# Julius wilhelm richard dedekind biography examples

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. By supplementing the geometric method in analysis, Dedekind contributed substantially to the modern treatment of the infinitely large and the infinitely small. Open access to the SEP is made possible by a world-wide funding initiative.

In the summer ofhe qualified, a few weeks after Riemann, as a university lecturer; in the winter semester of — he began his teaching activities as Privatdozentwith a lecture on the mathematics of probability and one on geometry with parallel treatment of analytic and projective methods.

When the Dirichlets were visited by friends from Berlin Rebecca Dirichlet was the sister of the composer Felix Mendelssohn-Bartholdy and had a large circle of friendsDedekind was invited too and enjoyed the pleasant sociability of, for example, the well-known writer and former diplomat, Karl August Varnhagen von Ense, and his niece, the writer Ludmilla Assing.

## Julius Wilhelm Richard Dedekind

Thus, although an instructor, he remained an intensive student as well. His own lectures at that time are noteworthy in that he probably was the first university teacher to lecture on Galois theory, in the course of which the concept of field was introduced. To be sure, few students attended his lectures: Thus Dedekind was the first of a long line of German mathematicians for whom Zurich was the first step on the way to a German professorial chair; to mention only a few, there were E.

##### Dedekind's Contributions to the Foundations of Mathematics

He remained in Brunswick until his death, in close association with his brother and sister, ignoring all possibilities of change or attainment of a larger sphere of activity.

The small, familiar world in which he lived completely satisfied his demands: He did not feel pressed to have a more marked effect in the outside world; such confirmation of himself was unnecessary.

Along with his recreational trips to Austria the Tyrolto Switzer land, and through the Black Forest, his visit to the Paris exposition of should also be mentioned. On 1 April he was made professor emeritus but continued to give lectures occasionally.

Seriously ill infollowing the death of his father, he subsequently enjoyed physical and intellectual health until his peaceful death at the age of eighty-four. He received honorary doctorates in Kristiania now Osloin Zurich, and in Brunswick. In he received numerous scientific honors on the occasion of the fiftieth anniversary of his doctorate. Dedekind belonged to those mathematicians with great musical talent. Both men had a conservative sense, a rigid will, an unshakable strength of principles, and a refusal to compromise.

Each led a strictly regulated, simple life without luxury. Cool and reserved in judgment, both were warm-hearted, helpful people who formed strong bonds of trust with their friends.

Both had a distinct sense of humor but also a strictness toward themselves and a conscientious sense of duty. Averse to any excess, neither was quick to express astonishment or admiration.

Both were averse to innovations and turned down brilliant offers for other professorial chairs. In their literary tastes, both numbered Walter Scott among their favorite authors.

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 Hilbertdoes 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 surfacesgiving an algebraic proof of the Riemann—Roch theorem. Inhe 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 Peanociting Dedekind, formulated an equivalent but simpler set of axiomsnow the standard ones. Dedekind made other contributions to algebra. For instance, aroundhe wrote the first papers on modular lattices. Inwhile on holiday in InterlakenDedekind 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 Kroneckerwho was philosophically opposed to Cantor's transfinite numbers.

Richard Dedekind remained unmarried and lived at Braunschweig with his unmarried sister Julia. Throughout his life Dedekind enjoyed good health. He recovered completely from the illness and was never sick again.

#### Dedekind, (Julius Wilhelm) Richard

He died of natural causes at the age of 84 on February 12, in his home town Braunschweig, Germany. See the events in life of Richard Dedekind in Chronological Order. Nicolaus Copernicus German, Polish. Peter Gustav Lejeune Dirichlet German. Felix Christian Klein German. Pictures of Richard Dedekind.

### Дедекинд, Юлиус Вильгельм Рихард

Lil Wayne United States. When the Collegium Carolinum was upgraded to a Technische Hochschule Institute of Technology inDedekind returned to his native Braunschweig, where he spent the rest of his life, teaching at the Institute. He retired inbut did occasional teaching and continued to publish.

He never married, instead living with his unmarried sister Julia.

### Richard Dedekind

He received honorary doctorates from the universities of Oslo, Zurich, and Braunschweig. Schnittnow a standard definition of the real numbers. The basic idea behind this notion is that an irrational number divides the rational numbers into two classes, with all the members of one class upper being strictly greater than all the members of the other lower class.

For example, the square root of 2 puts all the negative numbers and the numbers whose squares are less than 2 into the lower class, and the positive numbers whose squares are greater than 2 into the upper class. Based on this idea, Dedekind cuts are defined as pairs of such divided classes of rational numbers. Wherever a cut occurs and it is not on a real rational number, an irrational number which is also a real number is created by the mathematician.

This means that every location on the number line continuum contains either a rational or an irrational number. Thus, the Dedekind cuts are considered real numbers.

There are no empty locations, gaps, or discontinuities. Dedekind published his thought on irrational numbers and Dedekind cuts in his paper Stetigkeit und irrationale Zahlen [1] "Continuity and irrational numbers. Note that Dedekind's terminology is old-fashioned: