His main work was in astrometry and minor planets, although he published star catalogues and oversaw the production of journals in his later life.
In 1888 he passed Königsberg's state examinations and later in the same year attained a PhD with a thesis titled "Über Lamésche Funktionen mit komplexen Parametern" ("About Lamé functions with complex parameters").
Save for a year's leave to further his studies in Leipzig, Cohn remained at the observatory until 1 October 1909, being promoted to an assistantship in 1898 and becoming a full-time observer in 1900.
In 1893 he also attained the habilitation with a thesis titled "Über die in rekurrierender Weise gebildeten Größen und ihren Zusammenhang mit den algebraischen Gleichungen" ("On Recurring Values and Their Connection with Algebraic Equations"), allowing him to teach astronomy and mathematics at the University of Königsberg, leading to Cohn becoming an associate professor in 1985.
With the number of minor planets rapidly increasing, and the inaccuracies of past observations leading to them being frequently lost, Cohn created a principle under which, with the exception of preliminary computations, all orbits were to have an accuracy of ±15° in longitude.
[5] During this period he also restructured how the Berliner Jahrbuch was to be produced and in its next installment it provided positions for all minor planets passing opposition in the coming year.
[1][5] On 13 June 1913 he was elected an associate of the Royal Astronomical Society and in 1918 he published a paper outlining some practical improvements to the methods of orbit computation.
German astronomers Max Wolf and Gustav Stracke named the minor planet 972 Cohnia in honour of him, saying:[2] Der Planet 972 hat zum Andenken an den verstorbenen Direktor des Astronomischen Rechen-Instituts zu Berlin-Dahlem, Professor F. Cohn, den Namen erhalten.
Bei all seinen wissenschaftlichen Leistungen war der Verstorbene äußerst bescheiden und trat wenig nach aussen hervor, sodass wohl mancher, der ihm zum ersten Male im Leben begegnete, erstaunt gewesen sein wird über so tiefes Wissen und so gründliche Gelehrsamkeit.
In all his scientific achievements the deceased was exceedingly modest and boasted little, so that many who met him for the first time in his life would have been astonished by his profound knowledge.Paul Viktor Neugebauer, who also described Cohn as "socially inclined" and "a most agreeable companion," said the following:[5] He never attempted to influence the work of others, leaving each one free to choose his own line of work, even though these were not in accord with his personal interests.