Hellenica World

# .

Hermann Hankel (14 February 1839 - 29 August 1873) was a German mathematician who was born in Halle, Germany and died in Schramberg (near Tübingen), Imperial Germany.

Hermann Hankel

He studied and worked with, among others, Möbius, Riemann, Weierstrass and Kronecker.

The 1867 exposition on complex numbers and quaternions 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."[1] Furthermore, Hankel draws attention[2] to the linear algebra that Hermann Grassmann had developed in his Extension Theory in two publications. This attention was the first of many notations later made to Grassmann's early insights on the nature of space.

Hankel matrix/Hankel operator
Hankel function in the theory of Bessel functions
Hankel contour
Hankel transform

References

^ Efriam Fischbein (1987) Intuition in Science and Mathematics, page 99
^ Hankel 1867 page 16

Hermann Hankel (1863) Die Euler'schen Integrale bei unbeschränkter Variabilität des Argumentes, Voss.
Hermann Hankel (1867) Vorlesungen uber die complexen Zahlen und ihre Functionen, Voss.
Hermann Hankel (1869) Die Entwickelung der Mathematik in den letzten Jahrhunderte.
Hermann Hankel (1870) Untersuchungen über die unendlich oft oscillirenden und unstetigen Functionen.
Hermann Hankel (1874) Zur Geschichte der Mathematik in Alterthum und Mittelalter.
Hermann Hankel (1875) Die Elemente der projectivischen Geometrie in synthetischer Behandlung.