According to the Landnámabók (a book which describes the settlement of Iceland by the Norsemen), he built his house in modern-day Reykjavík and named the city as well. Medieval historian Ari Þorgilsson claimed that Arnarson was the first Nordic settler in Iceland, but Irish monks and hermits lived there before he arrived. He also claimed that the they left because they did not want to live with the newly arrived Norse pagans.