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Richard Dedekind, a student of Gauss, made a number of important advances
in the area of number theory. Completing his formal education at age
21, he spent his life working as a teacher. Unlike most of his contemporaries,
he spent most of his working life teaching at the high school level,
preferring the freedom to develop his theories outside of the realm
of university academics. Dedekind never married, and lived most of his
adult life with one of his sisters. One of Dedekind's most important
works, translated as Continuity and Irrational Numbers, directly addressed
the problems that the irrationals caused in the geometric interpretation
of continuity. The Cantor-Dedekind axiom and the related concept of
the Dedekind 'cut' established that there was a one to one correspondence
between the real numbers and the points on a line segment. Dedekind
also worked extensively in the area of algebraic number fields, with
his results being important to the foundations of ring theory. Later
in his life he gained some note as an editor, publishing editions of
Dirichlet, Gauss, and Riemann's works. He is frequently noted not only
for his ideas, but his delivery, developing a knack for efficiently
communicating complex thoughts to a wide range of people.
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