Grete Hermann
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Grete Hermann (2 March 1901 – 15 April 1984) was a German
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and
philosopher Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
noted for her work in
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
,
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
,
philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
and
education Education is the transmission of knowledge and skills and the development of character traits. Formal education occurs within a structured institutional framework, such as public schools, following a curriculum. Non-formal education als ...
. She is noted for her early philosophical work on the foundations of
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
, and is now known most of all for an early, but long-ignored critique of the no hidden variables proof by
John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...
.


Mathematics

Hermann studied mathematics at
Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...
under
Emmy Noether Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which ...
and Edmund Landau, where she achieved her
PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...
in 1926. Her doctoral thesis, ''The Question of Finitely Many Steps in Polynomial Ideal Theory'' (), published in '' Mathematische Annalen'', is the foundational paper for modern
computer algebra In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating expression (mathematics), ...
. It first established the existence of
algorithms In mathematics and computer science, an algorithm () is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for per ...
(including
complexity Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to c ...
bounds) for many of the basic problems of
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...
, such as ideal membership for
polynomial ring In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, ...
s. Hermann's algorithm for
primary decomposition In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many ''primary ideals'' (which are related ...
is still in contemporary use.


Assistant to Leonard Nelson

From 1925 to 1927, Hermann worked as assistant for Leonard Nelson. Together with Minna Specht, she posthumously published Nelson's work ''System der philosophischen Ethik und Pädagogik'', while continuing her own research.


Quantum mechanics

As a philosopher, Hermann had a particular interest in the foundations of physics. In 1934, she went to
Leipzig Leipzig (, ; ; Upper Saxon: ; ) is the most populous city in the States of Germany, German state of Saxony. The city has a population of 628,718 inhabitants as of 2023. It is the List of cities in Germany by population, eighth-largest city in Ge ...
"for the express purpose of reconciling a neo-Kantian conception of causality with the new quantum mechanics". In Leipzig, many exchanges of thoughts took place among Hermann, Carl Friedrich von Weizsäcker, and
Werner Heisenberg Werner Karl Heisenberg (; ; 5 December 1901 – 1 February 1976) was a German theoretical physicist, one of the main pioneers of the theory of quantum mechanics and a principal scientist in the German nuclear program during World War II. He pub ...
. The contents of her work in this time, including a focus on a distinction of
predictability Predictability is the degree to which a correct prediction or forecast of a system's state can be made, either qualitatively or quantitatively. Predictability and causality Causal determinism has a strong relationship with predictability. Perfec ...
and causality, are known from three of her own publications, and from later description of their discussions by von Weizsäcker, and the discussion of Hermann's work in chapter ten of Heisenberg's '' Physics and Beyond''. From Denmark, she published her work ''The foundations of quantum mechanics in the philosophy of nature'' (). This work has been referred to as "one of the earliest and best philosophical treatments of the new quantum mechanics". In this work, she concludes: In June 1936, Hermann was awarded the Richard Avenarius prize together with Eduard May and Th. Vogel.


Hidden variables

Based on her views on quantum causality, Hermann concluded that there was no way to explain quantum mechanics in terms of a hidden variable theory. However, she published a critique of
John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...
's 1932 proof from his book '' Mathematical Foundations of Quantum Mechanics'', that was widely claimed to show that such a theory was impossible. Hermann's work on this subject went unnoticed by the physics community until it was independently discovered and published by
John Stewart Bell John Stewart Bell (28 July 1928 – 1 October 1990) was a physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum mechanics, quantum physics regarding hidden-variable theory, hidden-variable theor ...
in 1966, and her earlier discovery was pointed out by
Max Jammer Max Jammer (; born Moshe Jammer, ; 13 April 1915 – 18 December 2010), was an Israeli physicist and philosophy of physics, philosopher of physics. He was born in Berlin, Germany. He was Rector and Acting President at Bar-Ilan University from 19 ...
in 1974. Some have posited that had her critique not remained nearly unknown for decades, her ideas would have put in question the unequivocal acceptance of the Copenhagen interpretation of quantum mechanics, by providing a credible basis for the further development of nonlocal hidden variable theories, which would have changed the historical development of quantum mechanics.


