Hermann Hankel

Hermann Hankel ( born February 14, 1839 in Halle ( Saale), † August 29 1873 in Schramberg ) was a German mathematician.

Life

In 1867 he became an associate professor in Leipzig, but received in the same year a reputation as a full professor in Erlangen. There he married Marie dippe and went in 1869 to a professorship in Tübingen, where the passionate academic teachers hoped for more students. He reformed the local mathematical teaching and devoted himself intensively to teaching.

In his " principle of the permanence of formal laws " ( 1867) and his " theory of the complex number systems " (1867 ) he examined algebras as the complex, real numbers, quaternions and the structures used in the geometry of algebraic systems of Mobius and Hermann Günther Grassmann, whose meaning he recognized as one of the first. These studies were designed to be a precursor to a textbook on complex analysis, but that he could not accomplish. It appeared only in 1870 a book on real functions, which builds on the appropriate examinations Riemann. His lectures on projective geometry were published after his death.

Special cylinder functions, the Hankel functions are named after him, as is the Hankel transform studied by him. Further work concerning the Riemann integration theory.

In the summer of 1872 he fell ill with meningitis, in which he nearly died. After he had always assumed already in his other works and the historical side of the topic, and after his active career as a research mathematician planned the writing of a larger work on mathematics history, he gave up request in a book published in 1874, an initial attempt. But the work is unfinished, because he again became seriously ill and on a vacation trip in the Black Forest died of a stroke.

Works

Besides the above mentioned books:

• The Eulerian integrals with unlimited variability of the argument habilitation dissertation, in Commission at Leopold Voss, Leipzig 1863
• A contribution to the assessment of the science of ancient Greece, German Quarterly Volume 4, 1867, p.120 -155
• Theory of complex number systems ( Lectures on the complex numbers and their functions, Part 1), Leopold Voss, Leipzig, 1867
• The development of mathematics in the last few centuries. L. Fr Fues'sche range bookstore, Tübingen, 1869
• The cylinder functions of the first and second type, Mathematische Annalen, 1869, S.467, online here:
• Studies on the infinite number of times oscillierenden and discontinuous functions. Tübingen 1870
• On the history of mathematics in antiquity and the Middle Ages. Teubner, Leipzig, 1874.
• Axel Harnack ( eds): The elements of projective geometry in synthetic treatment. Lectures, B. G. Teubner, Leipzig 1875
• Article gravity limit, Lagrange's theorem ( equation theory ) in Ersch, Gruber ( ed.) " General Encyclopedia of Sciences and Arts ', 1818 ff online here: Product gravitational