Philipp Furtwängler was a German

Germany

Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

 number theorist.

He wrote an 1896 doctoral dissertation at the University of Göttingen on cubic form

Cubic form

In mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form.In , Boris Delone and Dmitriĭ Faddeev showed that binary cubic forms with integer coefficients can be used to parametrize orders in cubic fields...

s (Zur Theorie der in Linearfaktoren zerlegbaren ganzzahlingen ternären kubischen Formen), under Felix Klein

Felix Klein

Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...

. Most of his academic life, from 1912 to 1938, was spent at the University of Vienna

University of Vienna

The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...

, where he taught for example Kurt Gödel

Kurt Gödel

Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...

. He was paralysed, and taught from a wheelchair. Some of his students were Henry Mann

Henry Mann

Henry Berthold Mann was a professor of mathematics and statistics at Ohio State University. Mann proved the Schnirelmann-Landau conjecture in number theory, and as a result earned the 1946 Cole Prize. He and his student developed the U-statistic of nonparametric statistics...

, Otto Schreier

Otto Schreier

Otto Schreier was an Austrian mathematician who made major contributions in combinatorial group theory and in the topology of Lie groups. He studied mathematics at the University of Vienna and obtained his doctorate in 1923, under the supervision of Philipp Furtwängler...

, and Olga Taussky-Todd.

He is now best known for his contribution to the principal ideal theorem

Principal ideal theorem

In mathematics, the principal ideal theorem of class field theory, a branch of algebraic number theory, is the statement that for any algebraic number field K and any ideal I of the ring of integers of K, if L is the Hilbert class field of K, thenIO_L\ is a principal ideal αOL, for OL the ring of...

.

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