# Martin Löb (1921-2006)

Martin Löb, Amsterdam, 14 November 1978 |

On Monday August 21th 2006, our esteemed former colleague Professor Martin Löb, holder of the chair of Mathematical Logic from 1971 to 1985 at the University of Amsterdam, passed away in Annen (Drente).

Obituary by Stan Wainer (Mathematics, University of Leeds)

to appear in the Guardian

**Martin Löb: A Pioneer of Mathematical Logic**

Martin Löb, a central figure in the early development of Mathematical Logic in UK, has died in Holland at the age of 85 following a lengthy illness. He was a man of strong intellect and great determination who, as a teenaged refugee from Nazi rule, had overcome the violent disruptions of wartime and against the odds, established a distinguished academic career.

After a boyhood in Berlin, he escaped to England just prior to the onset of the second world war. He lived first on a farm but, classed as an "enemy alien", he was deported in 1940, on the transport ship Dunera, to an internment camp at Hay in the Australian outback. The internees arrived in a poor state since conditions on board ship were bad, and they were torpedoed en-route! The camp was exposed to sandstorms and high temperatures, but in this unlikely and inhospitable place Löb began, aged 19, to learn advanced mathematics and logic at the "camp university" set up by the older academic refugees. (His teacher Felix Behrend later became a senior professor at the University of Melbourne.) It was three years before he was able to make the return journey, after the British Government had acknowledged its deplorable mistake in enforcing the internments. By this stage he was committed to further academic study and, as the war ended, he was accepted for a London University degree and obtained a teaching post in a boarding school. Then he had a stroke of luck. A research studentship was advertised, to work under R.L. Goodstein at Leicester, and Löb got it. His Ph.D. followed and by 1951, at the age of 30, he was an Assistant Lecturer at Leeds. He stayed for twenty fruitful years, becoming Reader and then Professor of Mathematical Logic, before accepting a prestigious chair (previously held by Evert Beth) at the University of Amsterdam where he remained until retirement. This was an exciting period for the foundations of mathematics, and Löb strove to consolidate the subject at Leeds. Joined briefly by Robin Gandy, he established the Leeds BA in Mathematics and Philosophy, the early international conferences which brought distinguished senior logicians such as Church and Tarski from USA, the seminar dinners at Whitelock's pub, and the European Soc. (he strongly believed in the European ideal). University expansion in the 1960s enabled him to attract more logicians and build a distinctive Mathematical Logic group, one of only few such in UK. His inspired leadership was the bedrock of what is now one of the leading centres for research in that field.

Löb's own research spanned proof theory, modal logic and computability theory. Throughout his life he thought deeply about difficult problems, making fundamental contributions to each of those areas, but it is Löb's Theorem (1955) for which he is best known. Gödel, in his celebrated Incompleteness Theorem of 1931, had constructed a self-referential statement of formal arithmetic asserting its own unprovability and shown, assuming consistency, that it has to be true. This prompted Henkin to ask about statements which assert their own provability, and Löb showed by a typically clever and succinct argument, that they also must be true. (Whereas Gödel's Theorem is essentially a formalised version of the Liar Paradox, Löb's Theorem formalises Löb's Paradox: the sentence "if this sentence is true then the moon is made of green cheese" is true(!) so the moon is indeed made of green cheese.) His work lies at the heart of much research, continuing to this day, on "reflection principles" and "provability logics", and it will forever remain at the central core of Mathematical Logic.

Martin was an intensely private, cultured and quietly strong-willed person, devoted to his Dutch wife Caroline and their daughters Maryke and Stefani. After his retirement from Amsterdam they moved to a quiet spot in the north of Holland, and there he stayed until his death, Caroline having sadly pre-deceased him. He valued his students highly and was concerned as much for their welfare as their academic progress. Only a few had the good fortune to complete their doctorates under him but two of them now head the departments where he worked, and he influenced many others in the early stages of their careers. He is remembered with affection, as a profound and dedicated logician and teacher, and a man of great inner strength and integrity.

Supplementary statement by Dick de Jongh (ILLC, University of Amsterdam):

**Martin Löb in Amsterdam**

Marin Löb's move to The Netherlands came at a time of intellectual and social turmoil, as Dutch universities were adjusting to the post-revolutionary realities after the 'Sixties', realities which Löb sometimes found daunting. But even so, he stood at the basis of the growth of logic, moving the center of the logic group from philosophy to mathematics, but also helping create an interdisciplinary "vakgroep" in between mathematics and philosophy as a successor to Beth's 'Instituut voor Grondslagenonderzoek, and predecessor of today's ILLC. Löb and Anne Troelstra, the successors of Beth and Heyting, held the two central chairs here, while an active group developed around them of junior professors, visitors, and students. The inspiration of Löb's Theorem made Amsterdam one of the places where the first results in 'provability logic' were obtained, a program started by de Jongh and the guest researcher Smorynski. Over the years, this program flourished, with further Dutch contributions by Frank Veltman, and especially, Albert Visser, and it is still a striking feature of the national logic scene today. Meanwhile, Löb himself concentrated on his favorite subject of proof theory, both in teaching and research. His best known result from this period is the undecidability of intuitionistic second order propositional logic, even with only implication and the universal quantifier. The wider implications of his intricate proof have not been fully understood even now. As for Nachwuchs, Löb supervised one PhD candidate in his Dutch period, Johan van Benthem, his eventual successor in 1986, whose thesis started the tradition of modal logic in Amsterdam with an integration of mathematical and philosophical themes. But a much wider circle of colleagues and students remembers him as an erudite and pleasant person who cared for others, once his confidence had been gained. When Löb retired in 1985, aged 65, the rather scattered field of logic in Amsterdam had been unified, and it was ready for its institutional consolidation during the following decades.

A newspaper survey of the importance of Löb's work will be written by Albert Visser (Utrecht).

Löb's influence can be seen, amongst others, in the following links to the field of Provability Logic:

http://plato.stanford.edu/entries/logic-provability/, http://en.wikipedia.org/wiki/Provability_logic

Johan van Benthem, Kees Doets, Peter van Emde Boas, Dick de Jongh, Anne Troelstra, Albert Visser

*(September 12th, 2006)*