Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was a German mathematician who did important work in abstract algebra (particularly ring theory), algebraic number theory and the foundations of the real numbers.
Dedekind was the youngest of four children of Julius Levin Ulrich Dedekind. As an adult, he never employed the names Julius Wilhelm. He was born, lived most of his life, and died in Braunschweig (often called "Brunswick" in English).
In 1848, he entered the Collegium Carolinum in Braunschweig, where his father was an administrator, obtaining a solid grounding in mathematics. In 1850, he entered the University of Göttingen. Dedekind studied number theory under Moritz Stern. Gauss was still teaching, although mostly at an elementary level, and Dedekind became his last student. Dedekind received his doctorate in 1852, for a thesis titled Über die Theorie der Eulerschen Integrale ("On the Theory of Eulerian integrals"). This thesis did not reveal the talent evident on almost every page Dedekind later wrote.
At that time, the University of Berlin, not Göttingen, was the leading center for mathematical research in Germany. Thus Dedekind went to Berlin for two years of study, where he and Riemann were contemporaries; they were both awarded the habilitation in 1854. Dedekind returned to Göttingen to teach as a Privatdozent, giving courses on probability and geometry. He studied for a while with Dirichlet, and they became close friends. Because of lingering weaknesses in his mathematical knowledge, he studied elliptic and abelian functions. Yet he was also the first at Göttingen to lecture on Galois theory. Around this time, he became one of the first to understand the fundamental importance of the notion of groups for algebra and arithmetic.
In 1858, he began teaching at the Polytechnic in Zürich (today ETH Zürich). When the Collegium Carolinum was upgraded to a Technische Hochschule (Institute of Technology) in 1862, Dedekind returned to his native Braunschweig, where he spent the rest of his life, teaching at the Institute. He retired in 1894, but did occasional teaching and continued to publish. He never married, instead living with his unmarried sister Julia.
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