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Heinrich Burkhardt studied at the University of Berlin, then at the Univesity of Göttingen and finally at the University of Munich. He obtained his doctorate in 1887 with a dissertation on invariant theory.
Burkhardt was appointed to the post of lecturer at the University of Göttingen then, in 1897, he was appointed to a professorship at the University of Zurich. From Zurich he later moved to a chair at the Technical University of Munich.
His main work was in analysis and the history of mathematics. One of his papers, published in 1888, was Hyperelliptic sigma functions. He published a two volume work Function Theory in 1897 and 1899.
One of Burkhardt's historical works Entwicklungen nach oscillierenden Funktionen und Integration der Differentialgleichungen der mathematischen Physik (1904-8) is rather chaotic, with unconnected textual quotations following each other, but nevertheless it is very useful as a historical source. It includes details of Cauchy's work in a number of different areas.
One of the founders of the Encyclopädie der mathematisches Wissenschaften was Meyer, and Burkhardt collaborated with him as joint author of the article on potential theory which they wrote for the Encyclopädie.
Other topics on which Burkhardt published included groups, differential equations, differential geometry and mathematical physics.
Janiszewski was among the many students that Burkhardt taught.
References elsewhere in this archive:
There is a Crater Burckhardt on the moon. You can see a list of lunar features named after mathematicians.