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Richard Dedekind was born on October 06, 1831 in Braunschweig, Germany, German, is Mathematician. Richard Dedekind was a German mathematician who became famous for his contributions to the field of abstract algebra,especially the algebraic theory for numbers, the ring theory, and the foundation of real numbers. During the course of his illustrious career he wrote a paper in which he described ‘what numbers actually are and what they should be’. He suggested an analysis of the number theory and defined an infinite set of numbers. Most of his life was spent in Braunschweig where he taught mathematics. Along with his own mathematical works such as formulating the ‘Dedekind’s Theorem’ he also edited the various works of Bernhard Riemann, Carl Gauss and Peter Dirichlet. One of his most notable contributions to the field of mathematics was editing the collection of works carried out by Riemann, Dirichlet and Gauss and publishing them in a single volume. Dedekind was brilliant in not only creating concepts and formulating theories but he was also able to express his ideas concisely and clearly which led to their easy acceptance. His analysis of infinite and real numbers was not given full recognition while he was still alive but became one of the major influences on the field of modern mathematics after his death.

** Richard Dedekind is a member of Scientists**

Who is it? | Mathematician |

Birth Day | October 06, 1831 |

Birth Place | Braunschweig, Germany, German |

Age | 188 YEARS OLD |

Died On | 12 February 1916(1916-02-12) (aged 84)\nBraunschweig, German Empire |

Birth Sign | Scorpio |

Alma mater | Collegium Carolinum University of Göttingen |

Known for | Abstract algebra Algebraic number theory Real numbers |

Fields | Mathematician Philosopher of mathematics |

Doctoral advisor | Carl Friedrich Gauss |

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.

— Edwards, 1983

1848

He first attended the Collegium Carolinum in 1848 before transferring to the University of Göttingen in 1850. There, Dedekind was taught number theory by professor Moritz Stern. Gauss was still teaching, although mostly at an elementary level, and Dedekind became his last student. Dedekind received his doctorate in 1852, for a thesis titled *Über die Theorie der Eulerschen Integrale* ("On the Theory of Eulerian integrals"). This thesis did not display the talent evident by Dedekind's subsequent publications.

1854

At that time, the University of Berlin, not Göttingen, was the main facility for mathematical research in Germany. Thus Dedekind went to Berlin for two years of study, where he and Bernhard Riemann were contemporaries; they were both awarded the habilitation in 1854. Dedekind returned to Göttingen to teach as a *Privatdozent*, giving courses on probability and geometry. He studied for a while with Peter Gustav Lejeune Dirichlet, and they became good friends. Because of lingering weaknesses in his mathematical knowledge, he studied elliptic and abelian functions. Yet he was also the first at Göttingen to lecture concerning Galois theory. About this time, he became one of the first people to understand the importance of the notion of groups for algebra and arithmetic.

1858

In 1858, he began teaching at the Polytechnic school in Zürich (now ETH Zürich). When the Collegium Carolinum was upgraded to a *Technische Hochschule* (Institute of Technology) in 1862, Dedekind returned to his native Braunschweig, where he spent the rest of his life, teaching at the Institute. He retired in 1894, but did occasional teaching and continued to publish. He never married, instead living with his sister Julia.

1863

Dedekind edited the collected works of Lejeune Dirichlet, Gauss, and Riemann. Dedekind's study of Lejeune Dirichlet's work was what led him to his later study of algebraic number fields and ideals. In 1863, he published Lejeune Dirichlet's lectures on number theory as *Vorlesungen über Zahlentheorie* ("Lectures on Number Theory") about which it has been written that:

1879

The 1879 and 1894 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. Ideals generalize Ernst Eduard Kummer's ideal numbers, devised as part of Kummer's 1843 attempt to prove Fermat's Last Theorem. (Thus Dedekind can be said to have been Kummer's most important disciple.) In an 1882 article, Dedekind and Heinrich Martin Weber applied ideals to Riemann surfaces, giving an algebraic proof of the Riemann–Roch theorem.

1880

Dedekind was elected to the Academies of Berlin (1880) and Rome, and to the French Academy of Sciences (1900). He received honorary doctorates from the universities of Oslo, Zurich, and Braunschweig.

1888

In 1888, he published a short monograph titled *Was sind und was sollen die Zahlen?* ("What are numbers and what are they good for?" Ewald 1996: 790), which included his definition of an infinite set. 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.

1900

Dedekind made other contributions to algebra. For instance, around 1900, he wrote the first papers on modular lattices. In 1872, while on holiday in Interlaken, Dedekind met Georg Cantor. Thus began an enduring relationship of mutual respect, and Dedekind became one of the very first mathematicians to admire Cantor's work concerning infinite sets, proving a valued ally in Cantor's disputes with Leopold Kronecker, who was philosophically opposed to Cantor's transfinite numbers.

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