# Julius Wilhelm Richard Dedekind

# Julius Wilhelm Richard Dedekind

**1831-1916**

**German Mathematician**

Abrilliant mathematician who made significant contributions in set theory, number theory, and mathematical induction, Julius Dedekind was also well known as the editor of the collected works of Peter Dirichlet (1805-1859), Carl Gauss (1777-1855), and Georg Riemann (1826-1866). Dedekind is the father of the "Dedekind cut," a method of representing rational numbers in terms of division into two sets by "cutting" the set of rational numbers with a single real number of value "r."

Dedekind was born in the duchy of Braunschweig, now part of Germany. He was the son of a professor at the Collegium Carolinum, and his mother was the daughter of another professor at Carolinum.

Dedekind's first interest in school was physics, not mathematics. However, the relative lack of rigor and logical structure in physics left him unsatisfied and he quickly turned to mathematics. He entered the Collegium Carolinum at age 16, receiving a solid grounding in basic mathematics, including calculus and analytic geometry. At that time, Carolinum was more an intermediate step between high school and university, so Dedekind left for more advanced studies at the University of Göttingen in 1850.

In spite of the presence of Gauss as a professor, Göttingen was not a hotbed of mathematics at that time. Dedekind took his first advanced course from Gauss in the autumn of 1850, a course in least squares. According to a contemporary, "fifty years later Dedekind remembered the lectures as the most beautiful he had ever heard." As Gauss's last doctoral student, Dedekind finished his dissertation in 1852. However, he realized he still had deficiencies in advanced mathematics, deficiencies he determined to rectify by further study.

In 1854, after two years of study, Dedekind was fully qualified to teach at the university level. He began teaching probability and geometry at Göttingen and, upon Gauss's death the following year, assumed Gauss's chair in the mathematics department. During this time he continued to take classes, mostly from Dirichlet, who quickly became a friend and research collaborator. Later, in 1858, Dedekind was offered a position at the Polytechnikum in Zurich, which he accepted immediately. By 1862 the Collegium Carolinum had been upgraded to university status as the Brunswick Polytechnikum and offered Dedekind a position. Dedekind accepted and moved back to his hometown, never to leave again.

Dedekind continued teaching until his retirement in 1894, receiving high praise for his teaching skills as well as continuing research in mathematics. It was during this time that he edited volumes on the lectures and papers of Riemann, Dirichlet, and Gauss. During this period, too, he developed concepts that helped advance the field of number theory and ring theory.

In addition to these contributions, Dedekind also earned renown for his explanatory style. He was able to express his ideas clearly and understandably so that most mathematicians were able to follow his arguments. This led to faster and more complete acceptance of his ideas than would have been the case otherwise. This, in turn, left a lasting mark on all of mathematics. According to another contemporary, Dedekind contributed "not only important theorems, examples, and concepts, but a whole style of mathematics that has been an inspiration to each succeeding generation."

By the time of his death, Dedekind had received numerous honors for his work, although he retained a deep sense of modesty throughout. He was elected to the Berlin Academy, the Rome Academy, the Académie des Sciences in Paris, and other similar organizations during his life, and received a number of honorary doctorates. Dedekind never married, living with relatives for most of his life. He died at the age of 84 in his native Brunswick.

**P. ANDREW KARAM**

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