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.

From 1916, Furtwängler became increasingly paralysed[1] and, without notes, lectured from a wheelchair while his assistant wrote equations on the blackboard.

[2] Some of Furtwängler's doctoral students were Wolfgang Gröbner, Nikolaus Hofreiter, Henry Mann, Otto Schreier, and Olga Taussky-Todd.

[3] 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).