His father was a teacher at the high school in Strasbourg. Kramp studied at the University of Strasbourg medicine. After that he was in the far outskirts of Strasbourg worked as a traveling doctor to Speyer, Meis home and Homberg and his doctorate in 1786 at the University of Strasbourg.
Kramp tried hard to mathematical methods in medicine. So he published in addition to a variety of medical work in 1793, a work on crystallography. As 1795 France finally taken over the left bank of the Rhine had ( Département de la Roer ), Kramp took a job as a teacher of physics and chemistry at the Cologne Central School. In 1809 he became professor of mathematics at the University of Strasbourg. Since 1817 he was a member of the Paris Academy of Sciences.
His mathematical work concerning, inter alia, the introduction of the term for the faculty. He also worked as Leonhard Euler, Friedrich Bessel, Adrien -Marie Legendre and Carl Friedrich Gauss in their generalization for real numbers. These works are, though similar, regardless of James Stirling and Alexandre- Théophile Vandermonde emerged. At the same time, Louis François Antoine Arbogast worked on the problem of generalization.