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Ludwig Hopf (23 October 1884 in
Nürnberg Nuremberg (, ; ; in the local East Franconian dialect: ''Nämberch'' ) is the largest city in Franconia, the second-largest city in the German state of Bavaria, and its 544,414 (2023) inhabitants make it the 14th-largest city in Germany. ...
,
Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...
– 23 December 1939 in
Dublin Dublin is the capital and largest city of Republic of Ireland, Ireland. Situated on Dublin Bay at the mouth of the River Liffey, it is in the Provinces of Ireland, province of Leinster, and is bordered on the south by the Dublin Mountains, pa ...
) was a German-Jewish theoretical
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
who made contributions to
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
,
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...
,
hydrodynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in ...
, and
aerodynamics Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an ...
. Early in his career he was the assistant to and a collaborator and co-author with
Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
.


Biography

Hopf was born into a family of prominent hops merchants and municipal counselors in Nürnberg, Germany, the son of Elise (née Josephthal) and Hans Hopf. From 1902-1909 he studied math and physics at the Universities of Munich and
Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
. Hopf studied under
Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld (; 5 December 1868 – 26 April 1951) was a German Theoretical physics, theoretical physicist who pioneered developments in Atomic physics, atomic and Quantum mechanics, quantum physics, and also educated and ...
at the
University of Munich The Ludwig Maximilian University of Munich (simply University of Munich, LMU or LMU Munich; ) is a public university, public research university in Munich, Bavaria, Germany. Originally established as the University of Ingolstadt in 1472 by Duke ...
, where he received his Ph.D. in 1909, on the topic of
hydrodynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in ...
. Shortly after this, Sommerfeld introduced Hopf to
Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
at a physics conference in
Salzburg Salzburg is the List of cities and towns in Austria, fourth-largest city in Austria. In 2020 its population was 156,852. The city lies on the Salzach, Salzach River, near the border with Germany and at the foot of the Austrian Alps, Alps moun ...
. Later that year, Einstein, needing an assistant at the
University of Zurich The University of Zurich (UZH, ) is a public university, public research university in Zurich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 from the existing colleges of the ...
, hired Hopf; it was an added bonus that Hopf was a talented pianist, since Einstein played the violin and liked to play duets. Hopf was an ardent fan of
psychoanalysis PsychoanalysisFrom Greek language, Greek: and is a set of theories and techniques of research to discover unconscious mind, unconscious processes and their influence on conscious mind, conscious thought, emotion and behaviour. Based on The Inte ...
, had studied Freud and, once in Zurich, attached himself to Freud's ex-disciple
Carl Jung Carl Gustav Jung ( ; ; 26 July 1875 – 6 June 1961) was a Swiss psychiatrist, psychotherapist, and psychologist who founded the school of analytical psychology. A prolific author of Carl Jung publications, over 20 books, illustrator, and corr ...
. Hopf introduced Einstein to Jung, and Einstein returned to Jung's house several times over the years. In 1910, Hopf collaborated and published with Einstein two papers on classical statistical aspects of radiation. Hopf’s collaboration with Sommerfeld on integral representations of
Bessel Functions Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex ...
resulted in the publication of a paper in 1911. Also in that year, Hopf accompanied Einstein to the Karl-Ferdinand University in Prague; however, he did not stay with Einstein long – due to “unsanitary conditions” in Prague. In 1912, Hopf married Alice Goldschmidt, with whom he had five sons and a daughter. During
World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...
, Hopf contributed to the design of military aircraft. In 1921, he accepted a position at the Rheinisch-Westfälische Technische Hochschule Aachen (RWTH Aachen University), Herbert A. Strauss and Werner Röder (general eds.), International Biographical Dictionary of Central European Emigrés 1933-1945, vol. II / Part 1: A-K, K.G. Saur, München (1983), p 538. a leading technical university in Germany, where he eventually became a professor in
hydrodynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in ...
and
aerodynamics Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an ...
. It was during his tenure at Aachen that he made a contribution to the ''Handbuch der Physik'' and co-authored a “highly esteemed” book on aerodynamics. In 1933, with the Nazis coming to power in Germany, Hopf was put on leave at Aachen due to his being a Jew, and in 1934 lost his position entirely. Hopf remained in Germany until 1939 and escaped the Nazi regime only at the last minute. The SS was seeking to arrest him and were thwarted by his son Arnold posing as his father. Arnold was arrested and sent to the
Buchenwald concentration camp Buchenwald (; 'beech forest') was a German Nazi concentration camp established on Ettersberg hill near Weimar, Nazi Germany, Germany, in July 1937. It was one of the first and the largest of the concentration camps within the Altreich (pre-1938 ...
, from which he was able to escape after 3–4 weeks and emigrate to Kenya. Ludwig left Germany for Great Britain with his wife and three of his children, taking a research position at Cambridge. He moved to Dublin in July 1939 to assume a professorship of mathematics at Trinity College.Moore, 1992, p. 359. Shortly after taking up his duties at Trinity, Hopf became seriously ill and died of thyroid failure on 21 December 1939. At his graveside, Schrödinger called Hopf "a friend to the greatest geniuses of his time," then adding "Indeed, he was one of them." Hopf was first cousins with mathematician
Heinz Hopf Heinz Hopf (19 November 1894 – 3 June 1971) was a German mathematician who worked on the fields of dynamical systems, topology and geometry. Early life and education Hopf was born in Gräbschen, German Empire (now , part of Wrocław, Poland) ...
and first cousins once removed with composer Franz Reizenstein.


Books

*Ludwig Hopf, ''Introduction to the Differential Equations of Physics.'' Translated by Walter Nef. New York:
Dover Publications Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, book ...
, 1948. (originally published by
Walter de Gruyter Walter de Gruyter GmbH, known as De Gruyter (), is a German scholarly publishing house specializing in academic literature. History The roots of the company go back to 1749 when Frederick the Great granted the Königliche Realschule in Be ...
, 1933). *Richard Fuchs and Ludwig Hopf, ''Aerodynamik.'' Nabu Press (2011). (Originally published by Richard Carl Schmidt & Co., 1922) *Ludwig Hopf, ''Die Relativitätstheorie.'' (Springer, 1931)


See also

* Einstein–Hopf Drag


Notes and sources

;Notes ;Sources * Holfter, Gisela and Dickel, Horst (2017). ''An Irish Sanctuary: German-Speaking Refugees in Ireland 1933-1945'' De Gruyter, Oldenburg * Brian, Denis ''Einstein: A Life'' (Wiley, 1996) * Clark, Ronald W. ''Einstein: The Life and Times'' (World, 1971) * * * Moore, Walter ''Schrödinger: Life and Thought'' (Cambridge, 1992) * Pais, Abraham ''’Subtle is the Lord…’ The Science and the Life of Albert Einstein'' (Clarendon, 1982) {{DEFAULTSORT:Hopf, Ludwig 1884 births 1939 deaths 20th-century German physicists Scientists from Nuremberg Academic staff of RWTH Aachen University People dismissed from faculty positions by Nazi Germany Jewish emigrants from Nazi Germany to the United Kingdom Jewish German physicists