**Hensel** invented the *p*-adic numbers, an algebraic theory which has proved important in later applications.

- Schellbach was an outstanding teacher of mathematics and with such a talented pupil he was soon able to give Hensel a deep love of the subject in addition to a sound technical knowledge.
- Hensel's studies were in Berlin and Bonn.
- It was Kronecker who was the greatest influence on Hensel and supervised his doctoral studies at the University of Berlin.
- Hensel submitted his thesis "Arithmetische Untersuchungen über Diskriminaten und ihre ausserwesentlichen Teiler" Ⓣ(Arithmetic research on discriminants and their non-essential factors) to Berlin in 1884 and he continued to work there, submitting his habilitation thesis and becoming a privatdozent in 1886.
- Kurt Hahn is known in Scotland as the founder (in 1934) of the internationally famous Gordonstoun School, near Elgin in the north east of the country, and known in Germany for his school at Salem.
- Hensel was appointed to a full professorship at the University of Marburg in 1901.
- Note that, remarkably, these dates span Hensel's career almost exactly, with the first volume appearing in the year between his doctorate and his habilitation, and the last volume appearing in the year he retired.
- Two other major volumes edited by Hensel were also devoted to Kronecker's works.
- In addition Hensel wrote a eulogy for Kummer "Gedächtnisrede auf Ernst Eduard Kummer" Ⓣ(Memorial address on Ernst Kummer) and we noted above that in fact Kummer was a distant relation.
- Hensel's work followed that of his doctoral supervisor Kronecker in the development of arithmetic in algebraic number fields.
- Hensel was interested in the exact power of a prime which divides the discriminant of an algebraic number field.
- This fact had already been pointed out in articles of Kronecker (who supervised Hensel's doctorate) and of Dedekind and Heinrich Weber, which had been published in 1881 and 1882, respectively, the paper of Kronecker based on a then unpublished manuscript from the year 1858.
- Hensel's invention led to the development of the concept of a field with valuation which has had a great influence on later mathematics.
- It was extremely fortunate for both Hasse and for Hensel that that they came to work together.
- In 1913 Hensel published a book on number theory.
- The first book that Hensel wrote was a joint collaboration with Georg Landsberg.
- Another book of major importance was Hensel's "Theorie der algebraischen Zahlen" Ⓣ(Theory of algebraic numbers) published in 1908.
- He continued to develop his theory in another book "Zahlentheorie" Ⓣ(Number theory) published in 1913, the book which was mentioned in Hasse's quote above and the one which led to him becoming Hensel's student.
- From 1901 Hensel was editor of the prestigious and influential Crelle's Journal.
- Hensel died in the summer of 1941, in the middle of World War II.

Born 29 December 1861, Königsberg, Prussia (now Kaliningrad, Russia). Died 1 June 1941, Marburg, Germany.

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Origin Russia

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive