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Matiyasevich’s theorem
- In 1970, he proved that Hilbert’s tenth problem, one of the challenges posed by David Hilbert in 1900, has no solution (building upon the work of Martin Davis, Hilary Putnam and Julia Robinson). This is now known as Matiyasevich’s theorem or the MRDP theorem.
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Richard Dedekind was a German mathematician who developed a major redefinition of irrational numbers in terms of arithmetic concepts. Although not fully recognized in his lifetime, his treatment of the ideas of the infinite and of what constitutes a real number continues to influence modern.
- The Editors of Encyclopaedia Britannica
Richard Dedekind (1831 – 1916) was a German mathematician and one of the students of Gauss. He developed many concepts in set theory, and invented Dedekind cuts as the formal definition of real numbers.
Richard Dedekind's major contribution was a redefinition of irrational numbers in terms of Dedekind cuts. He introduced the notion of an ideal in Ring Theory.
In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily unique up to the order of the factors.
Richard Dedekind (1831-1916) It is widely acknowledged that Dedekind was one of the greatest mathematicians of the nineteenth-century, as well as one of the most important contributions to number theory and algebra of all time.
In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζ K (s), is a generalization of the Riemann zeta function (which is obtained in the case where K is the field of rational numbers Q).
Modern algebra - Ring Theory, Geometry & Group Theory: In another direction, important progress in number theory by German mathematicians such as Ernst Kummer, Richard Dedekind, and Leopold Kronecker used rings of algebraic integers.
