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Thursday, September 24, 2015

Throwback Fact: Three German Mathematicians

Happy Oktoberfest! With the annual festival taking place right now in Germany, the Center of Math wanted to celebrate by talking about three famous German mathematicians for this week's Throwback Fact.

Carl Ludwig Siegel
 B: Berlin, Germany, December 31, 1896 - D: Göttingen, Germany, April 4, 1981
Source: Wikipedia
Siegel made significant contributions to mathematics throughout the 20th century and is considered by some to be one of the greatest mathematicians of this time. Born in Berlin, in his study at the Humboldt University of Berlin, Siegel was first introduced to number theory, a topic he would research throughout his career. Siegel went on to study at the University of Göttingen where he would complete his dissertation on Diophantine approximations. Afterward, Siegel taught as a professor at the university of Frankfurt and the University of Göttingen, but left in 1940 for the United States due to his opposition to the Nazi regime. After spending 5 years in the US, Siegel returned to Göttingen to be a professor where he remained until his retirement in 1959.

In his life, Siegel made many major contributions to the field of mathematics with his work on number theory, Diophantine equations, celestial mechanics, and much more. In 1978, Siegel was awarded the first Wolf Prize in Mathematics, which is one of the most prestigious awards in the field. Siegel also proved important theorems in the theory of analytical functions of several complex numbers, which the Siegel zero came from. Due to his many contributions, Siegel has become a popular name in the field of mathematics even in his death. 

Felix Christian Klein 
B: Düsseldorf, Prussia, April 25, 1849 - D: Göttingen, Germany, June 22, 1925
Source: Wikipedia
Felix Christian Klein, born in Düsseldorf, is famous for his work in the fields of geometry, group theory, and function theory. Klein studied  physics and mathematics at the University of Boon, where he originally intended to be a physicist. Klein received his doctorate under Julius Plucker, whose main interest was in geometry, which may have helped pique Klein's interest in the field. After receiving his doctorate, Klein served for a short time as a medical orderly in the Prussian army before being appointed as a lecturer at Göttingen. At only 23, Klein became a professor of mathematics at Erlang, then a professor at the University of Leipzig, and finally a professor at University of Göttingen where he would teach until his retirement. 

While teaching at Göttingen, Klein helped establish a mathematics research center that became world-renowned. Klein also served as editor of the Mathematische Annalen, which was one of the most highly regarded mathematical journals of its time, thanks to his leadership. Today, Klein is most remembered for his work in geometry and complex analysis, and his proof that non-Euclidean geometry is equiconsistent with Euclidean geometry, as well as developing mathematical curriculum in secondary schools which were accepted worldwide. Many amateur mathematicians may also be familiar with the paradoxical "Klein bottle," a surface with no boundary and only one side, similar to the Möbius strip. Due to his contributions and mathematical breakthroughs, Klein received the Copley Medal of the (Royal) Society (of London) and the De Morgan Medal of the London Mathematical Society. Moreover while it is hard to compare anything to his major breakthroughs and contributions to mathematics, one of his most inspiring accomplishments was his work to allow women to study at Göttingen, which opened the door to women in mathematics in Germany.   

Carl Gustav Jacob Jacobi 
B: Potsdam, Prussia, December 10, 1804 - D: Berlin, Germany, February 18, 1851
Source: Wikipedia
Carl Gustav Jacobi showed tremendous mathematical abilities at an early age, thanks to the education given to him by his uncle. By the time he was 12, Jacobi was already practicing mathematics at a collegiate level. Since he was to young to attend University, Jacobi studied at the Posdam Gymnaisum where he was interested in a variety of subjects such as history, philosophy, and, of course, mathematics. Jacobi then attended Berlin University where he finally made the decision to study mathematics. He received his doctorate from Berlin University and then became a professor, a position he held for most of his life. 

While working as a mathematics professor Jacobi made fundamental contributions to elliptic functions, dynamics, number theory, and differential equations. Sadly, Jacobi died at 46 from smallpox but left a huge mathematical legacy. Today, many mathematical objects and concepts are named after him, such as the Jacobi symbol, the Jacobi elliptic functions, and the Jacobian matrix of a vector-valued function.

Did you notice some people were missing? Of course we couldn't write about them all, so here are some German mathematicians we talked about in the past: Bernhard Riemann, Carl Gauss, David Hilbert, Emmy Noether, and Gottfried W. Leibniz. If you have any German mathematicians you want us to talk about, just comment the name and we may write about them for a future Throwback Fact post. 

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