Grete Hermann
Encyclopedia
Grete Hermann (* March 2, 1901 in Bremen
, † April 15, 1984 in Bremen
) was a German mathematician
and philosopher. She studied mathematics at Göttingen
under Emmy Noether
, where she achieved her Ph.D. in 1926. Her doctoral thesis, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, published in Mathematische Annalen
, is a foundational paper for computer algebra. It first established the existence of algorithms (including complexity bounds) for many of the basic problems of abstract algebra
, such as ideal
membership for polynomial ring
s. Hermann's algorithm for primary decomposition is still in use now.
As Adolf Hitler
came to power in Germany
, Hermann participated in the underground movement against the Nazis, but by 1936 she left Germany for Denmark
and later England
. She returned when World War II
was over. In her later years she was more interested in politics and philosophy than in physics and mathematics.
As a philosopher, Hermann had a particular interest in the foundations of physics. In 1935 she discovered a flaw in John von Neumann
's purported 1932 proof, which maintained that a hidden variable theory
of quantum mechanics
was impossible. The result went unnoticed by the physics community until it was rediscovered by John Stewart Bell
.
Werner Heisenberg
, in chapter ten of The Part and The Whole
discusses Hermann's work.
Bremen
The City Municipality of Bremen is a Hanseatic city in northwestern Germany. A commercial and industrial city with a major port on the river Weser, Bremen is part of the Bremen-Oldenburg metropolitan area . Bremen is the second most populous city in North Germany and tenth in Germany.Bremen is...
, † April 15, 1984 in Bremen
Bremen
The City Municipality of Bremen is a Hanseatic city in northwestern Germany. A commercial and industrial city with a major port on the river Weser, Bremen is part of the Bremen-Oldenburg metropolitan area . Bremen is the second most populous city in North Germany and tenth in Germany.Bremen is...
) was a German 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....
and philosopher. She studied mathematics at Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
under Emmy Noether
Emmy Noether
Amalie Emmy Noether was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of...
, where she achieved her Ph.D. in 1926. Her doctoral thesis, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, published in Mathematische Annalen
Mathematische Annalen
Mathematische Annalen is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann...
, is a foundational paper for computer algebra. It first established the existence of algorithms (including complexity bounds) for many of the basic problems of abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
, such as ideal
Ideal (ring theory)
In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal concept allows the generalization in an appropriate way of some important properties of integers like "even number" or "multiple of 3"....
membership for polynomial ring
Polynomial ring
In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more variables with coefficients in another ring. Polynomial rings have influenced much of mathematics, from the Hilbert basis theorem, to the construction of...
s. Hermann's algorithm for primary decomposition is still in use now.
As Adolf Hitler
Adolf Hitler
Adolf Hitler was an Austrian-born German politician and the leader of the National Socialist German Workers Party , commonly referred to as the Nazi Party). He was Chancellor of Germany from 1933 to 1945, and head of state from 1934 to 1945...
came to power in Germany
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...
, Hermann participated in the underground movement against the Nazis, but by 1936 she left Germany for Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
and later England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
. She returned when 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...
was over. In her later years she was more interested in politics and philosophy than in physics and mathematics.
As a philosopher, Hermann had a particular interest in the foundations of physics. In 1935 she discovered a flaw in John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
's purported 1932 proof, which maintained that a hidden variable theory
Hidden variable theory
Historically, in physics, hidden variable theories were espoused by some physicists who argued that quantum mechanics is incomplete. These theories argue against the orthodox interpretation of quantum mechanics, which is the Copenhagen Interpretation...
of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
was impossible. The result went unnoticed by the physics community until it was rediscovered by John Stewart Bell
John Stewart Bell
John Stewart Bell FRS was a British physicist from Northern Ireland , and the originator of Bell's theorem, a significant theorem in quantum physics regarding hidden variable theories.- Early life and work :...
.
Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
, in chapter ten of The Part and The Whole
The Part and The Whole
The book The Part and the Whole, written by Werner Heisenberg, the German physicist who discovered the uncertainty principle, tells, from his point of view, the history of exploring atomic science and quantum mechanics in the first half of the 20th century.As the subtitle "Talks about atomic...
discusses Hermann's work.