Bernt Michael Holmboe (1795–1850) and his mathematics textbooks

Abstract

Bernt Michael Holmboe (1795–1850) was the teacher at Christiania Kathedralskole who discovered Niels Henrik Abel's (1802–29) unique skills in mathematics, and who gave him guidance and private tuition. Holmboe was at the Kathedralskole, Oslo, from 1818 until 1826, and after that he was professor at the University of Christiania until his death in 1850. He published the first edition of Abel's complete works in 1839. Holmboe wrote several textbooks, two of them on basic mathematics and three on more advanced mathematics, and he was probably one of the most influential persons in the development of school mathematics in the first half of the nineteenth century in Norway. His presentation of geometry in the books was, however, not without opposition. In 1835, the applied mathematician Christopher Hansteen (1784–1873) wrote a textbook on geometry where he challenged the traditional Euclidean geometry, and he introduced the subject matter in a very non-Euclidean way. The controversy that followed in the newspapers was called later the ‘dispute about parallelism’. The core of it was whether someone in mathematics education should—as in the case of Hansteen—let utilitarian considerations overrule logical deduction and theoretical thinking.