Bernt Michael Holmboe

Bernt Michael Holmboe

Bernt Michael Holmboe (born March 23, 1795 in Vang , † March 28, 1850 in Christiania ) was a Norwegian mathematician .

His parents were Pastor Jens Holmboe and his wife Cathrine Holst, who had 17 children, nine of whom grew up, including Christopher Andreas Holmboe .

In 1834 he married Nikoline Finkenhagen for the first time. She died five years later. In 1842 he married Ingeborg Thorp, née Hannestad, for the second time.

education

Holmboe grew up in the rectory of Eidsberg, where his father was a pastor. He was first homeschooled with his brothers. In 1810 he came to the Cathedral School in Christiania. In 1814 he began his studies. He was an avid advocate of the voluntary student corps that was to be set up against the Swedes who invaded Norway to enforce compliance with the terms of the Kiel Peace . He passed the final exam with honors. In 1815 he became Amanuensis with the astronomer at the University of Christopher Hansteen , who the following year became professor of applied mathematics and was of great help to someone who could carry out the many astronomical calculations. In addition, he taught at the newly established commercial institute and studied mathematics at home in his free time, as he had already done during his school days.

Didactic concept

Holmboe had studied early on how best to teach math. Unexpectedly, in 1818 he got a job as a mathematics teacher at the cathedral school in Christiania, since this position suddenly became vacant at the end of 1817 under dramatic circumstances. The rector first turned to the younger brother Christopher Andreas, who had also been a student at the cathedral school and had also started his studies in 1814. Both had excelled in mathematics, but the rector thought Christopher Andreas was the better. In the meantime, however, he had started to study languages, so that the offer went to Bernt Michael, who took up the position on New Year's 1818 as an adjunct .

In the same year he was given responsibility for all mathematics lessons at the cathedral school. He made suggestions for the curriculum in the various grades and invited to events in which the teachers could take turns to present their respective subject on the occasion of the annual exams. He believed that the reason students complained that math was "mind-numbing and boring stuff" was that they didn't spend enough time becoming familiar with mathematical symbols. It is these signs that distinguish mathematics from the other sciences. The use of these signs must therefore be practiced, and the teachers must demonstrate their meaning to the pupils through constant repetition in the use of these signs. Such an introduction to mathematics required a systematic presentation by the teacher. If so many felt a disgust for mathematics and could not see the inner relationship between cause and effect in a mathematical formula, it was due to an unsystematic lecture.

He insisted that the students express in words what a formula contains, and vice versa, if the contents of a formula were presented to them in words, they should be able to express that text in mathematical symbols. So when the student saw the formula (a + b) - c = (a - c) + b, he had to be able to say immediately: Instead of subtracting a number from a sum of two other numbers, you can also subtract it from one of the summands and add the other summand to the result. His role model was the mathematical self-taught Joseph-Louis Lagrange . However, because he was self-taught, he was careful with stipulating the best way to teach mathematics. In addition, it was completely new for the time to give the students tasks to be solved independently.

Between 1825 and 1827 he wrote textbooks in arithmetic and geometry . They were in common use for the following decade and appeared in multiple editions. They were very abstract and theoretical. There were very few examples in his geometry textbook, and he considered construction to be a visualization of a concept and not a use of compasses and ruler. The lesson should train the pupil primarily in formal terms, in that he should enable his thinking to reason logically according to strict order.

The dispute with Hansteen

This led to a sharp argument with Christopher Hansteen, who took a completely different approach. It was the first public debate about a textbook in Norway - apart from previous arguments about different catechisms . The great public interest in this dispute lay in the very general debate about the educational goals at the beginning of the 19th century, namely the contrast between classical education as cultural mediation and application-oriented education as a social benefit (new humanists versus realists).

The occasion was a book review by Holmboes about a textbook by Hansteen published in 1835. He found from his teaching practice that the students had learned a certain amount of knowledge, but were not able to apply it. They only have what they have learned by heart, but they do not understand what they have learned at all. Many are not able to cut an angle in half with a pair of compasses and ruler because they have not mastered the use of compasses and rulers. They drew circles freehand "so that they looked more like a potato". You couldn't do geometry like that. He saw a cause in Holboe's purely theoretical textbook, and his own textbook for the level of trigonometry should counteract this. He used watch glasses, tiled stove tubes and corkscrews in his examples and explained in detail the use of compasses and rulers. In his book review, Holmboe declared Hansteen's textbook unsuitable for use in Norwegian grammar schools and made his criticism particularly of the definition of the parallel, which is why the dispute between the two professors was called the "dispute over parallels". This dispute shows, however, that both opponents were not up to date with the scientific knowledge of the time: they were apparently not aware of Lobachevski's or Bolyai's geometric works . But the discussion soon moved away from the parallels to the fundamentals of high school education. Against Hansteen's criticism that one could not do geometry with freely drawn circles, Holmboe objected that his student Niels Henrik Abel had learned mathematics from him and one could not say that its geometry was useless.

