# History of Stochastics in Göttingen and Obituary Konrad Jacobs

Stochastics, the branch of mathematics dealing with random events including statistics, probability theory, actuarial theory, econometrics and biometrics, has a long and distinguished tradition in Göttingen.

The term "statistics" originated in Göttingen when the political scientist **Gottfried Achenwall** (1723-1762) delivered a lecture entitled "Notitia politica vulgo statistica" (from italian statista = statesman).

In 1750, **Johann Tobias Mayer** (1723-1762) published the groundbreaking paper "Treatise on the Libration of the Moon about its Axis and the Apparent Motion of the Lunar Macula", which introduced a new method for handling astronomical data. Since more data had been observed than was necessary for computing the orbital parameters, he explained the different results obtained by using different choices of subsets of the data in the computation by additional error terms. He then calculated the final result as an average of the results obtained for the various subsets, and this technique was an important precursor of the least squares method. Tobias Mayer held the chair of astronomy in Göttingen from 1751 until his death.

In 1805, the French mathematician and astronomer **Adrien Marie Legendre** (1752-1833) published the "Method of Least Squares". For him, this method was an expedient ad hoc rule. In 1809, **Carl Friedrich Gauss** (1777-1855) published his astronomy masterpiece "Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium". Gauss had been professor of astronomy and director of the new astronomical observatory in Göttingen since 1807. In this paper, Gauss gave the first scientific justification of the method of least squares, using a maximum likelihood argument, which in turn led him to a new derivation of the normal distribution and the first application of this distribution to real data. (De Moivre had already obtained the normal distribution as a limit of normalized binomial distributions in 1733.) In the 1809 paper, Gauss also precipitated a priority dispute when he mentioned that he had been using the method of least squares regularly since 1795. (There is little doubt now that Gauss actually used the method of least squares several years before 1805; there are prominent witnesses, remarks in his mathematical diary, and traces in his earlier publications.)

In his series of papers "Theoria Combinationis Observationum Erroribus Minimae Obnoxiae I-III" (1821-1828), Gauss created his theory of random errors. He introduced the mean quadratic error and an estimate of the variance. Using his theorem (often mistakenly called theorem of Gauss-Markov), he derived the law of propagation of errors, and gave a better justification of the least squares method through minimization of the mean square error.

Gauss also made important contributions to the foundations of actuarial mathematics. When the Relief Fund for Widows and Orphans of Göttingen Professors, founded in 1739, ran into considerable financial problems, Gauss drafted an official report in which, for the first time ever, the calculation of insurance premiums were based on mortality rates and probability calculus.

The development of statistics in Germany in the second half of the nineteenth century was considerably influenced by the political economist **Wilhelm Lexis** (1837-1914), who studied the stability and homogeneity of series of observations of mass phenomena, and whose name lives on in the term "Lexis dispersion coefficient". The most famous of his students, **Ladislaus von Bortkiewicz** (1868-1931), played a significant role in the development of probability theory. He demonstrated the importance of the Poisson distribution using real life examples in his book "The Law of Small Numbers", and initiated the study of Poisson processes during his research on radioactive emissions.

On the first of October 1895, the first German institute of insurance science was founded at the University of Göttingen, as a result of joint efforts of **Felix Klein** (1849-1825) and his fellow student **Ludwig Kiepert** (1846-1934), who was then chairman of the Prussian Civil Service Association (today called Hannover Life Insurance).This was the first institute in Germany in which a curriculum in actuarial mathematics, insurance law, and insurance economics was offered. Successful studies led to the degree “Versicherungsverständiger” (insurance expert). The institute was divided into a mathematical section and an administrative section, and its first chairman was Wilhelm Lexis.

**Georg Bohlmann** (1869-1928), supported by Felix Klein, was appointed as the first lecturer of the new institute, and gave courses on actuarial mathematics. In an article for an encyclopedia of mathematics edited by Felix Klein in 1900, Bohlmann suggested an axiomatization of probability theory partly resembling the later axiomatization by Kolmogorov in 1933. He also was the first to give a formal definition of independence of events, the definition still in use. In 1903, Bohlmann accepted an offer to serve as head mathematician of the German branch of the New York Mutual Life Insurance Co. At that time, the astronomer **Martin Brendel** (1862-1939), succeeded in 1907 by **Felix Bernstein** (1878-1956), a former PhD-student of Hilbert, took over the lectures in actuarial mathematics. Numerous graduates of the new institute soon started playing a leading role in German insurance companies, and it served as a model for similar institutes founded in the subsequent years at other German universities.

