That same year he received the Crown Prince's gold medal (Kronprinsens gullmedalje) for a dissertation in pure mathematics.

He received a travel and education scholarship in 1861, studying applied mathematics and machine learning in what is now Germany, Switzerland and France.

Gulberg worked at the Royal Frederick University becoming a college fellow in 1867 and received a professorship in applied mathematics in 1869.

This law attracted little attention until, in 1877, Jacobus Henricus van 't Hoff arrived at a similar relationship and experimentally demonstrated its validity.

[5][6] In 1890, he published what is now known as the Guldberg rule, which states that the normal boiling point of a liquid is two-thirds of the critical temperature when measured on the absolute scale.