1teoría numérica feminine
- König worked on a wide range of topics in algebra, number theory, geometry, set theory, and analysis.
- He corresponded with Gabriel Cramer on mechanics, geometry, probability, number theory and the differential and integral calculus.
- He worked on convex functions, the Laplace transform, number theory and the mathematical theory of genetics.
- Other topics he worked on include algebraic geometry, number theory and integral equations.
- His main research topics were number theory, probability theory and mathematical statistics.