He went to Holland in 1662 intending to study mathematics under Huygens. He also studied in France and England before returning to his native Denmark. Mohr was little known in his own day as a mathematician. His book Euclides danicus Ⓣ, published in 1672, was forgotten about until it was discovered in a bookstore in 1928. Perhaps no copies were ever sold! J Hjelmslev wrote a forward to Euclides danicus Ⓣ and republished a German translation in 1928.
The book contains a proof that all Euclidean constructions can be carried out with compasses alone. Seidenberg writes in :-
The book is in two parts: the first consists of the constructions of the first six books of Euclid; the second, of various constructions. The problem of finding the intersection of two lines, which is of some theoretical importance, is solved incidentally in the second part in connection with the construction of a circle through two given points and tangents to a given line. ... In the body of the book Mohr does not state the issue until the very last paragraph ... In the dedication to Christian V, he does say that he believes he has done something new, and on the title page the issue is explicitly stated. Still, it would be easy for an inattentive reader to misjudge the value of the book.Mascheroni, who is credited with proving that all Euclidean constructions can be carried out with compasses alone, did not prove this until 125 years after Mohr's book was published. Mohr proves in the book that a line segment can be divided in golden section with compass alone, and the historical and pedagogical importance of this theorem is discussed by Zühlke in .
Mohr spent part of his life in Holland and part in Denmark. He fought in the Dutch-French wars around 1672 and became a prisoner of war. Mohr corresponded with a number of mathematicians including Leibniz who had received a work written by Mohr on root extraction. It had been sent to him by Oldenburg, the secretary of the Royal Society in London, in 1675 and Leibniz replied to Oldenburg in the following year praising Mohr's skill in geometry and analysis. Mohr was back in Denmark around 1681 but, having decided not to accept a post from King Christian V as supervisor of his shipbuilding, he returned to Holland in 1687. In the same year he married and he had one son who was born around 1692.
He corresponded with Tschirnhaus whom he had met on several occasions in Holland, France and England. In 1695 Mohr accepted the offer of a job from Tschirnhaus and he went to Kieslingswalde, with his wife and son, to take part in Tschirnhaus's mathematical projects.
Mohr's son claimed that his father had written three books on mathematics and philosophy which were all well received. This has led to a certain amount of interest from historians trying to identify the other two books, one of which has been identified (see for example ,  and ). Meyer writes in :-
In "Euclides Curiosus", Georg Mohr in 1673 gave an exposition of the fact that it is possible to do all the Euclidean constructions of the first five books with a straight ruler and a compass with one single opening. We present the history about "Euclides Curiosus" and give all the necessary constructions.The authors of  state some good reasons why the small volume, Gegenübung auf ein mathematisches Tractätlein Compendium Euclidis Curiosi Ⓣ, cannot have been written by Mohr himself (although Mohr is known to be the author of this compendium as we indicated above). Therefore they argue that the Gegenübung cannot be the missing third publication.
Article by: J J O'Connor and E F Robertson