Gustav Roch
Encyclopedia
Gustav Roch was a German
mathematician
who made significant contributions to the theory of Riemann surfaces in a career that was prematurely curtailed at the age of 26.
, Roch attended the Polytechnic Institute (Technische Bildungsanstalt) in Dresden
, initially focusing on chemistry
, encouraged by his father. However the mathematician Oscar Schlömilch
identified his exceptional talents and guided him towards a mathematical career. Combining studies at the Polytechnic Institute with private studies at another institute enabled Roch to be already publishing original research on the mathematical theory of electromagnetism
from 1859.
Later in 1859, Roch entered the University of Leipzig
, coming under the influence of Möbius
, and continuing his work on electromagnetism. In 1861, Roch went to work at the University of Göttingen, studying under Weber
, but also attending lectures by Bernhard Riemann
. After three terms in Göttingen
, Roch went to the University of Berlin, where he met Kronecker, Weierstrass and others. In 1862 he was awarded a masters degree from Leipzig and later a doctorate for his work on electromagnetism.
From this point his work took a more mathematical slant. In the following year he published the paper containing the result for which he is famous to this day, the Riemann–Roch theorem
(given its name by Max Noether
), which related the topological genus of a Riemann surface to purely algebraic properties, .
Only two years later, Roch's health was shattered due to a tuberculosis infection
. He moved to Venice
in the hope that warmer weather would aid his recovery, but he died there a month later.
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....
who made significant contributions to the theory of Riemann surfaces in a career that was prematurely curtailed at the age of 26.
Biography
Born in LeipzigLeipzig
Leipzig Leipzig has always been a trade city, situated during the time of the Holy Roman Empire at the intersection of the Via Regia and Via Imperii, two important trade routes. At one time, Leipzig was one of the major European centres of learning and culture in fields such as music and publishing...
, Roch attended the Polytechnic Institute (Technische Bildungsanstalt) in Dresden
Dresden
Dresden is the capital city of the Free State of Saxony in Germany. It is situated in a valley on the River Elbe, near the Czech border. The Dresden conurbation is part of the Saxon Triangle metropolitan area....
, initially focusing on chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, encouraged by his father. However the mathematician Oscar Schlömilch
Oscar Schlömilch
Oscar Xavier Schlömilch was a German mathematician, born in Weimar, working in mathematical analysis. He took a doctorate at the University of Jena in 1842, and became a professor at Dresden Polytechnic in 1849....
identified his exceptional talents and guided him towards a mathematical career. Combining studies at the Polytechnic Institute with private studies at another institute enabled Roch to be already publishing original research on the mathematical theory of electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
from 1859.
Later in 1859, Roch entered the University of Leipzig
University of Leipzig
The University of Leipzig , located in Leipzig in the Free State of Saxony, Germany, is one of the oldest universities in the world and the second-oldest university in Germany...
, coming under the influence of Möbius
August Ferdinand Möbius
August Ferdinand Möbius was a German mathematician and theoretical astronomer.He is best known for his discovery of the Möbius strip, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space. It was independently discovered by Johann Benedict...
, and continuing his work on electromagnetism. In 1861, Roch went to work at the University of Göttingen, studying under Weber
Weber
Weber is a surname of German origin, derived from the noun meaning "weaver". In some cases, following migration to English-speaking countries, it has been anglicised to the English surname 'Webber' or even 'Weaver'.Notable people with the surname include:...
, but also attending lectures by Bernhard Riemann
Bernhard Riemann
Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity....
. After three terms in Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
, Roch went to the University of Berlin, where he met Kronecker, Weierstrass and others. In 1862 he was awarded a masters degree from Leipzig and later a doctorate for his work on electromagnetism.
From this point his work took a more mathematical slant. In the following year he published the paper containing the result for which he is famous to this day, the Riemann–Roch theorem
Riemann–Roch theorem
The Riemann–Roch theorem is an important tool in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles...
(given its name by Max Noether
Max Noether
Max Noether was a German mathematician who worked on algebraic geometry and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century".-Biography:...
), which related the topological genus of a Riemann surface to purely algebraic properties, .
Only two years later, Roch's health was shattered due to a tuberculosis infection
Tuberculosis
Tuberculosis, MTB, or TB is a common, and in many cases lethal, infectious disease caused by various strains of mycobacteria, usually Mycobacterium tuberculosis. Tuberculosis usually attacks the lungs but can also affect other parts of the body...
. He moved to Venice
Venice
Venice is a city in northern Italy which is renowned for the beauty of its setting, its architecture and its artworks. It is the capital of the Veneto region...
in the hope that warmer weather would aid his recovery, but he died there a month later.