Political activism

As
Adolf Hitler Adolf Hitler (20 April 1889 – 30 April 1945) was an Austrian-born German politician who was the dictator of Nazi Germany from 1933 until Death of Adolf Hitler, his suicide in 1945. Adolf Hitler's rise to power, He rose to power as the lea ...
came to power in
Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...
, Hermann participated in the underground movement against the
Nazis Nazism (), formally named National Socialism (NS; , ), is the far-right politics, far-right Totalitarianism, totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During H ...
. She was a member of the Internationaler Sozialistischer Kampfbund (ISK).Grete Henry-Hermann
Friedrich Ebert Foundation, downloaded 22 January 2012


Emigration and later years

By 1936, Hermann left Germany for
Denmark Denmark is a Nordic countries, Nordic country in Northern Europe. It is the metropole and most populous constituent of the Kingdom of Denmark,, . also known as the Danish Realm, a constitutionally unitary state that includes the Autonomous a ...
and later
France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...
and
England England is a Countries of the United Kingdom, country that is part of the United Kingdom. It is located on the island of Great Britain, of which it covers about 62%, and List of islands of England, more than 100 smaller adjacent islands. It ...
. In London, in order to avoid standing out on account of her German provenance, she married a man called Edward Henry early in 1938. Her prescience was justified by events: two years later the British government invoked its hitherto obscure 1939 Defence Regulation 18B, identifying several thousand refugees who had fled Germany for reasons of politics or race as enemy aliens and placing them in internment camps. After
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
ended in 1945, she was able to combine her interests in physics and mathematics with
political philosophy Political philosophy studies the theoretical and conceptual foundations of politics. It examines the nature, scope, and Political legitimacy, legitimacy of political institutions, such as State (polity), states. This field investigates different ...
. She rejoined the Social Democratic Party (SPD) on returning in 1946 to what would become, in 1949, the German Federal Republic (
West Germany West Germany was the common English name for the Federal Republic of Germany (FRG) from its formation on 23 May 1949 until German reunification, its reunification with East Germany on 3 October 1990. It is sometimes known as the Bonn Republi ...
). Starting in 1947 she was one of those contributing behind the scenes to the Bad Godesberg Programme, prepared under the leadership of her longstanding ISK comrade Willi Eichler, and issued in 1959, which provided a detailed modernising platform that carried the party into government in the 1960s. She was nominated professor for philosophy and physics at the and played a relevant role in the Education and Science Workers' Union. From 1961 to 1978, she presided over the , an organisation founded by Nelson in 1922, oriented towards education, social justice, responsible political action and its philosophical basis.Philosophisch-Politische Akademie
(in German language), downloaded 22 January 2012


Works

;Articles: * Grete Hermann: ''Die naturphilosophischen Grundlagen der Quantenmechanik'', Naturwissenschaften, Volume 23, Number 42, 718–721,
preview
in German language) * Grete Hermann: ''Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Unter Benutzung nachgelassener Sätze von K. Hentzelt'', Mathematische Annalen, Volume 95, Number 1, 736–788,
abstract
in German language) — ''The question of finitely many steps in polynomial ideal theory'
(review and English-language translation)


References

*


Further reading

* C. Herzenberg: ''Grete Hermann: Mathematician, Physicist, Philosopher'', Bulletin of the American Physical Society, 2008 APS April Meeting and HEDP/HEDLA Meeting, Volume 53, Number 5, 11–15 April 2008 in St. Louis, Missouri
abstract
* Vera Venz: ''Zur Biografie von Grete Hermann'', GRIN 2009, First edition 2001, (in German language)


External links

*

at the Friesian School * ttp://www.frauen-im-aufbruch-ausstellung.de/en/women/grete-henry-hermann/ Grete Henry-Hermann: Politically minded scientist by F. Kersting
German language version
, exhibition catalog )
Grete Hermann: Mathematician, Philosopher and Physicist
by Giulia Paparo ( MA Thesis) at Academia.edu ccessible with free registration {{DEFAULTSORT:Hermann, Grete 1901 births 1984 deaths 20th-century German mathematicians 20th-century German philosophers 20th-century German physicists 20th-century German women scientists German women physicists German philosophers of science German women philosophers 20th-century German women mathematicians