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. --------------------------------------------------------------------- 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 -- [LOGIC] mailing list http://www.dvmlg.de/mailingliste.html Archive: http://www.illc.uva.nl/LogicList/ provided by a collaboration of the DVMLG, the Maths Departments in Bonn and Hamburg, and the ILLC at the Universiteit van Amsterdam