Ludwig Bieberbach

Encyclopedia

**Ludwig Georg Elias Moses Bieberbach**(4 December 1886 – 1 September 1982) was a German

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...

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....

.

## Biography

Born in Goddelau, near DarmstadtDarmstadt

Darmstadt is a city in the Bundesland of Hesse in Germany, located in the southern part of the Rhine Main Area.The sandy soils in the Darmstadt area, ill-suited for agriculture in times before industrial fertilisation, prevented any larger settlement from developing, until the city became the seat...

, he studied at Heidelberg and under Felix Klein

Felix Klein

Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...

at Göttingen, receiving his doctorate in 1910. His dissertation was titled

*On the theory of automorphic functions*. He began working as a Privatdozent

Privatdozent

Privatdozent or Private lecturer is a title conferred in some European university systems, especially in German-speaking countries, for someone who pursues an academic career and holds all formal qualifications to become a tenured university professor...

at 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....

in 1910 and as Professor ordinarius at the University of Basel

University of Basel

The University of Basel is located in Basel, Switzerland, and is considered to be one of leading universities in the country...

in 1913. He taught at the University of Frankfurt in 1915 and the University of Berlin

Humboldt University of Berlin

The Humboldt University of Berlin is Berlin's oldest university, founded in 1810 as the University of Berlin by the liberal Prussian educational reformer and linguist Wilhelm von Humboldt, whose university model has strongly influenced other European and Western universities...

from 1921–45.

Bieberbach wrote a habilitation thesis in 1911 about groups of Euclidean motions – identifying conditions under which the group must have a translational subgroup whose vectors span the Euclidean space – that helped solve Hilbert's 18th problem

Hilbert's problems

Hilbert's problems form a list of twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and several of them were very influential for 20th century mathematics...

. He worked on complex analysis

Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...

and its applications to other areas in mathematics. He is known for his work on dynamics in several complex variables, where he obtained results similar to Fatou

Pierre Fatou

Pierre Joseph Louis Fatou was a French mathematician working in the field of complex analytic dynamics. He entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an astronomy post in the Paris Observatory...

's. In 1916 he formulated the Bieberbach conjecture, stating a necessary condition for a holomorphic function

Holomorphic function

In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain...

to map the open unit disc injectively into the complex plane

Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis...

in terms of the function's Taylor series

Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....

. In 1984 Louis de Branges proved the conjecture (for this reason, the Bieberbach conjecture is sometimes called de Branges' theorem

De Branges' theorem

In complex analysis, the Bieberbach conjecture or de Branges's theorem, posed by and proven by , states a necessary condition on a holomorphic function to map the open unit disk of the complex plane injectively to the complex plane....

). There is also a Bieberbach theorem on space group

Space group

In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains.In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered distinct...

s. In 1928 Bieberbach wrote a book with Issai Schur

Issai Schur

Issai Schur was a mathematician who worked in Germany for most of his life. He studied at Berlin...

titled

*Über die Minkowskische Reduktiontheorie der positiven quadratischen Formen*.

Bieberbach was a speaker at the International Congress of Mathematicians

International Congress of Mathematicians

The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....

held at Zurich in 1932.

## Politics

Without being an active NaziNazism

Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...

like Oswald Teichmüller

Oswald Teichmüller

Oswald Teichmüller was a German mathematician who introduced quasiconformal mappings and differential geometric methods into complex analysis.-Life:...

, Bieberbach was, like Martin Heidegger

Martin Heidegger

Martin Heidegger was a German philosopher known for his existential and phenomenological explorations of the "question of Being."...

, a fellow traveller and Nazi sympathizer. He was involved in the repression of Jewish colleagues, including Edmund Landau

Edmund Landau

Edmund Georg Hermann Landau was a German Jewish mathematician who worked in the fields of number theory and complex analysis.-Biography:...

and his former coauthor Schur

Issai Schur

Issai Schur was a mathematician who worked in Germany for most of his life. He studied at Berlin...

. Bieberbach was heavily influenced by Theodore Vahlen, another German mathematician and anti-Semite, who along with Bieberbach founded the "Deutsche Mathematik

Deutsche Mathematik

Deutsche Mathematik was a mathematics journal founded by Ludwig Bieberbach and Theodor Vahlen in 1936. It is also the name of a movement closely associated with the journal whose aim was to promote "German mathematics" and eliminate "Jewish influence", similar to the Deutsche Physik movement...

" ("German mathematics") movement and journal of the same name. The purpose of the movement was to encourage and promote a "German" (in this case meaning intuitionistic

Intuitionism

In the philosophy of mathematics, intuitionism, or neointuitionism , is an approach to mathematics as the constructive mental activity of humans. That is, mathematics does not consist of analytic activities wherein deep properties of existence are revealed and applied...

) style in mathematics. Bieberbach's and Vahlen's idea of having German mathematics was only part of a wider trend in the scientific community in Nazi Germany towards giving the sciences racial character; there were also pseudoscientific movements for "German physics", "German chemistry", and "German biology". In 1945, Bieberbach was dismissed from all his academic positions because of his support of Nazism, but in 1949 was invited to lecture at the University of Basel

University of Basel

The University of Basel is located in Basel, Switzerland, and is considered to be one of leading universities in the country...

by Ostrowski

Alexander Ostrowski

Alexander Markowich Ostrowski , was a mathematician.His father Mark having been a merchant, Alexander Ostrowski attended the Kiev College of Commerce, not a high school, and thus had an insufficient qualification to be admitted to university...

, who considered Bieberbach's political views irrelevant to his contributions to the field of mathematics.

## Quotation

"… the spatial imagination is a characteristic of the Germanic races, while pure logical reasoning has a richer development among Romanic and Hebraic races. … In the intellectual sphere the race shows in the manner of creation, the evaluation of the results, and I guess also in the standpoint considering foundational questions. … Formalism wants to build a realm of mathematical truths which is independent of man, whereas Intuitionism is based on the idea that mathematical thinking is a human endeavor and thus cannot be separated from man." (in*Stilarten mathematischen Schaffens*, i.e. Styles of mathematical creation/endeavour, p. 357).