Only after the end of the Napoleonic Wars could Björn travel to Denmark and enrolled in 1817 at the University of Copenhagen, where he studied theology and mathematics.

The abstract thoughts of this gentle learned man were beyond the grasp of most of his compatriots, who regarded him as an eccentric with few of the practical skills they so highly valued.

[12] The only studied mathematician in Iceland in the 19th century, Björn was isolated from the academic community in Europe, and the intellectual environment made him turn to didactics and the applications of mathematics, and also to philosophy.

He did not lay a new baseline but started from the earlier coastal surveys the Danish Navy had undertaken in the period of 1774 to 1818,[14] extending the triangulation inland.

Olaf Nikolas Olsen had been appointed as the director of publication; he proposed to publish the map on four sheets, and he probably also defined the scale of 1:480,000 and the conical projection used.

[15] It was an immense work, and Björn realized soon enough that one man alone would not be able to triangulate the whole island in his lifetime, and focused his attention on the inhabited areas.

Yet he managed to survey a good part of the wilderness, too, even if he had to rely on the accounts of the local population in some remote areas.

Björn was well aware of the inaccuracies in some regions; already in 1834, he wrote that one "should neither have too high or too low expectations of the map, nor trust too greatly nor too little in its usefulness or accuracy".

[18] Njóla is a long didactic theological-philosophical poem Björn wrote mostly during his survey travels when the weather did not permit him to work or in the evenings.

[14] The poem begins by describing a night view of the skies, and then introduces the reader to astronomic distances, explaining how long a cannonball shot from the sun would take to reach each of the planets—and then the next star.

[20] He interweaves such physics and mathematics framed as poetry with theological and philosophical musings about the purpose of the universe, the nature of good and evil, and God's intent.