Tölvísi - A 19th Century Icelandic Textbook in Advanced Arithmetic and Algebra

In 1865, Björn Gunnlaugsson—recently retired after forty years of teaching at Iceland’s sole Latin school—published Tölvísi (“Number Wisdom”), the first Icelandic textbook on advanced arithmetic and algebra. The work closely resembles Danish textbooks by L. Fallesen (1834) and Christian Ramus (1855). It distinguishes itself through a more eloquent style and a particular emphasis on divisibility and the precision of approximations, reflecting Gunnlaugsson’s major scholarly achievement, a geodetic survey that produced the first reliable map of Iceland. Only half of the manuscript was ever printed, and it omitted practical subjects such as ratios, proportions, and interest calculations. The book was never adopted for classroom use. This paper examines the purpose of Tölvísi within its contemporary Icelandic culture.