| Summary: | Björn Gunnlaugsson (1788–1876) was a remarkable product of the Enlightenment movement in Iceland. He was never admitted to a school, but learnt mathematics by himself and from his tenant-farmer father before he entered the University of Copenhagen, where he twice won its gold medal. He taught mathematics for forty years and made valuable geodetic measurements as a basis of a map of Iceland. He wrote about various astronomical topics, and published his first book on mathematics at the age of 77. The book, which is the main subject of this paper, reveals his devotion and genuine knowledge of mathematics, and his philosophical and religious attitude towards mathematical concepts, structure and conventions. In order to clarify his way of thought, several topics will be explored: zero and infinity, divisibility, exponential laws and imaginary numbers. Peer reviewed
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