Ruth Moufang (10 January 1905 – 26 November 1977) was a

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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, structure, space, models, and change. History On ...

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 In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pro ...

under the direction of

Max Dehn Max Wilhelm Dehn (November 13, 1878 – June 27, 1952) was a German mathematician most famous for his work in geometry, topology and geometric group theory. Born to a Jewish family in Germany, Dehn's early life and career took place in Germany. ...

, and in 1932 spent a fellowship year in Rome. After her year in

Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...

, she returned to Germany to lecture at the

University of Königsberg The University of Königsberg (german: Albertus-Universität Königsberg) was the university of Königsberg in East Prussia. It was founded in 1544 as the world's second Protestant academy (after the University of Marburg) by Duke Albert of Prussi ...

and the University of Frankfurt. Denied permission to teach by the minister of education of

Nazi Germany Nazi Germany (lit. "National Socialist State"), ' (lit. "Nazi State") for short; also ' (lit. "National Socialist Germany") (officially known as the German Reich from 1933 until 1943, and the Greater German Reich from 1943 to 1945) was ...

, 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 David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...

. She was responsible for ground-breaking work on

non-associative 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 ...

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 of ...

s, including the

Moufang loop Moufang is the family name of the following people: *Christoph Moufang (1817–1890), a Roman Catholic cleric *Ruth Moufang (1905–1977), a German mathematician, after whom several concepts in mathematics are named: ** Moufang–Lie algebra ** Mo ...

s named after her. In 1933, Moufang showed

Desargues's theorem In projective geometry, Desargues's theorem, named after Girard Desargues, states: :Two triangles are in perspective ''axially'' if and only if they are in perspective ''centrally''. Denote the three vertices of one triangle by and , and tho ...

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 e ...

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 f ...

. Such connections between geometry and algebra had been previously noted by

Karl von Staudt Karl Georg Christian von Staudt (24 January 1798 – 1 June 1867) was a German mathematician who used synthetic geometry to provide a foundation for arithmetic. Life and influence Karl was born in the Free Imperial City of Rothenburg, which is n ...

and

. Ruth Moufang thus initiated a new branch of geometry called

Moufang plane In geometry, a Moufang plane, named for Ruth Moufang, is a type of projective plane, more specifically a special type of translation plane. A translation plane is a projective plane that has a ''translation line'', that is, a line with the property ...

s. 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 ''The Mathematical Intelligencer'' is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals. Volumes are released qua ...

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