Birthday: October 6, 1831 (Libra)

Born In: Brunswick, Germany

(German Mathematician Known for His Important Contributions to Number Theory, Abstract Algebra and Modern Set Theory)

73

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Also Known As: Julius Wilhelm Richard Dedekind

Died At Age: 84

father: Julius Levin Ulrich Dedekind

mother: Caroline Marie Hanriette Emperius

siblings: Julia

Died on: February 12, 1916

place of death: Brunswick, Germany

Notable Alumni: Collegium Carolinum

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education: University Of Göttingen, Collegium Carolinum, Humboldt University Of Berlin

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Richard Dedekind was born as Julius Wilhelm Richard Dedekind in Braunschweig, a city in northern Germany on October 6, 1831. He never used the names ‘Julius’ and ‘Wilhelm’ when he grew up. He was born, spent the greater part of his life, and ultimately died in Braunschweig, which is sometimes called Brunswick in English.

His father was a lawyer named Julius Levin Ulrich Dedekind who worked as an administrator for the ‘Collegium Carolinum’ at Braunschweig which was a cross between a high school and university.

His mother was Caroline Mare Henriette Emperius, the daughter of a professor who also worked at the ‘Collegium Carolinum’.

Richardwas the youngest of the four children in the Dedekind family and had an elder sister named Julia with whom he lived for the major part of his life. Just like Richard would, she also remained unmarried throughout her life.

He did not have any great interest in mathematics while he was studying from 1838 to 1847 at the school named ‘Gymnasium Martino-Catharineum’ in Braunschweig and found the subjects of physics and chemistry illogical and quite boring.

Though physics and chemistry were the main subjects that he had to study, his lack of interest in them made him take up mathematics as the only subject worth studying and turned to algebra, calculus and analytic geometry while studying at the ‘Collegium Carolinum’in Braunschweig from 1848 to 1850. His years at the ‘Collegium Carolinum’ provided a solid mathematical base which helped him later.

In 1850 he entered the ‘University of Gottingen’ to study mathematics under MoritzA. Stern, G. Ulrich and Carl Friedrich Gauss. He studied ‘number theory’ under Stern and elementary mathematics under Gauss as his last student. He completed his doctoral work under Gauss’s supervision within a period of four semesters and received his doctorate degree from this university in 1852, for the thesis ‘Uber die Theorie der Eulerschen Integrate’ or ‘On the Theory of Eulerian Integrals’.

As most of the research on mathematical problems was carried out at the ‘University of Berlin’ and not the ‘University of Gottingen’, Dedekind went to Berlin and studied in the university for two years. During that period Bernhard Riemann was his contemporary and both of them received ‘habilitation’ in 1854 from the ‘University of Berlin’.

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Richard Dedekind started his career by serving as a ‘Privatdozent’ or ‘unsalaried lecturer’ at the ‘University of Gottingen’ and taught geometry and probability there from 1854 to 1858. While there he became good friends with Peter Gustav Lejeune Dirichlet and studied abelian and elliptic functions as he wanted to strengthen the mathematical knowledge he had.

When Dirichlet was appointed to fill the chair after Gauss died in 1855, Dedekind found that working under him was extremely useful. He attended the lectures on potential theory, theory of numbers, definite integrals and partial differential equations given by Dirichlet and soon became friends with him. His interest in mathematics got a fresh lease of life after carrying out various discussions with Dirichlet.

In 1856 Dedekind became the first person to give a lecture on ‘Galois Theory’ during a course on mathematics that he gave at Gottingen after studying the works of Galois.

In 1858 he became a mathematics teacher at the Polytechnic school in Zurich, later known as ETH Zurich, and taught there for the next five years as a salaried teacher. During this period he derived the concept of the ‘Dedekind Cut or Schnitt’ which has become the standard for defining real numbersand describes how rational numbers are divided into two sets by an irrational number.

In September 1859, Dedekind visited Berlin with Riemann when Riemann was elected to the ‘Berlin Academy of Sciences’ where he met other famous mathematicians including Borchardt, Kummer, Wierstrass and Kronecker.

He returned to Braunschweig in 1862 and took up the job of teaching mathematics at the Technische Hochschule which had been known as ‘Collegium Carolinum’till 1860 and had recently been upgraded.He spent the later part of his career teaching mathematics at this school.

In 1863 he published the lectures given by Dirichlet on the number theory, in the form of a book. His study of the work done by Dirichlet helped him in his studies of the number fields in algebra later.

In 1872 he developed the analysis of irrational numbers and even published a book on his findings.

In 1872 he met Georg Cantor, a fellow mathematician, in the city of Interlaken while holidaying in the Black Forest in Germany. They shared their ideas and agreed to start working together on the set theory which helped Cantor to resolve the disputes he had with Leopold Kronecker who was an opponent of ‘transfinite numbers’ suggested by Cantor. Dedekind and Cantor maintained ties with each other for a long time afterwards.

In 1882 he collaborated with Heinrich Martin Weber to put forward an algebraic proof of the ‘Riemann-Roch Theorem’.

He came out with the short essay ‘Was sind und was sollen die Zahlen’ or ‘What are numbers and what should they be?’ in 1888 which described what an ‘infinite set’ means. In this monograph he suggested that natural numbers had their foundation on axioms, which was verified by Giuseppe Peano who created a set of simpler but equivalent axioms the next year.

Dedekind taught mathematics at the ‘Technische Hochschule’ in Braunschweig till 1894 when he retired from active teaching.

Even after retirement, he kept on writing and publishing various works in the field of mathematics and also took classes occasionally.He published his works on the modular lattices found in algebra in 1900.

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Richard Dedekind published the book ‘’ Vorlesungen über Zahlentheorie’ or ‘Lectures on Number Theory’ in German in 1863 which contained the lectures given by Dirichlet earlier on the subject. The third and fourth editions of this book were published in 1879 and 1894 respectively in which supplements written by Dedekind introduced a notion of groups for arithmetic and algebra which became fundamental to the ring theory. Though the word ‘ring’ was not originally mentioned by Dedekind, it was included later by Hilbert.

He wrote the book ‘Stetigkeit und Irrationale Zahlen’ or ‘Continuity and Irrational Numbers’ in 1872 which made him quite famous in the world of mathematics.

In 1882 he published a paper which he had prepared jointly with Heinrich Weber in which he analyzed the ‘theory of Riemann surfaces’ which proved the ‘Riemann-Roch Theorem’ algebraically.

Richard Dedekind was elected to the ‘Gottingen Academy’ in 1862, the ‘Berlin Academy’ in 1880, and the ‘Academy of Rome’, the ‘Leopoldino-Carolina Naturae Curiosorum Academia’ and the ‘Academie des Sciences’ in Paris in 1900.

The ‘Kristiania University’ in Oslo, the ‘Zurich University ‘and the ‘University of Braunschweig’ awarded him honorary doctorate degrees.

Richard Dedekind remained unmarried and lived at Braunschweig with his unmarried sister Julia.

Throughout his life Dedekind enjoyed good health. The only time that he was seriously ill was during the time his father died which was ten years after he had joined the ‘Technische Hochschule’. He recovered completely from the illness and was never sick again.

He died of natural causes at the age of 84 on February 12, 1916 in his home town Braunschweig, Germany.

Richard Dedekind loved to go on holidays to the Black Forests of Germany, the Austrian Tyrol and Switzerland.

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