Heinrich Franz Friedrich Tietze (August 31, 1880 – February 17, 1964) was an

Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...

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 ...

, famous for the

Tietze extension theorem In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem) states that Continuous function (topology), continuous functions on a closed subset of a Normal space, normal topological space can be extend ...

on functions from topological spaces to the real numbers. He also developed the

Tietze transformations In group theory, Tietze transformations are used to transform a given presentation of a group into another, often simpler presentation of the same group. These transformations are named after Heinrich Franz Friedrich Tietze who introduced them in ...

for group presentations, and was the first to pose the

group isomorphism problem In abstract algebra, the group isomorphism problem is the decision problem of determining whether two given finite group presentations refer to isomorphic groups. The isomorphism problem was formulated by Max Dehn, and together with the word pr ...

Tietze's graph In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges. It is named after Heinrich Franz Friedrich Tietze, who showed in 1910 that the Möbius strip can be subdivided into six regi ...

is also named after him; it describes the boundaries of a subdivision of the Möbius strip into six mutually-adjacent regions, found by Tietze as part of an extension of the four color theorem to non-orientable surfaces.

Education and career

Tietze was the son of

Emil Tietze Emil Ernst August Tietze (15 June 1845, Breslau – 4 March 1931, Vienna) was an Austrian geologist. He received his education at the Universities of University of Breslau, Breslau and University of Tübingen, Tübingen. Afterwards, he joined ...

and the grandson of

Franz Ritter von Hauer Franz Ritter von Hauer, or Franz von Hauer (January 30, 1822 – March 20, 1899), was an Austrian geologist. Biography Hauer was born in Vienna, the son of Joseph von Hauer (1778-1863), who was equally distinguished as a high Austrian offic ...

, both of whom were Austrian geologists. He was born in Schleinz,

Austria-Hungary Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of ...

, and studied mathematics at the

Technische Hochschule A ''Technische Hochschule'' (, plural: ''Technische Hochschulen'', abbreviated ''TH'') is a type of university focusing on engineering sciences in Germany. Previously, it also existed in Austria, Switzerland, the Netherlands (), and Finland (, ). ...

in Vienna beginning in 1898. After additional studies in Munich, he returned to Vienna, completing his doctorate in 1904 and his habilitation in 1908. From 1910 until 1918 Tietze taught mathematics in Brno, and was promoted to

ordinary professor Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia. Overview Appointment grades * (Pay grade: ''W3'' or ''W2'') * (''W3'') * (''W2'') * (''W2'', ...

in 1913. He served in the Austrian army during

World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...

, and then returned to Brno, but in 1919 he took a position at the

University of Erlangen A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, th ...

, and then in 1925 moved again to the

University of Munich The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's sixth-oldest university in continuous operatio ...

, where he remained for the rest of his career. One of his doctoral students was Georg Aumann. Tietze retired in 1950, and died in

Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the third-largest city in Germany, after Berlin and Ha ...

West Germany West Germany is the colloquial term used to indicate the Federal Republic of Germany (FRG; german: Bundesrepublik Deutschland , BRD) between its formation on 23 May 1949 and the German reunification through the accession of East Germany on 3 O ...

Awards and honors

Tietze was a fellow of the Bavarian Academy of Sciences and a fellow of the Austrian Academy of Sciences.

Publications

* * *
''Über die mit Lineal und Zirkel und die mit dem rechten Zeichenwinkel lösbaren Konstruktionsaufgaben'', Mathematische Zeitschrift vol.46, 1940

mit Leopold Vietoris ''Beziehungen zwischen den verschiedenen Zweigen der Topologie'', Enzyklopädie der Mathematischen Wissenschaften 1929

''Über die Anzahl der stabilen Ruhelagen eines Würfels'', Elemente der Mathematik vol.3, 1948
* ''Über die topologische Invarianten mehrdimensionaler Mannigfaltigkeiten'', Monatshefte für Mathematik und Physik, vol. 19, 1908, p.1-118
''Über Simony Knoten und Simony Ketten mit vorgeschriebenen singulären Primzahlen für die Figur und für ihr Spiegelbild'', Mathematische Zeitschrift vol.49, 1943, p.351
(Knot theory) *

References

External links

* {{DEFAULTSORT:Tietze, Heinrich Franz Friedrich Austrian mathematicians 1880 births 1964 deaths Group theorists Members of the Austrian Academy of Sciences Austro-Hungarian mathematicians University of Erlangen-Nuremberg faculty Ludwig Maximilian University of Munich faculty TU Wien alumni Topologists