Bernstein, already well known for his work in set theory (which is still used today), soon focused much of his attention on actuarial science and human genetics. During the First World War, he ran courses on actuarial theory for retraining disabled veteran officers. He was chief designer of the “German Savings Premium Loan” issued in 1919, and served as Loan Commissioner of the Reich under Minister of Finance Erzberger (1921). His clarification of the heredity of the ABO-blood groups brought him international renown even in nonmathematical circles. In 1918, the mathematical section of the Institute of Actuarial Science was transformed into the Institute for Mathematical Statistics and Actuarial Theory (now called Institute for Mathematical Stochastics). Bernstein was appointed chairman, and through Hilbert’s efforts, was offered a full professorship in 1921. In 1933, Bernstein became an early victim of the persecution of Jews, and after his dismissal, he decided not to return to Göttingen after a scientific trip to the USA. In 1949, he was appointed Professor Emeritus in Göttingen.

**Hans Georg Muenzner** (1906-1997), a student of Bernstein, was director of the Institute from the time of his habilitation (1937) up until his appointment as professor in Berlin (1956).He regularly offered courses in statistics and actuarial mathematics.

In 1958, **Konrad Jacobs** took over the administration of the Institute, first as lecturer (Dozent), and then – after a call in 1959 from another university – as Full Professor. He worked in game theory, ergodic theory and information theory, and his demanding and superbly organized lectures attracted many talented students. He encouraged his many doctoral students to spend several years abroad to study in leading foreign universities, and in 1965, he accepted a call from Erlangen. Most of his PhD-students became professors in Germany or abroad.

**Georg Reichel**, the head mathematician of the Gothaer Insurance Co, offered lectures and seminars in the Institute between 1962 and his retirement in 1985. He guided many students, and his work was continued by **Hans-Jochen Bartels** and **Catherine Pallenberg**.

In 1971, **Ulrich Krengel** was appointed Full Professor and Director of the Institute, succeeding his teacher Konrad Jacobs. Since the importance of the field of stochastics was now much better recognized, two additional professorships were created, and these have been held from the seventies by **Manfred Denker** and **Heinrich Hering** (until 2005). In addition, **Edgar Brunner**, professor of medical statistics, offers Institute lectures, seminars and practical courses on applied statistics, and visiting professors from abroad add a variety of courses.

Since 1985, the Mathematics Faculty of the University of Göttingen offers a curriculum in “Wirtschaftsmathematik” (business mathematics). The Institute for Mathematical Stochastics has the primary responsibility for this curriculum, which includes courses on practical applications of statistics.

In 2002, Ulrich Krengel became Professor Emeritus, succeeded by **Axel Munk**. The main activities of the Institute shifted to practically-oriented statistics, to research funded by non-university sponsors and to training of students with computers. In 2001, the Center of Statistics was established, which unites seven faculties offering diverse courses in various branches of statistics. This new Center, founded and directed by Manfred Denker, offers a PhD-curriculum in “Applied Statistics and Empirical Methods”. In addition, since 2004, a graduate school “Identification in Mathematical Models” has offered joint programs with the Institute for Numerical and Applied Mathematics.

(T. P. Hill and U. Krengel)

**The contemporary/Present-day Institute for Mathematical Stochastics**

In October 2006 **Martin Schlather **succeeded Heinrich Hering. His main activities are in the field of spatial stochastics, computer statistics and extreme value theory. He also succeeded Manfred Denker as speaker of the Center for Statistics.

Since 2003 the IMS takes part in the Graduate School 1023 “Identification in Mathematical Models: Synergy of Stochastic and Numerical Methods”. Furthermore the IMS participates in the Collaborative Research Center “Nanoscale Photonic Imaging” since October 2007 and in the Collaborative Research Center 803 “Functionality Controlled by Organization in and between Membranes” since January 2009. In April 2008 the (binational) German-Swiss Research Group FOR 916 “Statistical Regularization and Qualitative Constraints” has been established at the IMS. Since 2010 the IMS is engaged in the Graduate School 1644 “Scaling Problems in Statistics”.

The Institute moved to the North Campus of the University in the summer of 2008.

**Jeanette Woerner**, who held the position of a Junior professor for Mathematical Statistic at the IMS from 2003 until 2008, accepted the offer for professorship for Stochastics at the TU Dortmund in October 2008. She was succeeded by **Ulrike Schneider **in 2009. In October 2009 **Anja Sturm** accepted the offer for the professorship “Stochastics and its Applications”.

Since October 2011 **Ulrike Schneider** is a professor at the University of Vienna. Her successor is **Andrea Krajina** since April 2012.

Ulrich Krengel und Axel Munk

(08. Mai 2012)

# Obituary Konrad Jacobs (1928-2015)

Obituary Konrad Jacobs (Short version)

A more detailed obituary was published in Jahresbericht der Deutschen Mathematiker-Vereinigung 2017.

(Eberlein, E., Föllmer, H., Keane, M., Krengel, U. and Strassen, V., *Konrad Jacobs (1928-2015)*, Jahresber Dtsch Math-Ver, DOI 10.1365/s13291-017-0159-4).