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Gustav A. Roch | |
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 Gustav Roch (1839-1866) | |
| Born | (1839-12-09)9 December 1839 |
| Died | 21 November 1866(1866-11-21) (aged 26) |
| Nationality | Saxon |
| Known for | Riemann–Roch theorem |
| Scientific career | |
| Fields | Mathematics |
Gustav Adolph Roch (German:[ʀɔχ]; 9 December 1839 – 21 November 1866) was aGermanmathematician who made significant contributions to the theory ofRiemann surfaces. Roch’s career was cut short by his untimely death at the age of 26.
Born inLeipzig, Roch attended thePolytechnic Institute (Technische Bildungsanstalt) inDresden, initially focusing onchemistry, encouraged by his father. However the mathematicianOscar 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 ofelectromagnetism from 1859.
Later in 1859, Roch entered theUniversity of Leipzig, coming under the influence ofAugust Ferdinand Möbius, and continuing his work on electromagnetism. In 1861, Roch went to work at theUniversity of Göttingen, studying underWilhelm Eduard Weber, but also attending lectures byBernhard Riemann. After three terms inGöttingen, Roch went to theUniversity of Berlin, where he metLeopold Kronecker,Karl Weierstrass and others. In 1862 he was awarded amagister artium 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, theRiemann–Roch theorem (given its name byMax 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 atuberculosis infection. He moved toVenice in the hope that warmer weather would aid his recovery, but died there a month later. This loss came only four months after that of his former professor and mentorBernhard Riemann.
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