His further work was supervised by the head of the chair of applied mathematics of the University of Dorpat Anders Lindstedt.
In a report to the Faculty of Physics and Mathematics of the University of Dorpat Lindstedt acknowledges Molien as having unquestionably exceptional scientific talent (unzweifelhaft ungewöhnliche wissenschaftliche Begabung).
He also attended lectures of Carl Neumann, Eduard Study, Wilhelm Killing and Georg Scheffers.
At that time Klein was dealing with deep problems of algebra and theory of functions of a complex variable.
The obtained results he submitted to the Faculty of Physics and Mathematics of the University of Dorpat as a master thesis titled "Ueber die lineare Transformation der elliptischen Functionen".
On 30 September 1892, Molien defended his dissertation, also titled "Über Systeme höherer komplexer Zahlen".
In 1894 French mathematicians awarded him a golden medal dedicated to the seventieth birthday of Charles Hermite.
Since the University of Dorpat had only one professorship in pure mathematics, Molien had to stay for years at docent's position.
Only in December 1900 Molien was given a professor's position, but not in Dorpat, but in the starting Tomsk Technological Institute in Siberia.
He was one of the strongest chess players in Dorpat and was particularly known for his blindfold play (Ken Whyld, personal communication, 1995).
He knew German, Estonian, French, Swedish already before he entered gymnasium where he learned Greek, Hebrew, Latin, English, Italian.