
Martin Löb, Amsterdam,
14 November 1978

On Monday August 28th 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):
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,
has 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. 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, a town exposed to
sandstorms and high temperatures. In this unlikely and inhospitable
place he began, aged 19, to learn advanced mathematics at the "camp
university" set up by older academic internees. His teacher Felix
Behrend later became a senior professor at the University of Melbourne.
In the following year, when the British Government acknowledged its
"deplorable mistake" in enforcing their internment, Löb and many others
were freed to make the return journey (which was not without incident
 the ship was torpedoed but suffered only slight damage). He worked
on a farm and when the war ended, took a degree at London and began
school teaching. At this point 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 at the University of Amsterdam where
he remained until retirement. This was an exciting period for the foundations
of mathematics and Löb worked hard 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,
and the seminar dinners at Whitelock's pub. 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 selfreferential 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. (WhereasGödel'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 person, devoted
to his Dutch wife Caroline and their daughters Marijke and Stephanie.
After his retirement from Amsterdam they moved to a quiet spot in
the north of Holland where he remained until his death, Caroline having
predeceased him. His students remember him with great affection,
as a profound teacher and a man of the highest 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 postrevolutionary 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 student 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/logicprovability/,
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)
