must have been in the second year of my studying maths, in the spring of 1983, when I first met Professor Troelstra while participating in a logic seminar. We read Dana Scott's Lectures on a Mathematical Theory of Computation, and I was immediately tasked with presenting Chapter 3.

Half a year later, I was student-assistent under him. I helped with bibliographical research for the Omega-bibliography, of which Troelstra and Diller compiled the part on Constructivism.

Troelstra could be rather rigid when it came to social conventions. Dutch, like many other continental European languages, has a polite/formal form and a familiar form for addressing a person (different ways to say "you"). In those days, it was still customary to address a student in the polite form, whereas for a colleague one would of course use the familiar form. When I did my bibliographical chores, I was a colleague and was talked to in the familiar form. When, after a discussion about this work, I asked him whether I could ask a question about his course in lambda calculus, which I was following, he switched at once to the polite form.

I accompanied him on trips to Münster in Germany. Once a year, a delegation of teachers, postdocs, PhD students and undergraduates went for a short weekend-seminar to the department of Diller and Pohlers (and once a year, the M$uuml;nsteraner reciprocated with a visit to Amsterdam). Once when we passed a sculpture of a nymph-like person, her naked torso rising out of a rough substance, he commented: "the artist probably thought: if I reveal more of her body, it can only lead to disappointment". He had definitely a sense of humour.

Maybe once a year, he invited the whole logic group to his place for dinner. At the end of the evening he would put a large crate, full with books, on the floor, and everyone was invited to take what (s)he liked.

In the fall of 1986 I had been working on my master thesis, but my assistentship had ended and I had several jobs, so the thesis work had been put on hold. Troelstra was not in the habit of telling you what he thought of your work, and naturally I assumed I would do my master's some time and then find a position outside academia. But I was in for a surprise, when early february 1987 he was on the phone. "You should finish your thesis and get your master diploma, for you can start by March 1 as PhD student." It was not a question. At the ceremony for my master diploma (my parents were present) he called me a "rough diamond", which was sort of a compliment, I suppose. The emphasis was on "rough".

As a PhD student I of course got to know Troelstra better as a mathematician. I did my first steps in topos theory, reading work by Peter Johnstone and Martin Hyland. Although he had not worked in this field, he always held it in some kind of timorous esteem, although he stressed the importance of applications. Abstraction had its limits. He had lots of criticisms, mainly on my style of writing ("too succinct", "too terse"); later I realized that he taught me a lot during this period. Reading my manuscripts was sometimes a strain for him, and he complained that supervising me would shorten his life by a year. I came to appreciate how he could "feel" a result, even if he was not familiar with the formal details.

Again, he was not going to give you any compliments so after 3 years of work on my thesis I was just dead certain that it had been a total failure. I would leave academia without a thesis. But again there was a surprise: "you should do some research in the library for an overview of the field. And gather your results, for it is about time to start writing up".

One aspect of doing a PhD with Troelstra was that, starting right after the ceremony, one should no longer use the polite form with him and call him "Anne". This took some getting used to, but I managed eventually.

In the northern Dutch province of Friesland (which is not where Anne was born or grew up, but is, I presume, where his ancestors came from) the name "Anne" is a common boys' name. A funny story was told by Dana Scott at the memorial conference which Ieke Moerdijk, Harold Schellinx and I organized to celebrate Anne's 60th birthday: when he first met Dana, he told him that he had thought Dana was a girl. He probably didn't reflect on how his own name might sound to an English speaker.

I am grateful to have been able to study under a scholar of Anne's calibre. His staunch honesty will remain a beacon for me the rest of my life.

Back to my home page