# Georg Alexander Pick

### Quick Info

Vienna , Austria

Theresienstadt, Bohemia, now Czech Republic

**Georg Pick**was an Austrian mathematician best known for his formula on the area of a polygon in a lattice of points.

### Biography

**Georg Pick**was born into a Jewish family. His mother was Josefa Schleisinger and his father was Adolf Josef Pick, the head of a private institute. Georg was educated at home by his father up to the age of eleven when he entered the fourth class of the Leopoldstaedter Communal Gymnasium. He sat his school leaving examinations in 1875 which qualified him for university entrance.

Pick entered the University of Vienna in 1875. He published a mathematics paper in the following year when only seventeen years old. He studied mathematics and physics, graduating in 1879 with a qualification which would allow him to teach both of these subjects. In 1877 Leo Königsberger had moved from Technische Hochschule in Dresden to take up a chair at the University of Vienna. He became Pick's supervisor and, on 16 April 1880, Pick was awarded his doctorate for his dissertation

*Über eine Klasse abelscher Integrale*Ⓣ. Emil Weyr had been appointed as second examiner of the thesis.

After the award of his doctorate, Pick was appointed as an assistant to Ernest Mach at the Karl-Ferdinand University in Prague. Mach had moved from Graz, where he was professor of mathematics, to Prague in 1867 to take up the chair of physics there. He, like Pick, had studied at the University of Vienna and, by the time Pick became his assistant, he was regarded as one of the leading scientists in Europe. Pick now aimed at becoming a lecturer in Prague and in order to obtain the right to lecture he had to write an habilitation thesis. This he did quite quickly and received the right to lecture in Prague in 1881 with his habilitation thesis

*Über die Integration hyperelliptischer Differentiale durch Logarithmen*Ⓣ.

Except for the academic year 1884-85 which Pick spent studying under Klein at the University of Leipzig, he remained in Prague for the rest of his career. He was promoted to extraordinary professor of mathematics in 1888, then he was appointed as ordinary professor (full professor) in 1892 at the German University of Prague. His mathematical work was extremely broad and his 67 papers range across many topics such as linear algebra, invariant theory, integral calculus, potential theory, functional analysis, and geometry. However more than half of his papers were on functions of a complex variable, differential equations, and differential geometry. Terms such as 'Pick matrices', 'Pick-Nevanlinna interpolation', and the 'Schwarz-Pick lemma' are sometimes used today. He is best remembered, however, for Pick's theorem which appeared in his eight page paper of 1899

*Geometrisches zur Zahlenlehre*Ⓣ published in Prague in

*Sitzungber. Lotos, Naturwissen Zeitschrift*.

Pick's theorem is on reticular geometry. The plane becomes a lattice on setting up two systems of parallel equally spaced straight lines in the plane. These Pick calls the 'main reticular lines' and their points of intersection are called 'reticular points'. A line joining any two reticular points is called a 'reticular line'. Notice that the main reticular lines are reticular lines but there are many other reticular lines. A polygon whose edges are reticular lines Pick calls a reticular polygon. Pick's theorem states that the area of a reticular polygon is $L + \large\frac{1}{2}\normalsize B - 1$ where $L$ is the number of reticular points inside the polygon and $B$ is the number of reticular points on the edges of the polygon. The result did not receive much attention after Pick published it, but in 1969 Steinhaus included it in his famous book

*Mathematical Snapshots*. From that time on Pick's theorem has attracted much attention and admiration for its simplicity and elegance.

At the German University of Prague Pick became dean of the philosophy faculty in 1900-01. He supervised about 20 students for their doctorates, the most famous being Charles Loewner who worked under Pick's supervision and was awarded his doctorate for his thesis on geometric function theory in 1917. There is another aspect of Pick's life which merits attention. In 1910 he was on a committee set up by the German University of Prague to consider appointing Einstein to the university. Pick was the driving force behind the appointment and Einstein was appointed to a chair of mathematical physics at the German University of Prague in 1911. He held this post until 1913 and during these years the two were close friends. Not only did they share scientific interests, but they also shared a passionate interest in music. Pick, who played in a quartet, introduced Einstein into the scientific and musical societies of Prague. In fact Pick's quartet consisted of four professors from the university including Camillo Körner, the professor of mechanical engineering.

After Pick retired in 1927 he was named professor emeritus and returned to Vienna, the town of his birth. However, in 1938 he returned to Prague after the Anschluss on 12 March when German troops marched into Austria. At the end of September 1938 the Prague government was asked to give Germany all districts of Bohemia and Moravia with populations that were 50 percent or more German. The leaders of Czechoslovakia resigned rather than agree, but those who took over gave the regions to Germany. Hitler's armies invaded on 14 March 1939 and Hitler installed his representative in Prague to run the country. Pick had been elected as a member of the Czech Academy of Sciences and Arts, but after the Nazis took over Prague, Pick was excluded from the Academy. The Nazis set up a camp at Theresienstadt in Nordboehmen on 24 November 1941 to house elderly, privileged, and famous Jews. Of around 144,000 Jews sent to Theresienstadt about a quarter died there and around 60% were sent on to Auschwitz or other death camps. Pick was sent to Theresienstadt on 13 July 1942 and he died there two weeks later aged 82.

He was described as follows:-

Pick was a bachelor ... uncommonly correct in clothes and attitude.

### References (show)

- B Fritzsche and B Kirstein (eds.), G Herglotz, I Schur, G Pick, R Nevanlinna and H Weyl,
*Ausgewählte Arbeiten zu den Ursprüngen der Schur-Analysis, Gewidmet dem grossen Mathematiker Issai Schur (1875-1941),*Teubner-Archiv zur Mathematik**16**(B. G. Teubner Verlagsgesellschaft mbH, Stuttgart, 1991). - R Fritsch, Georg Pick und Ludwig Berwald - zwei Mathematiker an der Deutschen Universität in Prag,
*Schr. Sudet.dtsch. Akad. Wiss. Künste Forsch.beitr. Nat.wiss. Kl.***22**(2001), 9-16.

### Additional Resources (show)

Other websites about Georg Pick:

Written by J J O'Connor and E F Robertson

Last Update August 2005

Last Update August 2005