Name: Julius Wilhelm Richard Dedekind (or just Richard Dedekind, since he opted not to use his first two names)
Born: October 6, 1831 (Brunswick, Germany)
Died: February 12, 1916 (Brunswick, Germany)
Most Famous for: Inventing what are now called Dedekind Cuts, which help to construct the set of real numbers.
Also Famous for: Work in abstract group theory and theory of continuity; Galois theory; concepts of rings, units, ideals.
Dedekind, the youngest of four children of a law professor and a daughter of a professor, never married, and lived with his sister Julie for most of his adult life. Dedekind earned his PhD at the University of Göttingen under Karl Gauss, writing his thesis on Eulerian integrals. After graduating, he studied under and closely befriended Peter Dirichlet at the same University, where he remained as a professor until his death. He also attended lectures taught by Bernhard Riemann early in his career.
His invention of Dedekind Cuts is critical because it solves a problem which dated back to the Greeks who, without a proper construction or even definition of irrational numbers at their disposal, refused to believe that √2, the diagonal of a 1x1 square, was an actual number. These findings were published in 1872 in Continuity and Irrational Numbers.
Dedekind wrote several other influential books, among them On the Theory of Algebraic Whole Numbers (where he first introduced the concept of an ideal) and What Are Numbers and What Should They Be? published in 1888. What Are Numbers... deals with the set of natural numbers and treats the formation of arithmetic from a set of axioms. However, these axioms creating the natural numbers are arithmetic are more commonly known as the Peano Postulates, or the Peano axioms, as Giuseppe Peano's publication of 1889 was more widely accepted than Dedekind's.