Paul Stäckel studied at Berlin and obtained his doctorate in 1885 working under Kronecker and Weierstrass. He taught in Berlin, Königsberg, Kiel, Hannover, Karlsruhe and Heidelberg.
Stäckel worked on differential equations and applied these to analytic mechanics. He was interested in the existence of solutions of differential equations. Later in life he became interested in set theory and prime numbers.