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\noindent{\bf Emil Julius GUMBEL}\\
b. 18 July 1891 - d. 10 September 1966
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{\bf Summary.} In spite of a scientific career disrupted by exile (to France in
1932, then to the United States in 1940) the German-born pacifist E.J. Gumbel
was the principal
architect of the statistical theory of extreme values.
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Emil Julius Gumbel was born in Munich (M\"unchen), Germany,
into a family of Jewish origin thoroughly assimilated into the Bavarian
middle class and aristocracy. He was a student at the prestigious
Kaiser-Wilhelms-Gymnasium where he graduated with his Abitur in July 1910.
He then pursued his studies in mathematics and political economy at the
Ludwig-Maximilian University in Munich. He specialized in statistics and
obtained an actuarial diploma in February 1913. For the following two
semesters (summer 1913 and winter 1913/14) he worked as Georg von Mayr's (q.v.)
assistant in his statistical and actuarial seminar, and he
was then put in charge
of tutorials in mathematical statistics. At the same time, Gumbel
wrote his thesis under von Mayr, and on 24 July 1914, he received his
doctorate in political economy with the highest grading. His thesis,
{\it Die Berechnung des Bev\"{o}lkerungsstandes durch Interpolation}
appeared in 1916 in the supplements of E. Roesle's periodical
{\it Archiv f\"{u}r soziale Hygiene und Demographie}.
Meanwhile, war had broken out and Gumbel, like many of his German
contemporaries, threw himself passionately into it. Enrolled early as
a volunteer, he rapidly became aware and disillusioned by the deceptions
perpetrated in the name of German imperial power. Before he could venture
onto the battlefield, Gumbel was initially exempted for reasons of health,
and later, at the beginning of 1916, permanently excused from military
service. In the meantime, he had installed himself in Berlin, where
he worked in the Civil Service as an engineer in
aeronautical workshops, and later at Telefunken, while militantly active as a
pacifist, and again taking up studies (in physics) at Humboldt
University. He there came in contact with Albert Einstein
and Ladislaus von Bortkiewicz (q.v.) at
the university and with Einstein also in the pacifist league {\it Bund Neues
Vaterland}.
Bortkiewicz, who was to give a decisive orientation to
the career and statistical work of Gumbel, had succeeded Wilhelm
Lexis (q.v.) as leader of the Continental Statistical School. Bortkiewicz and
Lexis had views opposed to those of Georg von Mayr ,
who was reluctant to use the
calculus of probabilities in dealing with statistical data.
By the end of the first world war, Gumbel had devoted his main efforts to
the political struggle. He had placed his statistical expertise
at the service of the pacifist and anti-nationalist cause, publishing
pamphlets and enquiries on the assassinations carried out by the extreme right,
and left largely unpunished by German justice. It was only in 1923
that Gumbel, with Bortkiewicz's help, received his
Habilitation at Heidelberg, becoming a Privatdozent in mathematical
statistics. The hostility of an increasing number of his colleagues
and students to his ideas and his political activity was to
plunge his university career into chaos. He was suspended several times,
leaving Germany for Moscow in 1926 to work on the mathematical archives of
Marx (MEGA project). Despite his nomination as professor extraordinarius,
against the advice of his Faculty, Gumbel was eventually ousted from his
position at Heidelberg on the eve of the Third Reich. He then found refuge
in France,
where he was invited to the Institut Henri Poincar\'e by Emile Borel (q.v.). In
1934 he was welcomed as a foreign assistant at the Institut de Science
Financi\`ere et d'Assurances in Lyon. With the support of Maurice
Fr\'echet (q.v.) he was appointed to the CNRS (The National Council for
Scientific Research)
in 1937. The possibility of a university career in France was not to be
fulfilled, however,
as war broke out again and forced him
into a new exile in the USA, where he remained until his death.
Gumbel's support of Bortkiewicz's ideas became more apparent in the 1920's
and 1930's.
The most notable example of this is
a work published by Gumbel in 1932, {\it Das Zufallsgesetz des Sterbens
(The Statistical Law
Governing Mortality)},
which brought to a close both his research on the
subject and his activities in Germany; a few months later he was forced into
exile. In fact, having spent much effort in rejecting all attempts
to establish as demographic laws empirical mathematical
formulae depending on interpolation, or on theoretically dubious fitted curves,
Gumbel found himself defending the paradoxical idea of a
mathematical law relating mortality to age. Its probabilistic nature
revealed his debt to Bortkiewicz. It was essentially based on work of Lexis:
who had adjusted
mortality tables using a Gaussian distribution for those ages
considered to be beyond normal.
Gumbel extended the formula to the
entire table, by considering as variables not the age at death,
but the life expectancy at each age. He was then able to enunciate
his probabilistic principle as ``Unser Leben ist in Gottes Hand,[...]
Das Schicksal zieht ein schwarzes Los aus der Urnen der Lebendigen. (Our
life is in God's hand
[...] Destiny draws a black ball from the ballot-boxes of those living."
The statistics of mortality could then be treated as analogous
to an urn model, a model which was then considered
to be the basis of the calculus of probabilities (as in K. Pearson's (q.v.)
curves
or ``Laws"). Hence the word ``Gesetz (Law)" in the title of Gumbel's work,
which is an
allusion to the famous {\it Das Gesetz der kleinen Zahlen} (1898)
of Bortkiewicz.
