He is also known for contributions to space geometry, hypercomplex numbers, and criticism of early physical chemistry.

Paul Gordan, an expert in invariant theory was at Leipzig, and Study returned there as Privatdozent.

Study gave a plenary address at the International Congress of Mathematicians in 1904 at Heidelberg[2] and another in 1912 at Cambridge, UK.

[6] Study showed an early interest in systems of complex numbers and their application to transformation groups with his article in 1890.

In the 1993 biography of Cartan by Akivis and Rosenfeld, one reads:[9] In 1985 Helmut Karzel and Günter Kist developed "Study's quaternions" as the kinematic algebra corresponding to the group of motions of the Euclidean plane.

He cites and proves the following theorem of Study: The oriented lines in R3 are in one-to-one correspondence with the points of the dual unit sphere in D3.

In 1905 Study wrote "Kürzeste Wege im komplexen Gebiet" (Shortest paths in the complex domain) for Mathematische Annalen (60:321–378).

Like James Joseph Sylvester, Paul Gordan believed that invariant theory could contribute to the understanding of chemical valence.

In 1900 Gordan and his student G. Alexejeff contributed an article on an analogy between the coupling problem for angular momenta and their work on invariant theory to the Zeitschrift für Physikalische Chemie (v. 35, p. 610).