Cortes de richard dedekind biography

Among other things, he provides a definition independent of the concept of number for the infiniteness or finiteness of a set by using the concept of mapping and treating the recursive definition, which is so important to the theory of ordinal numbers. Dedekind's brilliance consisted not only of the theorems and concepts that he studied but, because of his ability to formulate and express his ideas so clearly, he introduced a new style of mathematics that been a major influence on mathematicians ever since.

As Edwards writes in [ 12 ] :- Dedekind's legacy Many honours were given to Dedekind for his outstanding work, although he always remained extraordinarily modest regarding his own abilities and achievements. References show. Biography in Encyclopaedia Britannica. Geburtstag Braunschweig, R Dedekind, Gesammelte mathematische Werke Braunschweig, L Corry, Eudoxus' theory of proportions as interpreted by Dedekind Spanish , Mathesis 10 1 , 1 - Exact Sci.

H M Edwards, Dedekind's invention of ideals, Bull. London Math. H M Edwards, The genesis of ideal theory, Arch. Exact Sciences 23 , - Histoire Sci. Geburtstag, Mitt. H Niederreiter, Richard Dedekind and the development of the theory of finite fields, Abh. H Stein, Eudoxos and Dedekind : on the ancient Greek theory of ratios and its relation to modern mathematics, Synthese 84 2 , - Additional Resources show.

Honours show. Dedekind's theorem [2] states that if there existed a one-to-one correspondence between two sets, then the two sets were "similar". He invoked similarity to give the first precise definition of an infinite set : a set is infinite when it is "similar to a proper part of itself," in modern terminology, is equinumerous to one of its proper subsets.

Dedekind edited the collected works of Lejeune Dirichlet , Gauss , and Riemann.

Cortes de richard dedekind biography

Dedekind's study of Lejeune Dirichlet's work led him to his later study of algebraic number fields and ideals. Although the book is assuredly based on Dirichlet's lectures, and although Dedekind himself referred to the book throughout his life as Dirichlet's, the book itself was entirely written by Dedekind, for the most part after Dirichlet's death.

The and editions of the Vorlesungen included supplements introducing the notion of an ideal, fundamental to ring theory. The word "Ring", introduced later by Hilbert , does not appear in Dedekind's work. Dedekind defined an ideal as a subset of a set of numbers, composed of algebraic integers that satisfy polynomial equations with integer coefficients.

The concept underwent further development in the hands of Hilbert and, especially, of Emmy Noether. Thus Dedekind can be said to have been Kummer's most important disciple. In an article, Dedekind and Heinrich Martin Weber applied ideals to Riemann surfaces , giving an algebraic proof of the Riemann—Roch theorem. In , he published a short monograph titled Was sind und was sollen die Zahlen?

He also proposed an axiomatic foundation for the natural numbers, whose primitive notions were the number one and the successor function. The next year, Giuseppe Peano , citing Dedekind, formulated an equivalent but simpler set of axioms , now the standard ones. Dedekind made other contributions to algebra. For instance, around , he wrote the first papers on modular lattices.

Retrieved Aug. London Math. The First Moderns. Chicago: University of Chicago Press. ISBN Frege, Dedekind, and Peano on the foundations of arithmetic. Assen, Netherlands : Van Gorcum. The Search for Mathematical Roots Princeton Uni. There is an online bibliography of the secondary literature on Dedekind. Also consult Stillwell's "Introduction" to Dedekind Mathematics Encyclopedia.

Hellenica World - Scientific Library. Richard Dedekind. Work While teaching calculus for the first time at the Polytechnic, Dedekind came up with the notion now called a Dedekind cut German: Schnitt , now a standard definition of the real numbers. External links O'Connor, John J. Also consult Stillwell's "Introduction" to Dedekind Contents move to sidebar hide.

Article Talk. Read Edit View history. Tools Tools. Download as PDF Printable version. In other projects. Wikimedia Commons Wikiquote Wikisource Wikidata item. German mathematician — For other uses, see Dedekind surname. Braunschweig , Duchy of Brunswick. Braunschweig , German Empire. Life [ edit ]. Work [ edit ]. Bibliography [ edit ]. See also [ edit ].

Notes [ edit ]. Remarkable Mathematicians. Cambridge University Press. ISBN Oxford University Press.