Gumbel's French period is arguably his most fertile one, with his
scientific activities hardly affected by political harassment. During
the 1930's he remained an active militant anti-Nazi, together with
other exiled intellectuals. When he came to France, he brought with him
a new idea, that of extreme values,
which was to occupy his thoughts for the rest of his
life and ensure his enduring renown. Certain formulas
of fit, for example those of de Moivre (q.v.) and Wittstein,
consider a survival
table as stopping at the age at which no further survivors remain.
Around 1930, the Danish mathematician Steffensen rekindled
discussion on the topic by pointing out the difficulties of such a hypothesis,
in that statistical distributions most used by actuaries,
among them mainly those of Gompertz-Makeham, and of Gauss-Lexis, only
tend to zero asymptotically. Gumbel's innovation consisted in the
redefinition of the limiting age, on the basis of the calculus of
probabilities. He introduced a new random variable, the ``oldest age"
of a generation, whose mode was to be called ``final age" and whose expectation
only designated the ``limiting age".
The new distribution differs in general from that describing the population.
By approximating the size of the population, the distribution of
the maximum age may be modelled by one of the asymptotic laws of
extreme values. Having used his ideas on different tables, Gumbel
collected his contributions in a 1937 monograph of the series in mathematical
statistics edited by G. Darmois (q.v.) entitled {\it La dur\'ee
extr\^eme de la vie humaine}.
In developing his ``theory of the maximum value",
Gumbel rediscovered, extended and correlated several publications
on extremes carried out at the
turn of the century by various authors who were apparently unaware of each
other's work.
Some belonged to the Continental School such as Bortkiewicz and
R. von Mises (q.v.),
to whom one might add the Pole Jerzy Neyman (q.v.), and the American E.L. Dodd.
Another contingent consisted of British biometricians,
F. Galton (q.v.), K. Pearson, L.H.C. Tippett and
R.A. Fisher (q.v.). Finally, the
Frenchmen J. Bertrand (q.v.), J. Haag, and especially M. Fr\'echet and the
Italian B.de Finetti also made substantial contributions to
the extreme value problem. The theoretical structure was completed
in 1943 with the statement and proof of the theorem on the limit
of extremes, in central limit style, by B.V. Gnedenko,
There are only three kinds
of limit laws possible for the maximum value, all characterized by their
``max-stability": the distribution of the maximum value,
apart from a change of scale and unit, remains the same as that of the sample
from which it comes. This relates the statistical theory
of extremes to that of the addition of random variables, as for example
in Paul L\'evy's work. One of the three limiting distributions had
been found by M. Fr\'echet in 1926. The second was named after Weibull
(1887-1979),
a Swedish engineer , who applied it to problems of
confidence from the mid 1930's. Finally, Gumbel stressed the
theoretical and practical interest of the last distribution,
which was logically
given his name. This, apart from a change of scale, has distribution function
$G(x) = exp(exp(-x)), x \geq 0 $.
Gumbel, by his interdisciplinary and transnational skills, his
polyglot abilities, and his applied mathematician's flair, was able to
bring to light and exploit a body of theoretical work and prove its
practical use by applying his results to several areas.
The first was demography, followed by cases of radioactivity in collaboration
with the Curies,
and finally and most importantly the fields
of hydrology and meteorology. From 1937 on, first in France and after 1940
in the USA, he became an expert forecaster of river floods, and later
of their drought levels, and other
extreme climatic phenomena.
Unable to find a university position in the USA, Gumbel acted as a
consultant to different government organizations, even including
NATO. It was only in 1953 that he was appointed to a chair at Columbia
University. He was also elected to the membership of the ISI, with
the support of M. Fr\'echet among others.
His contributions are summarized in his book {\it Statistics of Extremes}.
This was published in New York in 1958 and is the first treatise devoted
entirely to this field. It was widely disseminated, mainly to engineers,
with further editions in 1960 and up to 1979, while a Japanese
translation appeared in 1963 and a Russian edition under the direction
of Gnedenko in 1965.
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\begin{thebibliography}{3}
\bibitem{1} Gumbel, E. J.(1922). {\it Vier Jahre politischer Mord}. Verlag der
Neuen Gesellschaften, Berlin.
\bibitem{2} Gumbel, E. J.(1932). Das Zufallsgesetz des Sterbens.{\it
Erg\"{a}nzungshefte zum Deutschen Statistischen Zentralblatt}, Heft 12,
66 pp, Leipzig \& Berlin.
\bibitem{3} Gumbel, E. J.(1958). {\it Statistics of Extremes}. 375 pp, Columbia
University Press, New York.
\bibitem{4} Hertz, S. (1997). {\it Emil Julius Gumbel (1891-1966) et la
statistique des extr\^emes}. Th\`ese de doctorat (dir. P. Cr\'epel),
Universit\'e de Lyon-1.
\bibitem{5} Jansen, C. (1991). {\it Emil Julius Gumbel. Portrait eines
Zivilisten.}
Wunderhorn, Heidelberg.
\bibitem{6} Vogt, Annette (1991). {\it Emil Julius Gumbel. Auf der Suche nach
Wahrheit.}
Dietz, Berlin.
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\hfill{S\'ebastien Hertz}
\end{thebibliography}
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