On 20 June 1846, Hermes was born in Königsberg, a former German city (presently Kaliningrad, Russia).
On 5 April 1879, Hermes received a doctorate degree and his dissertation was on the "Reduction of the problem of cyclotomy on linear equations (for prime numbers of the form 2m+1)" (German: "Zurückführung des Problems der Kreistheilung auf lineare Gleichungen (für Primzahlen von der Form 2m+1)").
In 1894, Hermes completed his decade-long effort to find and write down a procedure for the construction of the regular 65537-gon exclusively with a compass and a straightedge.
In his maiden speech as the director at the Osnabrück Realgymnasium on 11 April 1899, he praised the concept of duty of the influential philosopher Immanuel Kant, who was also a resident of Königsberg.
He finished with the words "Geduld ist die Pforte der Freude."