Georg Mohr was educated by his parents and learnt enough mathematics from them to want to study further. He went to Holland intending to study mathematics under Huygens. He also studied in France and England.
Mohr was little known as a mathematician. His book Euclides danicus published in 1672 was forgotten about until discovered in a bookstore in 1928. Perhaps no copies were ever sold!
The book contains the theorem and its proof that all Euclidean constructions can be carried out with compasses alone. Mascheroni, who is credited with this result, did not prove it until 125 years after Mohr's book was published.
Mohr spent part of his life in Holland and part in Denmark. He fought in the Dutch-French wars around 1672 and was a prisoner of war. He was back in Denmark around 1681 but, having decided not to accept a post as supervisor of the king's shipbuilding, he returned to Holland in 1687.
He corresponded with Tschirnhaus whom he had met on several occasions in Holland, France and England. In 1695 Mohr accepted a job from Tschirnhaus. Mohr also corresponded with Leibniz.