Arngrímur also, however, criticized substantial works such as Cosmographia universalis of the German scholar Sebastian Münster.

The Brevis commentarius de Islandia was reprinted in 1598 in Richard Hakluyt's Principal Navigations of the English Nation.

[3] Through this and other writings–particularly his most important work, the Crymogæa of 1609–Arngrímur became an influential figure, inspiring leading Danish and Icelandic historians of subsequent generations, most prominently Ole Worm.

[4] In his historical writings Arngrímur had access to texts no longer extant, most importantly a large fragment of Skjöldunga saga which was later lost completely.

He also had in his possession for 40 or so years the Hauksbók manuscript, within which the only complete extant version of the Völuspa and the Hervararsaga ok Heidreks is featured, among a number of others.