Neth has worked mainly in group theory and combinatorial geometry. He has also made important contributions to the theory of polytopes and regular polyhedra, as well as to graph theory. In particular, he is known for developing the notion of the "staircase polytope", which is a polytope whose faces are simpler staircase polytopes.
Neth taught mathematics at the University of Tübingen for over thirty years, from 1962 until his retirement in 1995. He was also a member of the Heidelberg Academy of Sciences and received numerous honors for his contributions to mathematics, including the Leibniz Prize of the Deutsche Forschungsgemeinschaft in 1987.