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 (Germany), Switzerland and France.
The same year that he received the Crown Prince's gold medal (Kronprinsens gullmedalje) for his dissertation in pure mathematics, he was awarded a travel and education scholarship to study applied mathematics and machine learning in Germany, Switzerland, and France.