|Known for||Hankel matrix, Hankel function|
|Was||Mathematician Historian Historian of mathematics|
|Type||Academia Mathematics Social science|
|Birth||14 February 1839, Halle (Saale), Germany|
|Death||29 August 1873, Schramberg, Germany (aged 34 years)|
Hermann Hankel (14 February 1839 – 29 August 1873) was a German mathematician who was born in Halle, Germany and died in Schramberg (Black Forest), Imperial Germany. He studied and worked with, among others, Möbius, Riemann, Weierstrass and Kronecker. His 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." Furthermore, Hankel draws attention 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.
Hermann Hankel (1863) Die Euler'schen Integrale bei unbeschränkter Variabilität des Argumentes, Voss, Leipzig. Hermann Hankel (1867) Vorlesungen über die complexen Zahlen und ihre Functionen, 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.