Holmboe discovered the mathematical talent of mathematicians Abel and Ole Jacob Broch , both of whom were his students. In 1839 he published the works of Abel.

Professional career

In 1826 Holmboe became lecturer at the university and in 1834 professor of pure mathematics. He was also a teacher of mathematics at the military college from its foundation in 1826 until his death. From 1832 to 1848 he was a member of the supervisory committee for the utility and support companies, which was the first public control authority for the entire insurance industry in the country. In 1844 he was one of the founders of "Den norske Livrenteforening" (Norwegian life insurance company) and in 1847 he became a member of the management of the life insurance company "Gjensidige", which was founded that year by his student Ole Jacob Broch.

A prize is named after Holmboe, "Holmboeprisen", which is awarded every spring by the Norwegian Mathematics Council to mathematics teachers who have excelled in teaching their subject and financed by the Abel Fund. The price is 100,000 NKr. endowed and is shared between the award winner and his school.

Works

• Forsøg paa en Fremstilling af Mathematikens Principer, including af denne Videnskabs Forhold til Philosophien . (Attempt to present the principles of mathematics and their relationship to philosophy) Invitation from the Christiania Cathedral School. 1822.
• Lærebog i mathematics. Første Deel. Indeholdende Indledning til Mathematiken including Begyndelsesgrundene til Arithmetikken (textbook of mathematics. First part, containing an introduction to mathematics with a foundation of arithmetic). 1825.
• Lærebog i mathematics. Andean Deel. Independent Begyndelsesgrundene til geometries. (Textbook of mathematics. Part two, including the basics of geometry) 1827.
• "Kort Fremstilling af Niels Henrik Abels Liv og videnskabelige Virksomhed". (Brief description of the life of Niels Henrik Abel and his scientific achievements) in: Magazin for Naturvidenskaberne . 1829.
• Stereometry. 1833.
• Plan- og sfærisk trigonometry . (Plane and spherical trigonometry) 1834.
• “Om Prof. Hansteens nye Parallellære i hans nye Lærebog i Plangeometrien.” Book review in Morgenbladet 1835 No. 339.
• Gjenmæle Fremdkaldt ved Hr. prof. Hansteens Belysning af min Registration af hans Lærebog i Geometries . (Reply to Prof. Hansteen's discussion of my book review of his textbook in geometry) 1836.
• Tabel over Solens Declination for Aarene 1819-1831, og for Aarene 1835-1848 . Table of the declination of the sun for the years 1819–1831 and the years 1835–1848.
• De evolutione functionum cos. nx et sin. nx, dissertation . 1836. University program for the celebration of the 25th anniversary of the university.

Holmboe also published Abel's mathematical works, which is why he is mainly known.

Remarks

1. ↑ The "Annenexamen" was an Examen philosophicum, an intermediate examination, the passing of which was a prerequisite for further studies for a state examination.
2. ↑ The previous teacher, Hans Peter Bader, hit a student in such a way that he died a few days later. As a result, the students boycotted his classes and the principal had to quickly find a replacement.
3. ↑ “Adjunkt” was a teacher who was professionally trained, but not yet fully trained as a teacher. He was initially an assistant teacher.
4. ↑ "Den norske Livrenteforening" is the oldest Norwegian life insurance company. At first it was a mutual company, but then became a joint stock company under the name "Norske Liv". It merged with "Vesta Liv", which arose from the separation of the damage insurance company "TrygVesta" from the Swedish insurance company "Skandia". Since the merger it has been operating under the name "Livsforsikringsselskapet Nordea Liv Norge AS".
5. ↑ "Gjensidige" is today under the name "Gjensidige Forsikring BA", a mutual insurance company, the largest damage insurer in Norway.

literature

• Arild Stubhaug: “Den inspirerende læreren” in: forskning.no , accessed on February 20, 2019.