He attended the Kreuzschule in Dresden and studied medicine at the University of Leipzig with Ernst Leberecht Wagner from 1866 till 1870, when he received his doctorate in pathology.

As a ship's physician on the New York Line 1872/73 he examined seasickness – his works were classified by Prof. Gavingel of Le Havre as the first scientific study on this topic at all.

His investigations in Schneeberger Bergkrankheit, responsible for the commonly early death of miners in the Ore Mountains, are credited as the first unveiling of working conditions as cause of an interior disease (lung cancer).

Hesse's wife, Angelina Fannie, noticed that the jams and jellies that she made using agar-agar did not melt in the hot summer weather.

Hesse found that the mixture of nutrients and agar-agar remained solid up to 140 degrees Fahrenheit, and passed the recipe on to Koch who used it successfully in his work.