Maria-Viktoria Hasse (May 30, 1921 – January 10, 2014) was a German mathematician who became the first female professor in the faculty of mathematics and science at

TU Dresden TU Dresden (for german: Technische Universität Dresden, abbreviated as TUD and often wrongly translated as "Dresden University of Technology") is a public research university, the largest institute of higher education in the city of Dresden, th ...

. She wrote books on

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

and

category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

, and is known as one of the namesakes of the

Gallai–Hasse–Roy–Vitaver theorem In graph theory, the Gallai–Hasse–Roy–Vitaver theorem is a form of duality between the colorings of the vertices of a given undirected graph and the orientations of its edges. It states that the minimum number of colors needed to properly c ...

graph coloring In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices o ...

Education and career

Hasse was born in

Warnemünde (, literally ''Mouth of the Warnow'') is a seaside resort and a district of the city of Rostock in Mecklenburg, Germany. It is located on the Baltic Sea and, as the name implies, at the estuary of the river Warnow. is one of the world's busie ...

. She went to the Gymnasium in

Rostock Rostock (), officially the Hanseatic and University City of Rostock (german: link=no, Hanse- und Universitätsstadt Rostock), is the largest city in the German state of Mecklenburg-Vorpommern and lies in the Mecklenburgian part of the state, c ...

, and after a term in the

Reich Labour Service The Reich Labour Service (''Reichsarbeitsdienst''; RAD) was a major organisation established in Nazi Germany as an agency to help mitigate the effects of unemployment on the German economy, militarise the workforce and indoctrinate it with Naz ...

from 1939 to 1940, studied mathematics, physics, and philosophy at the

University of Rostock The University of Rostock (german: link=no, Universität Rostock) is a public university located in Rostock, Mecklenburg-Vorpommern, Germany. Founded in 1419, it is the third-oldest university in Germany. It is the oldest university in continen ...

and

University of Tübingen The University of Tübingen, officially the Eberhard Karl University of Tübingen (german: Eberhard Karls Universität Tübingen; la, Universitas Eberhardina Carolina), is a public research university located in the city of Tübingen, Baden-Wü ...

from 1940 to 1943, earning a diploma in 1943 from Rostock. She continued at Rostock as an assistant and lecturer, earning a doctorate (Dr. rer. nat.) in 1949 and a

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

in 1954. Her doctoral dissertation, ''Über eine singuläre Intergralgleichung 1. Art mit logarithmischer Unstetigkeit'' n a singular integral equation of the 1st kind with logarithmic discontinuity was supervised by Hans Schubert; her habilitation thesis was ''Über eine Hillsche Differentialgleichung'' Hill's_differential_equation.html" ;"title="Hill differential equation">Hill's differential equation">Hill differential equation">Hill's differential equation She worked as a professor of algebra at TU Dresden from 1954 until her 1981 retirement. The Rostock CPR gives the date of her start at Dresden as 1964, but this would leave a ten-year gap in her work life, and Voss is clear that she arrived before the 1962 start of Lieselott Herforth.

Contributions

With Lothar Michler, Hasse wrote ''Theorie der Kategorien'' ategory Theory(Deutscher Verlag, 1966). She also wrote ''Grundbegriffe der Mengenlehre und Logik'' asic Concepts of Set Theory and Logic(Harri Deutsch, 1968). In the theory of

, the

provides a duality between colorings of the vertices of a graph and

orientations ''Orientations'' is a bimonthly print magazine published in Hong Kong and distributed worldwide since 1969. It is an authoritative source of information on the many and varied aspects of the arts of East and Southeast Asia, the Himalayas, the India ...

of its edges. It states that the minimum number of colors needed in a coloring equals the number of vertices in a

longest path In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called ''simple'' if it does not have any repeated vertices; the length of a path may ...

, in an orientation chosen to minimize the length of this path. It was stated in 1958 in a graph theory textbook by

Claude Berge Claude Jacques Berge (5 June 1926 – 30 June 2002) was a French mathematician, recognized as one of the modern founders of combinatorics and graph theory. Biography and professional history Claude Berge's parents were André Berge and Geneviève ...

, and independently published by Hasse,

Tibor Gallai Tibor Gallai (born Tibor Grünwald, 15 July 1912 – 2 January 1992) was a Hungarian mathematician. He worked in combinatorics, especially in graph theory, and was a lifelong friend and collaborator of Paul Erdős. He was a student of Dénes K� ...

, B. Roy, and L. Vitaver. Hasse's publication of this result was the second chronologically, in 1965.

References

{{DEFAULTSORT:Hasse, Maria 1921 births 2014 deaths 20th-century German mathematicians German women mathematicians Graph theorists Set theorists Category theorists University of Rostock alumni TU Dresden faculty 21st-century German mathematicians Reich Labour Service members 20th-century German women 21st-century German women