Philipp Furtwängler (April 21, 1869, Elze, Germany – May 19, 1940, Vienna, Austria) was a German number theorist.
He wrote an 1896 doctoral dissertation at the University of Göttingen on cubic forms (Zur Theorie der in Linearfaktoren zerlegbaren ganzzahlingen 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. He was paralysed, and taught from a wheelchair. Some of his students were Henry Mann, Otto Schreier, and Olga Taussky-Todd.
He is now best known for his contribution to the principal ideal theorem.