Camillo Herbert Grötzsch (21 May 1902 – 15 May 1993) was a German

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, mathematical structure, structure, space, Mathematica ...

known primarily for his work on

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 helpful in many branches of mathematics, including algebraic ...

, specifically

univalent function In mathematics, in the branch of complex analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective. Examples The function f \colon z \mapsto 2z + z^2 is univalent in the open unit disc, as f( ...

s and

conformal mapping In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U and V be open subsets of \mathbb^n. A function f:U\to V is called conformal (or angle-preserving) at a point u_0\i ...

s, and

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

. He was the first to introduce the concept of a

quasiconformal mapping In mathematical complex analysis, a quasiconformal mapping is a (weakly differentiable) homeomorphism between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. Quasiconformal mappings are a generali ...

. He was the discoverer and eponym of the

Grötzsch graph In the mathematical field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number 5. It is named after German mathematician Herbert Grötzsch, who used it as an example ...

, a

triangle-free graph In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with ...

that requires four colors in any

graph coloring In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a Graph (discrete mathematics), graph. The assignment is subject to certain constraints, such as that no two adjacent elements have th ...

, and

Grötzsch's theorem In the mathematics, mathematical field of graph theory, Grötzsch's theorem is the statement that every triangle-free graph, triangle-free planar graph can be graph coloring, colored with only three colors. According to the four-color theorem, eve ...

, the result that every triangle-free

planar graph In graph theory, a planar graph is a graph (discrete mathematics), graph that can be graph embedding, embedded in the plane (geometry), plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. ...

requires at most three colors.

Biography

Camillo Herbert Grötzsch was born in

Döbeln Döbeln (; , ) is a town in Saxony, Germany, part of the Mittelsachsen district. It sits on the banks of the Freiberger Mulde, Freiberger Mulde river. Location and geography Döbeln is situated in the Central Saxon Hills, Central Saxon Hill co ...

in 1902. His father, Emil Camillo Grötzsch, received his doctorate under

Sophus Lie Marius Sophus Lie ( ; ; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He also made substantial cont ...

and was a mathematics teacher. Grötzsch studied mathematics at the

University of Jena The University of Jena, officially the Friedrich Schiller University Jena (, abbreviated FSU, shortened form ''Uni Jena''), is a public research university located in Jena, Thuringia, Germany. The university was established in 1558 and is cou ...

from 1922 to 1926 under

Paul Koebe Paul Koebe (15 February 1882 – 6 August 1945) was a 20th-century German mathematician. His work dealt exclusively with the complex numbers, his most important results being on the uniformization of Riemann surfaces in a series of four papers in ...

. He followed Koebe to the

University of Leipzig Leipzig University (), in Leipzig in Saxony, Germany, is one of the world's oldest universities and the second-oldest university (by consecutive years of existence) in Germany. The university was founded on 2 December 1409 by Frederick I, Electo ...

and received his doctorate there in 1929. In 1931 Grötzsch obtained his

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

at the

University of Giessen University of Giessen, official name Justus Liebig University Giessen (), is a large public research university in Giessen, Hesse, Germany. It is one of the oldest institutions of higher education in the German-speaking world. It is named afte ...

, where he taught until his termination for refusing to join the

Sturmabteilung The (; SA; or 'Storm Troopers') was the original paramilitary organisation under Adolf Hitler and the Nazi Party of Germany. It played a significant role in Adolf Hitler's rise to power, Hitler's rise to power in the 1920s and early 1930s. I ...

in 1935. he subsequently worked in

Leipzig Leipzig (, ; ; Upper Saxon: ; ) is the most populous city in the States of Germany, German state of Saxony. The city has a population of 628,718 inhabitants as of 2023. It is the List of cities in Germany by population, eighth-largest city in Ge ...

on J. C. Poggendorf's ''Biographisch-literarisches Handworterbuch zur Geschichte der exacten Wissenschaften'' until 1939. During the

Second World War World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

, Grötzsch served in the artillery until 1942 and the home service until 1944. In 1944 he worked on

jet engine A jet engine is a type of reaction engine, discharging a fast-moving jet (fluid), jet of heated gas (usually air) that generates thrust by jet propulsion. While this broad definition may include Rocket engine, rocket, Pump-jet, water jet, and ...

research at the

Aerodynamics Research Institute The ''Aerodynamische Versuchsanstalt'' (AVA) in Göttingen was one of the four predecessor organizations of the 1969 founded "German Research and Experimental Institute for Aerospace", which in 1997 was renamed German Aerospace Center (DLR). ...

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

. After the war, Grötzsch joined at the

University of Marburg The Philipps University of Marburg () is a public research university located in Marburg, Germany. It was founded in 1527 by Philip I, Landgrave of Hesse, which makes it one of Germany's oldest universities and the oldest still operating Prote ...

in 1945. In 1948 he moved to the

Martin Luther University Halle-Wittenberg Martin Luther University Halle-Wittenberg (), also referred to as MLU, is a public research university in the cities of Halle and Wittenberg. It is the largest and oldest university in the German state of Saxony-Anhalt. MLU offers German and i ...

, where he would remain until his retirement in 1967. Grötzsch was elected to the Leopoldina in 1959. In 1967 he received the National Prize of the German Democratic Republic. The keynote speech in honor of his 75th birthday was given by

Lipman Bers Lipman Bers ( Latvian: ''Lipmans Berss''; May 22, 1914 – October 29, 1993) was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also k ...

. In 1951 Grötzsch married Annemarie Jung, daughter of mathematician

Heinrich Jung Heinrich Wilhelm Ewald Jung (4 May 1876, Essen – 12 March 1953, Halle (Saale)) was a German mathematician, who specialized in geometry and algebraic geometry. Biography Heinrich Jung was born as the son of a ''Bergrat'' (a mining officer of high ...

; they had three children. Grötzsch died in Halle in 1993. Groetzsch-graph

Publications

*Herbert Grötzsch, Über die Verzerrung bei schlichten nicht-konformen Abbildungen und über eine damit zusammenhängende Erweiterung des Picardschen Satzes, Sitzungsberichte sächs. Akad. Wiss., Math.-Phys. Klasse, vol. 80, 1928, pp. 503–507

References

* * * * Reiner Kühnau, ''Herbert Grötzsch zum Gedächtnis''. Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 99, 1997, pp. 122–145 (1997) * Reiner Kühnau, ''Einige neuere Entwicklungen bei quasikonformen Abbildungen''. Jahresbericht Deutscher Mathematikervereinigung, vol. 94, pp. 141–192 (1992) * Horst Tietz, ''Herbert Grötzsch in Marburg''. Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 99, 1997, pp. 146–148

External links

Oberwolfach Photo Collection
{{DEFAULTSORT:Grotzsch, Herbert 1902 births 1993 deaths 20th-century German mathematicians Graph theorists Complex analysts People from Halle (Saale)