Lakatos credits von Seidel with discovering, in 1847, the crucial analytic concept of uniform convergence, while analyzing an incorrect proof of Cauchy"son In 1857, von Seidel decomposed the first order monochromatic aberrations into five constituent aberrations. They are now commonly referred to as the five Seidel Aberrations.
The lunar crater Seidel is named after him.
The Gauss–Seidel method is a useful numerical iterative method for solving linear systems
Bavarian Academy of Sciences and Humanities.