At 17 he entered the Cathedral School in Skálholt, then three years later, in 1683, went to Denmark (with his father, who was part of a trade lobbying contingent)[1] to study at the University of Copenhagen.

There he earned the degree of attestus theologiæ after two years, and also became an assistant to the Royal Antiquarian, Thomas Bartholin, helping him prepare his Antiquitates danicæ and transcribing, translating, and annotating thousands of pages of Icelandic material.

[1][3] When he returned to Denmark, he resumed working for Moth but in 1697 was also appointed secretary at The Royal Secret Archives (Det Kongelige Gehejmearkiv).

[4][5] With vice-lawman Páll Vídalín, he was assigned by King Frederick IV of Denmark to survey conditions in Iceland; this took ten years, from 1702 to 1712, most of which time he spent there.

[1] However, the mission as set out by the King was extremely broad, including investigating the feasibility of sulphur mining, assessing the fisheries, and auditing the administration of justice.

Complaints of judicial abuse poured in, and officials were incensed by the two men's inquiries into past court cases and in turn complained to Copenhagen about them.

It is likely that this started with Bartholin, who, when he had to return to Iceland temporarily in 1685 because his father had died, ordered him to bring back every manuscript he could lay hands on, and then sent him to Norway and Lund in 1689–90 to collect more.

His house burned down in the Copenhagen fire of 1728; with the help of friends, he was able to save most of the manuscripts, but some things were lost, including almost all the printed books and at least one unique item.

In particular, he considerably helped Þormóður Torfason, the Royal Historian of Norway, in preparing his work for publication,[12] having first made his acquaintance when he travelled there for Bartholin,[1] and the second edition of Íslendingabók ever published (in Oxford) is actually substantially Árni's translation and commentary, although Christen Worm is credited as editor.

He lived only a little more than a year after the Copenhagen fire, dependent on friends for lodgings and having to move three times; the winter was harsh and when he fell ill, he had to have assistance to sign his will.

[citation needed] The character Arnas Arnæus in Nobel Prize-winner Halldór Kiljan Laxness's novel Iceland's Bell (Íslandsklukkan) is based on him; the novel concerns the manslaughter case against Jón Hreggviðsson, a farmer whose conviction was eventually reversed in part due to Árni and Vídalín's investigations.