Logic List Mailing Archive

Anne Troelstra (1939-2019)

Anne Troelstra (1939-2019)
https://www.illc.uva.nl/NewsandEvents/News/Obituaries/Anne-Troelstra-1939-2019-/

Sadly, we have to inform you that Anne Troelstra, after a short illness, 
suddenly died on March 7th, aged 79. A world-renowned eminent researcher, 
a supportive colleague, a teacher who trained many students to become 
important scholars, is no longer with us. Beginning in 1957 as a 
mathematics student, he remained at the University of Amsterdam all his 
life, except for a number of visiting professorships. He rose quickly to 
take his place as the successor of Brouwer and Heyting. As a full 
professor from 1970, he was the universally recognized authority on 
intuitionism and constructivism in general, leaving behind a number of 
books that will remain landmarks for many years to come. Retiring in 2000, 
he made a further name for himself as an author on natural history travel 
narratives. Anne was regularly seen at the ILLC until this year. His 
impressive personality, always intensely occupied with his present 
interests, will be greatly missed.

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Anne Sjerp Troelstra (August 10, 1939--March 7, 2019)

Anne Troelstra was born on August 10th, 1939, in Maartensdijk. In 1957, he 
enrolled as a student of mathematics at the University of Amsterdam -- and 
eventually his interests converged on intuitionism with Arend Heyting as 
his advisor. Students he was close to include Olga Bakker and E.W. Beth's 
students Dick de Jongh and Hans Kamp. With Dick de Jongh, he even wrote a 
pioneering paper on intuitionistic propositional logic, published in 1966, 
that contained the first definition of the central notion of a p-morphism, 
as well as the simplest form of the duality between Heyting algebras and 
relational frames. After obtaining his master's degree in 1964, Anne at 
once became an assistant professor, according to a custom of the time. It 
took him just two years from there to finish his dissertation, supervised 
by Heyting. Besides intuitionism, a main interest of Heyting was geometry 
and perhaps not accidentally Anne's PhD thesis was a study of 
intuitionistic topology. This subject made him aware of the role of 
continuity in intuitionistic mathematics, a concept that was to play an 
important part in his research in the years to come, in many different 
forms.

Anne then obtained a scholarship to Stanford to visit Georg Kreisel, and 
spent the academic year 1966-7 there, with Olga whom he had married the 
year before. Anne sharpened and modified Kreisel's ideas on choice 
sequences, and together they created formalizations of analysis resulting 
in a large article where the typically intuitionistic concept of a lawless 
sequence of numbers that successfully evades description by any fixed law, 
reached its final form. In August 1968, Anne played a central role in the 
famous Buffalo Conference on Intuitionism and Proof Theory, a meeting of 
all important logicians of the day with an interest in constructivism. He 
gave a series of ten lectures there, which turned into his first book, 
published in 1969, that contained the core of his seminal ideas on 
intuitionistic formal systems and their meta-mathematical investigation. 
Back home in 1968, he became a lector (associate professor) in 1968, and a 
full professor in 1970. Further early recognition was to follow. In 1976, 
he became a member of the Dutch Royal Academy of Sciences.

The meta-mathematics of intuitionistic systems was a chaotic jumble of 
results when Anne entered it. Here he showed his greatest strength: 
creating order in a vast and diverse area. In 1973, the order was there in 
his book Metamathe-matical Investigation of Intuitionistic Arithmetic and 
Analysis. Especially striking are the clarification of the properties of 
different models, various types of realizability, and functional 
interpretations. The last chapters on special topics were written by Jeff 
Zucker, Craig Smorynski, and Bill Howard, but the lion's share had been 
written by Anne, editor and architect of the whole. This book, known in 
the community as "Springer 344" still functions as a landmark for serious 
researchers in the subject. Over time, this work developed into the much 
larger Constructivism in Mathematics, in two volumes co-authored with Dirk 
van Dalen, published in 1988, the standard text on constructivism right 
until today.

