Ruth Moufang (10 January 1905 – 26 November 1977) was a
German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ge ...
mathematician.
Biography
Born to German chemist Eduard Moufang and Else Fecht Moufang. Eduard Moufang was the son of Friedrich Carl Moufang (1848-1885) from Mainz, and Elisabeth von Moers from Mainz. Ruth Moufang's mother was Else Fecht, who was the daughter of Alexander Fecht (1848-1913) from Kehl and Ella Scholtz (1847-1921). Ruth was the younger of her parents' two daughters, having an elder sister named Erica.
Education and career
She studied mathematics at the
University of Frankfurt. In 1931 she received her Ph.D. on
projective geometry under the direction of
Max Dehn, and in 1932 spent a fellowship year in Rome. After her year in
Rome, she returned to Germany to lecture at the
University of Königsberg and the University of Frankfurt.
Denied permission to teach by the minister of education of
Nazi Germany, she worked in private industry at the Krupps Research Institute, where she became the first German woman with a doctorate to be employed as an industrial mathematician. In 1946 she was finally allowed to accept a teaching position at the University of Frankfurt, and in 1957 she became the first woman professor at the university.
Research
Moufang's research in projective geometry built upon the work of
David Hilbert. She was responsible for ground-breaking work on
non-associative algebraic structure
In mathematics, an algebraic structure consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplication), and a finite set ...
s, including the
Moufang loops named after her.
In 1933, Moufang showed
Desargues's theorem does not hold in the
Cayley plane
In mathematics, the Cayley plane (or octonionic projective plane) P2(O) is a projective plane over the octonions.Baez (2002).
The Cayley plane was discovered in 1933 by Ruth Moufang, and is named after Arthur Cayley for his 1845 paper describing ...
. The Cayley plane uses
octonion
In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface or blackboard bold \mathbb O. Octonions have ...
coordinates which do not satisfy the
associative law
In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement ...
. Such connections between geometry and algebra had been previously noted by
Karl von Staudt and
David Hilbert.
Ruth Moufang thus initiated a new branch of geometry called
Moufang planes.
She published 7 papers on this topic, these are ''Zur Struktur der projectiven Geometrie der Ebene'' Ⓣ (1931); ''Die Einführung in der ebenen Geometrie mit Hilfe des Satzes vom vollständigen Vierseit'' Ⓣ (1931); ''Die Schnittpunktssätze des projektiven speziellen Fünfecksnetzes in ihrer Abhängigkeit voneinander'' Ⓣ (1932); ''Ein Satz über die Schnittpunktsätze des allgemeinen Fünfecksnetzes'' Ⓣ (1932); ''Die Desarguesschen Sätze von Rang 10'' Ⓣ (1933); ''Alternativkörper und der Satz vom vollständigen Vierseit'' D9 Ⓣ (1934); and ''Zur Struktur von Alternativkörpern'' Ⓣ (1934). Moufang published only one paper on group theory, ''Einige Untersuchungen über geordenete Schiefkörper'' Ⓣ, which appeared in print in 1937.
References
*
*
"Ruth Moufang", Biographies of Women Mathematicians Agnes Scott College
Agnes Scott College is a private women's liberal arts college in Decatur, Georgia. The college enrolls approximately 1,000 undergraduate and graduate students. The college is affiliated with the Presbyterian Church and is considered one of the ...
* Bhama Srinivasan (1984) "Ruth Moufang, 1905—1977"
Mathematical Intelligencer 6(2):51–5.
{{DEFAULTSORT:Moufang, Ruth
1905 births
1977 deaths
20th-century German mathematicians
Algebraists
Goethe University Frankfurt alumni
Academic staff of the University of Königsberg
Academic staff of Goethe University Frankfurt
Scientists from Darmstadt
German women academics
20th-century women mathematicians
German women mathematicians
20th-century German women scientists