(b. Ohlau, Silesia, Germany, 2 September 1850; d. Zurich, Switzerland, 25 June 1941)
Pringsheim studied at Berlin and Heidelberg in 1868-1869, received the Ph.D. at Heidelberg in 1872, and qualified as Privatdozent at Munich in 1877. He was appointed extraordinary professor at Munich in 1886 but did not become full professor until 1901. He retired in 1922. Pringsheim was a member of the Bavarian Academy of Sciences.
Pringsheim, who came from a rich family, was a lover and promoter of music and fine arts. In his youth he had been a friend of Richard Wagner; and with his wife, Hedwig Dohm, he made his home into a center of Munich’s social and cultural life. The novelist Thomas Mann, who was his son-in-law, wrote a novel based on the Pringsheim family. Pringsheim’s refined wit was famous. His sprightly Bierrede was the acme of the yearly meeting of the Deutsche Mathematiker-Vereinigung and was mentioned by mathematicians throughout the year. His puns were famous: Once when he was asked about his son, who at that time worked as a physicist under Nernst, he answered “Peter ist in Berlin und lernt da den Nernst der Lebens kennen.”
After 1933 he was subjected to persecution as a “non-Aryan”; Pringsheim was forced to sell his house to the Nazi party, which tore it down to erect a party building. Having been forced to give up his library and to move several times, he was finally allowed to sell his celebrated majolica collection to a London dealer, although he had to surrender the greater part of the proceeds. In 1939 he moved to Zurich, where he died two years later.
In mathematics Pringsheim was the most consequent follower of Weierstrass. His field was pre-Lebesgue real functions and complex functions; his work is characterized by meticulous rigor rather than by great ideas. His best-known discovery concerns power series with positive coefficients; they have a singularity in the intersection of the positive axis and the circle of convergence. His elaboration of the theory of integral transcendental functions was exemplary and influential, and his extremely simple proof of Cauchy’s integral theorem has been generally accepted.
Pringsheim was a brilliant lecturer and conversationalist, but his writings do not reflect this brilliance. This is even true of his celebrated Festrede, a paragon of stylistic and oratorical splendor only for those who had heard him speak. The voluminous edition of his courses is one of the dreariest specimens of epsilontics.
Pringsheim’s writings include Die Grundlagen der modernen Wertlehre: Daniel Bernoulli, Versuch einer neuen Theorie der Wertbestimmung von Glücksfällen, Sammlung Älterer und Neuerer Staatswissenschaftlicher Schriflcn, no. 9 (Leipzig, 1896); “Grundlagen der allgemeinen Funktionenthcorie,” in Encyklopädie der mathematischen Wissenscheften, II, pt. 1, fuse. 1 (1899), 1-52; “Über den Goursafschen Beweis des Cauchy’schen Integralsaizes,“in Transactions of the American Mathematical Society, 2 (1901), 413-421; “Elemeniare Theorie der ganzen transcendenten Funktionen von endlichcr Ordnung,” in Mathematische Annalen, 58 (1904), 257-342; “Über Wert und angeblichen Unwert der Mathematik,” in Jahresbericht der Deutschen Mathematiker-Vereinigung, 13 (1904), 357-382; “Algebraische Analysis,” in Encyklopädie der mathematischen Wissenschaften, II, pt. 3, fasc. (1908), 1-46; “Table genéralé,” in Acta mathematica (1913), 164, with portrait; and Vorlesungen über Zahlen tmd Funktionenlehre, 2 vols, in 5 pts. (Leipzig-Berlin, 1916-1932).
An obituary is O. Perron, “Alfred Pringsheim,” in Jahresbericht der Deutschen Mathematiker- Vereinigung56 (1952), 1-6.