Logician and proposer of Löb's theorem
Martin Löb, who has died in Holland aged 85, was a central figure in the early development of mathematical logic in Britain. He was a man of strong intellect who, as a teenage refugee from Nazi rule, overcame the violent disruptions of wartime and, against the odds, established a distinguished academic career.
After a boyhood in Berlin, Löb escaped to England just before the on-set of the second world war. However, 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 camp was exposed to sandstorms and high temperatures, but, in this unlikely 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 Melbourne University).
It was three years before Löb was able to return to the UK, after the British government acknowledged its mistake in enforcing the internments. As the war ended, he was accepted for a London University degree as well as obtaining a teaching post in a boarding school. A research studentship was advertised to work under RL Goodstein at Leicester, and Löb got it. His PhD followed and, by 1951, at the age of 30, he was an assistant lecturer at Leeds University. He stayed for 20 fruitful years, becoming reader and then professor of mathematical logic, before accepting a chair (previously held by Evert Beth) at the University of Amsterdam in the early 1970s, 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 Alonzo Church and Alfred Tarski from the US, seminar dinners at Whitelock's pub, and the European Society (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 a few such in Britain. 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, making fundamental contributions to each of those areas, but it is Löb's theorem (1955) for which he is best known. Kurt 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 Leon 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.
Löb was an intensely private, cultured and quietly strong-willed person, devoted to his Dutch wife Caroline, who predeceased him, and their daughters Maryke and Stefani. After his retirement from Amsterdam, they moved to a quiet spot in the north of Holland, where he stayed until his death.
Löb valued his students highly and was concerned as much for their welfare as their academic progress. Two of them now head the departments where he worked. He was a profound and dedicated logician and teacher, and a man of great inner strength and integrity.
Martin Hugo Löb, mathematical logician, born March 31 1921; died August 21 2006
3 Oct 2006 © Guardian Newspapers Limited 2006