He was a protege of Ludwig Prandtl and is credited as one of the pioneers in the establishment of the scientific discipline known today as compressible flow or gas dynamics.

He was privileged to learn from several of the great minds in these fields, including David Hilbert, Carl Runge, Hermann Minkowski, and Ludwig Prandtl.

[2][4] In particular, Meyer developed the theory for how gases traveling at supersonic speed slow down abruptly through oblique shock waves, and how they accelerate smoothly through what we now call a Prandtl–Meyer expansion fan.

[1] Prandtl first showed images of such flows captured by Schlieren photography,[5] then the underlying theory appeared in Meyer's Ph.D. dissertation,[6] hence the present terminology for the Prandtl–Meyer function and the Prandtl–Meyer expansion fan.

By the time of his death at almost age 90 in 1972, not even his family or his neighbors in Bad Bevensen, Germany were aware of the formative role he had played, with Ludwig Prandtl, in the scientific discipline known as compressible flow or gas dynamics.