His father Franz Sommerfeld (1820–1906) was a physician from a leading family in Königsberg, where Arnold's grandfather had resettled from the hinterland in 1822 for a career as Court Postal Secretary in the service of the Kingdom of Prussia.

[3][4][5] Sommerfeld studied mathematics and physical sciences at the Albertina University of his native city, Königsberg, East Prussia.

With his turned up moustache, his physical build, his Prussian bearing, and the fencing scar on his face, he gave the impression of being a colonel in the hussars.

In October 1897 Sommerfeld began the appointment to the Chair of Mathematics at the Bergakademie in Clausthal-Zellerfeld; he was successor to Wilhelm Wien.

[7][8][10] At Klein's request, Sommerfeld took on the position of editor of Volume V of Enzyklopädie der mathematischen Wissenschaften; it was a major undertaking which lasted from 1898 to 1926.

Later, at the University of Munich, Sommerfeld's students Ludwig Hopf and Werner Heisenberg would write their Ph.D. theses on this topic.

[7][8][10][13] For his contributions to the understanding of journal bearing lubrication during his time at Aachen, he was named as one of the 23 "Men of Tribology" by Duncan Dowson.

He was selected for these positions by Wilhelm Röntgen, Director of the Physics Institute at Munich,[17] which was looked upon by Sommerfeld as being called to a "privileged sphere of action".

During his 32 years of teaching at Munich, Sommerfeld taught general and specialized courses, as well as holding seminars and colloquia.

[19] For the seminar and colloquium periods, students were assigned papers from the current literature and they then prepared an oral presentation.

[20] Four of Sommerfeld's doctoral students,[21] Werner Heisenberg, Wolfgang Pauli, Peter Debye, and Hans Bethe went on to win Nobel Prizes, while others, most notably, Walter Heitler, Rudolf Peierls,[22] Karl Bechert, Hermann Brück, Paul Peter Ewald, Eugene Feenberg,[23] Herbert Fröhlich, Erwin Fues, Ernst Guillemin, Helmut Hönl, Ludwig Hopf, Adolf Kratzer, Otto Laporte, Wilhelm Lenz, Karl Meissner,[24] Rudolf Seeliger, Ernst C. Stückelberg, Heinrich Welker, Gregor Wentzel, Alfred Landé, and Léon Brillouin[25] became famous in their own right.

Three of Sommerfeld's postdoctoral supervisees, Linus Pauling,[26] Isidor I. Rabi[27] and Max von Laue,[28] won Nobel Prizes, and ten others, William Allis,[29] Edward Condon,[30] Carl Eckart,[31] Edwin C. Kemble,[32] William V. Houston,[33] Karl Herzfeld,[34] Walther Kossel, Philip M. Morse,[35][36] Howard Robertson,[37] and Wojciech Rubinowicz[38] went on to become famous in their own right.

Sommerfeld owned an alpine ski hut to which students were often invited for discussions of physics as demanding as the sport.

Since any reputable scientist could have their article published without refereeing, time between submission and publication was very rapid – as fast as two weeks.

[45] In the winter semester of 1922/1923, Sommerfeld gave the Carl Schurz Memorial Professor of Physics lectures at the University of Wisconsin–Madison.

For example, he proposed a solution to the problem of a radiating hertzian dipole over a conducting earth, which over the years led to many applications.

The process was lengthy due to academic and political differences between the Munich Faculty's selection and that of both the Reichserziehungsministerium (REM; Reich Education Ministry) and the supporters of Deutsche Physik,[48][49] which was anti-Semitic and had a bias against theoretical physics, especially including quantum mechanics.

The appointment of Wilhelm Müller – who was not a theoretical physicist, had not published in a physics journal, and was not a member of the Deutsche Physikalische Gesellschaft[50] – as a replacement for Sommerfeld, was considered such a travesty and detrimental to educating a new generation of physicists that both Ludwig Prandtl, director of the Kaiser Wilhelm Institut für Strömungsforschung (Kaiser Wilhelm Institute for Flow Research), and Carl Ramsauer, director of the research division of the Allgemeine Elektrizitäts-Gesellschaft (General Electric Company) and president of the Deutsche Physikalische Gesellschaft, made reference to this in their correspondence to officials in the Reich.