Hermann Hankel
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Hermann Hankel (14 February 1839 – 29 August 1873) was a German
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
. Having worked on
mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...
during his career, he is best known for introducing the Hankel transform and the Hankel matrix.


Biography

Hankel was born on 14 February 1839 in Halle,
Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...
. His father, Wilhelm Gottlieb Hankel, was a physicist. Hankel studied at Nicolai Gymnasium in Leipzig before entering Leipzig University in 1857, where he studied with Moritz Drobisch, August Ferdinand Möbius and his father. In 1860, he started studying at University of Göttingen, where he acquired an interest in function theory under the tutelage of
Bernhard Riemann Georg Friedrich Bernhard Riemann (; ; 17September 182620July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the f ...
. Following the publication of an award winning article, he proceeded to study under Karl Weierstrass and
Leopold Kronecker Leopold Kronecker (; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, abstract algebra and logic, and criticized Georg Cantor's work on set theory. Heinrich Weber quoted Kronecker as having said, ...
in Berlin. He received his doctorate in 1862 at Leipzig University. Receiving his teaching qualifications a year after, he was promoted to an associate professor at Leipzig University in 1867. At the same year, he received his full professorship in University of Erlangen–Nuremberg and spent his last four years in University of Tübingen. He died from an illness on 29 August 1873 in Schramberg, near Tübingen. He was married to Marie Hankel. In 1867, he published ''Theorie der Complexen Zahlensysteme'', a treatise on complex analysis. His works on the theory of functions include 1870's ''Untersuchungen über die unendlich oft oscillirenden und unstetigen functionen'' and his 1871 article “Grenze” for the Ersch-Gruber Encyklopädie. His work for '' Mathematische Annalen'' has highlighted the importance of Bessel functions of the third kind, which were later known as Hankel functions. His 1867 exposition on complex numbers and
quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quater ...
s is particularly memorable. For example, Fischbein notes that he solved the problem of products of negative numbers by proving the following theorem: "The only multiplication in R which may be considered as an extension of the usual multiplication in R+ by ''respecting the law of distributivity'' to the left and the right is that which conforms to the rule of signs." Furthermore, Hankel draws attentionSee . to the linear algebra that Hermann Grassmann had developed in his ''Extension Theory'' in two publications. This was the first of many references later made to Grassmann's early insights on the nature of
space Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...
.


Selected publications

* Hermann Hankel (1863)
Die Euler'schen Integrale bei unbeschränkter Variabilität des Argumentes
', Voss, Leipzig. * * Hermann Hankel (1869)
Die Entwickelung der Mathematik in den letzten Jahrhunderten
', Fues, Tübingen. * Hermann Hankel (1870)
Untersuchungen über die unendlich oft oscillirenden und unstetigen Functionen
', Fues, Tübingen. * Hermann Hankel (1874)
Zur Geschichte der Mathematik in Alterthum und Mittelalter
', Teubner, Leipzig. * Hermann Hankel (1875)
Die Elemente der projectivischen Geometrie in synthetischer Behandlung
', Teubner, Leipzig.


Notes


References

*. *. "''Riemann's conditions for integrability and their influence on the birth of the concept of measure''" (English translation of title) is an article on the history of measure theory, analyzing deeply and comprehensively every early contribution to the field, starting from Riemann's work and going to the works of Hermann Hankel, Gaston Darboux, Giulio Ascoli, Henry John Stephen Smith, Ulisse Dini, Vito Volterra, Paul David Gustav du Bois-Reymond and Carl Gustav Axel Harnack.


External links

* * * {{DEFAULTSORT:Hankel, Hermann 1839 births 1873 deaths 19th-century German mathematicians German historians of mathematics German mathematical analysts Complex analysts People from Halle (Saale) People from the Province of Saxony University of Göttingen alumni Humboldt University of Berlin alumni Leipzig University alumni Academic staff of Leipzig University Academic staff of the University of Erlangen-Nuremberg Academic staff of the University of Tübingen Mathematicians from the Kingdom of Prussia