He was known for using what he called the inverse or semi-inverse approach, which applied vector field analysis, to obtain numerous exact solutions of the nonlinear equations of gas dynamics, many of them representing rotational flows of nonuniform total energy.
His work applied geometrical solutions to fluid dynamics.
In continuum mechanics, "Nemenyi's theorem" proves that, given any net of isothermal curves, there exists a five parameter family of plane stress systems for which these curves are stress trajectories.
Nemenyi's five constant theory for the determination of stress trajectories in plane elastic systems, was subsequently proven by later mathematicians.He was the father of the statistician Peter Nemenyi and the probable father of former World Chess Champion Bobby Fischer.