Richard Dedekind

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 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.

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.

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.