| Life | Work | Mathematics | Bibliography | Back to the front page Work Milena Hering
Riemann did a lot of work in the theory of complex functions in his PhD
thesis. So he derived the Cauchy-Riemann equations ([Werke, p.6]) and the
Riemann mapping
theorem and developed the idea of a Riemann surface and multiple planes.
The Riemann Hypothesis, which he statet in ``Über die Anzahl der
Primzahlen unter einer gegebenen Grösse", Monatsberichte der Berliner
Akademie, November 1859, about the zero roots of the He also constructed the Riemann integral and found a necessary and a sufficient condition for a function to be integrable. [Katz]
|
is
not solved yet. In his
Habilitationsvortrag: ``Uber die Hypothesen, welche der Geometrie
zugrundeliegen" (first published in 1867 in Göttingen), he developed
the
notion of an n-dimensional
manifold and tried to set a metric upon it. In this context he
constructed the
Riemannian normal coordinates.