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Kurt Hensel was born in the East Prussia in the city then called Königsberg. He studied mathematics in Berlin and Bonn. Among his teachers were Lipschitz, Weierstrass, Kirchhoff, Helmholtz and especially Kronecker. He devoted several years to the editing of Kronecker's collected works. His work followed that of Kronecker in the development of arithmetic in algebraic number fields.
In 1897 the Weierstrass method of power-series development for algebraic functions led him to the invention of the p-adic numbers. Hensel was interested in the exact power of a prime which divides the discriminant of an algebraic number field. The p-adic numbers can be regarded as a completion of the rational numbers in a different way from the usual completion which leads to the real numbers.
His invention led to the development of the concept of a field with valuation which has had a great influence on later mathematics. He was able to use his methods to prove many results in the theory of quadratic forms and number theory.
It was not until 1921 that the potential of the p-adic numbers was demonstrated by Hasse when he formulated the local-global principle. He showed, at least for quadratic forms, that an equation has a rational solution if and only if it has a solution in the p-adic numbers for each prime p and a solution in the reals.
Hensel was a professor at the University of Marburg until his retirement in 1930. From 1901 he was editor of the prestigious and influencial Crelle's Journal.
Texto original por: J J O'Connor and E F Robertson
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| List of References (4 books/articles)
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| A Poster of Kurt Hensel | Mathematicians born in the same country
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| Other references in MacTutor | Chronology: 1890 to 1900 |
| JOC/EFR December 1996 | School of
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