Richard Dedekind: An Algebraic Foundation for Calculus.
In 1858, while giving lectures on differential calculus, mathematician Richard Dedekind noted the lack of a truly scientific foundation of the arithmetic with which he taught his class. Realizing this flaw, Dedekind was motivated to improve matters in the foundations of the calculus. Dedekind made a number of highly significant contributions to mathematics and his work would change the style of mathematics into what is familiar to us today. One remarkable piece of work was his redefinition of irrational numbers in terms of "Dedekind cuts-. His work on mathematical induction, including the definition of finite and infinite sets, and his work in number theory, particularly in algebraic number fields, is also of major importance.
Julius Wilhelm Richard Dedekind was born October 6, 1831 in Brunswick, in what is today the country of Germany. The youngest of four children, his father was a professor at the Collegium Carolinum, and his mother the daughter of a professor at the same school. Dedekind attended school in Brunswick at the Gymnasium Martino-Catharineum from the age of seven. Early on, Dedekind was very interested in physics, however, he began to lose interest and became dissatisfied with the subject, as he judged it to have an imprecise logical structure; his attentions turned towards mathematics. He entered the Collegium Carolinum, an educational institution between the academic high school and the university level, at the age of 16. There he received a good understanding of basic mathematics, studying differential and integral calculus, analytic geometry, and the foundations of analysis. He entered the University of GÖttingen in 1850. .
The lectures he attended and friendships he developed in GÖttingen would shape Dedekind's future endeavors. One professor in particular, Wilhelm Weber, had an inspiring effect on Dedekind through his lectures on experimental physics.