|Died||May 19, 1940 (aged 71)|
|Known for||Principal ideal theorem|
|Doctoral advisor||Felix Klein|
|Doctoral students||Wolfgang Gröbner, Nikolaus Hofreiter, Henry Mann, Otto Schreier, Olga Taussky-Todd|
Friederich Pius Philipp Furtwängler (April 21, 1869 – May 19, 1940) was a German number theorist.
Furtwängler wrote an 1896 doctoral dissertation at the University of Göttingen on cubic forms (Zur Theorie der in Linearfaktoren zerlegbaren ganzzahligen ternären kubischen Formen), under Felix Klein. Most of his academic life, from 1912 to 1938, was spent at the University of Vienna, where he taught for example Kurt Gödel, who later said that Furtwängler's lectures on number theory were the best mathematical lectures that he ever heard; Gödel had originally intended to become a physicist but turned to mathematics partly as a result of Furtwängler's lectures. From 1916, Furtwängler became increasingly paralysed and, without notes, lectured from a wheelchair while his assistant wrote equations on the blackboard.
Some of Furtwängler's doctoral students were Wolfgang Gröbner, Nikolaus Hofreiter, Henry Mann, Otto Schreier, and Olga Taussky-Todd. Through these and others, he has over 3000 academic descendants.
He is now best known for his contribution to the principal ideal theorem in the form of his Beweis des Hauptidealsatzes für Klassenkörper algebraischer Zahlkörper (1929).
- with Helmut Hasse and W. Jehne: Allgemeine Theorie der algebraischen Zahlen. Vol. 8. Teubner, 1953.
- Eisenstein reciprocity
- Hilbert class field
- Keller's conjecture
- Kummer–Vandiver conjecture
- Principalization (algebra)
- Moore, Gregory (Sep–Oct 2005). "The Incomplete Gödel". American Scientist. 93 (5): 464. doi:10.1511/2005.55.464.
- Philipp Furtwängler at the Mathematics Genealogy Project
- Furtwängler family tree
- Whaples, George (1956). "Review of Allgemeine Theorie der algebraischen Zahlen by Ph. Furtwängler. Reworked by H. Hasse and W. Jehne". Bull. Amer. Math. Soc. 62: 73. doi:10.1090/S0002-9904-1956-09988-4.
- "Österreichisches Biographisches Lexikon 1815–1950 (ÖBL). Vol. 1, Austrian Academy of Sciences, Vienna 1957, p. 383. ". In:
- Nikolaus Hofreiter (1961), "Furtwängler, Friedrich Pius Philipp", Neue Deutsche Biographie (in German), vol. 5, Berlin: Duncker & Humblot, pp. 740–740