Eduard Stiefel
Encyclopedia
Eduard L. Stiefel was a Swiss
mathematician
. Together with Cornelius Lanczos
and Magnus Hestenes
, he invented the conjugate gradient method
, and gave what is now understood to be a partial construction of the Stiefel–Whitney class
es of a real vector bundle, thus co-founding the study of characteristic classes.
Stiefel entered the Swiss Federal Institute of Technology
in 1928. He received his Ph.D. in 1935 under Heinz Hopf
; his dissertation was titled "Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten". Stiefel completed his habilitation
in 1942. Besides his academic pursuits, Stiefel was also active as a military officer, rising to the rank of colonel in the Swiss army during World War II
.
Stiefel achieved his full professorship at ETH Zurich
in 1948, the same year he founded the Institute for Applied Mathematics. The objective of the new institute was to design and construct an electronic computer (the Elektronische Rechenmaschine der ETH, or ERMETH). He spent a year in the United States
commencing in August, 1951. During this time, he met Magnus Hestenes and many other scientists at the National Bureau of Standards and these professional associations served him well during the remainder of his career at Zurich
.
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. Together with Cornelius Lanczos
Cornelius Lanczos
Cornelius Lanczos Löwy Kornél was a Hungarian-Jewish mathematician and physicist, who was born on February 2, 1893, and died on June 25, 1974....
and Magnus Hestenes
Magnus Hestenes
Magnus Rudolph Hestenes was an American mathematician. Together with Cornelius Lanczos and Eduard Stiefel, he invented the conjugate gradient method....
, he invented the conjugate gradient method
Conjugate gradient method
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too...
, and gave what is now understood to be a partial construction of the Stiefel–Whitney class
Stiefel–Whitney class
In mathematics, in particular in algebraic topology and differential geometry, the Stiefel–Whitney class is an example of a \mathbb Z_2characteristic class associated to real vector bundles.-General presentation:...
es of a real vector bundle, thus co-founding the study of characteristic classes.
Stiefel entered the Swiss Federal Institute of Technology
ETH Zurich
The Swiss Federal Institute of Technology Zurich or ETH Zürich is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland....
in 1928. He received his Ph.D. in 1935 under Heinz Hopf
Heinz Hopf
Heinz Hopf was a German mathematician born in Gräbschen, Germany . He attended Dr. Karl Mittelhaus' higher boys' school from 1901 to 1904, and then entered the König-Wilhelm- Gymnasium in Breslau. He showed mathematical talent from an early age...
; his dissertation was titled "Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten". Stiefel completed his habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
in 1942. Besides his academic pursuits, Stiefel was also active as a military officer, rising to the rank of colonel in the Swiss army during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
.
Stiefel achieved his full professorship at ETH Zurich
ETH Zurich
The Swiss Federal Institute of Technology Zurich or ETH Zürich is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland....
in 1948, the same year he founded the Institute for Applied Mathematics. The objective of the new institute was to design and construct an electronic computer (the Elektronische Rechenmaschine der ETH, or ERMETH). He spent a year in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
commencing in August, 1951. During this time, he met Magnus Hestenes and many other scientists at the National Bureau of Standards and these professional associations served him well during the remainder of his career at Zurich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
.