Ruth Moufang
Encyclopedia
Ruth Moufang was a German mathematician
.
Born to a German chemist Dr. Eduard Moufang and Else Fecht Moufang, 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. Her research in projective geometry built upon the work of David Hilbert
. She was responsible for ground-breaking work on non-associative
algebraic structure
s, including the Moufang loop
s named after her.
Her most important contribution to the foundations of geometry was the discovery that if one replaces Desargues' theorem
with the theorem of the complete quadrilateral (also known as the invariance of the fourth harmonic point) together with the incidence axioms of Hilbert, one obtains an alternative
division algebra
instead of a skew field.
Denied permission to teach by the minister of education of Nazi Germany
, she worked in private industry until 1946, when she became the first woman professor at the University of Frankfurt.
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....
.
Born to a German chemist Dr. Eduard Moufang and Else Fecht Moufang, she studied mathematics at the University of Frankfurt. In 1931 she received her Ph.D. on projective geometry
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
under the direction of Max Dehn
Max Dehn
Max Dehn was a German American mathematician and a student of David Hilbert. He is most famous for his work in geometry, topology and geometric group theory...
, and in 1932 spent a fellowship year in Rome. After her year in Rome
Rome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
, she returned to Germany to lecture at the University of Königsberg
University of Königsberg
The University of Königsberg was the university of Königsberg in East Prussia. It was founded in 1544 as second Protestant academy by Duke Albert of Prussia, and was commonly known as the Albertina....
and the University of Frankfurt. Her research in projective geometry built upon the work of David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
. She was responsible for ground-breaking work on non-associative
Non-associative algebra
A non-associative algebra over a field K is a K-vector space A equipped with a K-bilinear map A × A → A. There are left and right multiplication maps...
algebraic structure
Algebraic structure
In abstract algebra, an algebraic structure consists of one or more sets, called underlying sets or carriers or sorts, closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties...
s, including the Moufang loop
Moufang loop
In mathematics, a Moufang loop is a special kind of algebraic structure. It is similar to a group in many ways but need not be associative. Moufang loops were introduced by Ruth Moufang.-Definition:...
s named after her.
Her most important contribution to the foundations of geometry was the discovery that if one replaces Desargues' theorem
Desargues' theorem
In projective geometry, Desargues' theorem, named in honor of Gérard Desargues, states:Denote the three vertices of one triangle by a, b, and c, and those of the other by A, B, and C...
with the theorem of the complete quadrilateral (also known as the invariance of the fourth harmonic point) together with the incidence axioms of Hilbert, one obtains an alternative
Alternative algebra
In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have*x = y*x = y...
division algebra
Division algebra
In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field, in which division is possible.- Definitions :...
instead of a skew field.
Denied permission to teach by the minister of education of Nazi Germany
Nazi Germany
Nazi Germany , also known as the Third Reich , but officially called German Reich from 1933 to 1943 and Greater German Reich from 26 June 1943 onward, is the name commonly used to refer to the state of Germany from 1933 to 1945, when it was a totalitarian dictatorship ruled by...
, she worked in private industry until 1946, when she became the first woman professor at the University of Frankfurt.