Julius Dedekind German mathematician Date of Birth: 06.10.1831 Country: Germany

Biography of Julius Dedekind

Julius Wilhelm Richard Dedekind was a German mathematician known for his work in abstract algebra and the foundations of real numbers. He was born in Braunschweig, Germany, as the youngest of four children in the family of Julius Levin Ulrich Dedekind, a professor of law and education. Despite being named Julius Wilhelm, he never referred to himself as such.

Dedekind spent most of his life in Braunschweig, where he was born, grew up, and eventually passed away. His life was not eventful, except for his contributions to the field of mathematics. In 1848, he enrolled in Collegium Carolinum in Braunschweig, where his father served as the director. It was here that he studied the foundations of mathematics.

In 1850, Dedekind entered the University of Göttingen, the leading and oldest university in Lower Saxony, where he attended a number theory course taught by Professor Moritz Stern. At that time, Carl Friedrich Gauss, who worked at the University of Göttingen, was teaching an introductory course, and Dedekind became his last student. Among his university friends was Bernhard Riemann. In 1852, at the age of 21, Dedekind obtained his doctoral degree for his dissertation on Euler's integral theory. However, he later acknowledged that this work did not fully showcase his talent.

Recognizing that the Berlin University was a hub of mathematical research, Dedekind moved to Berlin and studied there for two years alongside Riemann. He then returned to Göttingen and, as a Privatdozent, taught courses on probability theory and geometry. In 1855, Gauss passed away, and Dedekind's chair was occupied by Dirichlet, with whom Dedekind developed a close friendship that had a profound influence on him. Dedekind later wrote that Dirichlet made him a "new person." They worked together until Dirichlet's death in 1859.

Initially, Dedekind focused on elliptic and Abelian functions. He was the first in Göttingen to teach Galois theory and introduced the concept of fields proposed by Galois into wide usage. In 1858, Dedekind began teaching at the Eidgenössische Technische Hochschule Zürich (ETH Zurich). In 1859, together with Riemann, he made a trip to Berlin, where they met with Weierstrass, Kummer, and other prominent mathematicians of the Berlin school. When Collegium Carolinum transformed into the Technische Universität Braunschweig in 1862, Dedekind returned to his hometown of Braunschweig and spent the rest of his life teaching at the institution.

In 1894, Dedekind retired but continued to occasionally give lectures and publish. He never married and lived with his unmarried sister, Julia. Dedekind was elected to the Berlin Academy (1880), the Accademia dei Lincei in Rome, and the French Academy of Sciences (1900). He received honorary doctorates from the universities of Oslo, Zürich, and Braunschweig. In 1871, Dedekind generalized the theory of polynomials and algebraic numbers, introducing abstract algebraic structures such as rings, ideals, and modules. Together with Kronecker, he developed the general theory of divisibility. Dedekind's research was published as an appendix to Dirichlet's "Number Theory." Some biographers believe that this book, published after Dirichlet's death, was actually written by Dedekind. The level of generality in his results, applicable to various areas of mathematics, further stimulated the development of abstract algebra, a foundation that was completed by Emmy Noether.

In 1871, Dedekind met Georg Cantor. Their acquaintance blossomed into a lifelong friendship and collaboration. Dedekind became one of the early supporters of Cantor's set theory, and many of his works served as tangible examples of applying the new methods. Dedekind also innovatively employed an axiomatic approach in describing new abstract mathematical concepts. In 1888, he proposed the first version of axiomatic system for the natural numbers. A year later, Peano proposed a similar (slightly simplified) system of axioms, which became known as Peano's axioms. In the early 20th century, the axiomatic method was fully embraced by the Hilbert school as the foundation of mathematics.

Alongside Weierstrass, Dedekind laid the foundations of the theory of real numbers in 1876. While Weierstrass used the formal decimal notation as a model for real numbers, Dedekind proposed a different approach based on "Dedekind cuts" of rational numbers. Modern courses on mathematical analysis often present Dedekind's theory.

Dedekind served as an editor for posthumous editions of selected works by Dirichlet, Gauss, and Riemann.