Of course, Anne also published in depth on special topics. A central 
notion in the study of intuitionistic formal systems is realizability, 
introduced by Stephen Kleene in the 1940ies. Anne's thorough studies of 
the subject resulted in a long article in the proceedings of the Second 
Scandinavian Logic Symposium of 1971. The interest remained with him for 
life. In 1998, a chapter on realizability by his hand came out in the 
Handbook of Proof Theory. Characteristically, Anne's text had been 
finished a few years before, faithfully meeting his deadline, but delays 
by other authors kept him updating, somewhat grumblingly, with all new 
results in the area. What he published had to be the complete state of the 
art.

Other topics pursued in depth by Anne, through the 70s, 80s and 90s are 
the history of intuitionism and the philosophical basis of the theory of 
choice sequences. In his important 1977 book Choice Sequences, he proved 
lawless sequences to be essentially just a figure of speech by an 
elimination theorem, showing how statements about lawless sequences can be 
expressed in a theory containing only lawlike sequences. But he did stress 
that the notion of lawless sequence still serves a purpose as a clear 
notion derived by informal rigor.

Moving beyond intuitionism proper over the years, Anne broadened his scope 
to proof theory in general and wrote two more books which again created 
new order in diverse fields. In 1992, a textbook Lectures on Linear Logic 
came out proposing improved formats for a then still only partially 
understood new paradigm. He contributed the majority of the chapters in a 
book with Helmut Schwichtenberg called Basic Proof Theory, 1996, that is 
still a standard resource.

An important part of Anne's life were his PhD students, of whom he 
supervised 17, and with many of whom he maintained a close relationship. 
His first PhD student Daniel Leivant finished a thesis in 1975 on the 
meta-mathematics of intuitionistic arithmetic, and later made his career 
in computer science. Initially a scarce commodity, in the 1980s, the 
number of PhD students increased, and Anne's students wrote on a broad 
variety of topics, such as intuitionistic meta-mathematics, combinatory 
algebra, category theory, Martin-Löf type theory, bounded arithmetic, 
linear logic, and provability logic. Many of these topics reflected the 
introduction by Anne, often in a close collaboration with Dirk van Dalen 
in Utrecht, of new topics on the Dutch scene. These students then carried 
the torch further by themselves. For instance, Ieke Moerdijk became an 
international leader at the interface in topos theory and logic and 
category theory generally, while Jaap van Oosten became a worldwide 
authority on realizability. In the Netherlands alone, four of Anne's 
students have become full professors, in mathematics, computer science, AI 
and philosophy. But Anne was an dedicated teacher at all academic levels, 
whose precision, clarity and scholarship influenced generations of 
students in Amsterdam.

Anne retired in 2000, but not to rest. All his life, he had a deep 
interest in natural history and a wide knowledge of the plants of the 
Netherlands and abroad. His annual linocuts of plants discovered on his 
travels in Europe were famous. To those on a walk while listening to him, 
what looked like an ordinary city street to the untrained eye would turn 
into a rich landscape of flora, history, and natural wonders. This very 
year 2019, an article by him will appear on new species of blackberries, 
his special interest. Anne also made a further name for himself as an 
author on natural history travel narratives, chronicling the exotic 
characters and adventures of the past denied to the average academic of 
today. His major Bibliography of Natural History Narratives was published 
in 2016.

Anne will be missed in the first place because he will no longer be there 
to tell us what he thinks about a question that you may have about 
constructivism. You always knew that you would get a completely honest 
answer from somebody who knew all the issues and had already thought much 
further than you. But it is just as much the personal qualities that will 
be missed. Anne was a very special, and to some, occasionally intimidating 
person: penetrating, honest, critical, ironic, sharp at times, but always 
open to arguments and unfailingly supportive of his students and 
colleagues. He will be deeply missed by all.

Our thoughts go out to his wife Olga and to his daughters Willemien and 
Ine.

Johan van Benthem
Dick de Jongh
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