# Bernt Michael Holmboe

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

His parents were the priest Jens Holmboe and his wife Cathrine Holst They had 17 children, nine of whom grew up.

In 1834 he married his first wife, Niko Line Finkenhagen. She died five years later. In 1842 he married his second wife Ingeborg Thorp, born Hannestad.

## Training

Holmboe grew up at the vicarage of Eidsberg, where his father was pastor. He was initially taught by his brothers at home. In 1810 he came to the cathedral school in Christiania. In 1814 he began his studies. He was an avid supporter of the student volunteers corps, which should be placed against the Swedes, who marched into Norway to enforce compliance with the conditions of the Kiel Peace. He put the Anne exam with distinction. In 1815 he was amanuensis, was a great help with the astronomers at the University Christopher Hansteen, the professor of applied mathematics it was a year and for someone who could perform the many resulting astronomical calculations. In addition, he taught at the newly established trading institution and studied mathematics in his spare time at home, as he had already operated during school hours.

## Didactic concept

Holmboe had early looks at how mathematics is best to teach. Unexpectedly, he was awarded in 1818 at the Cathedral School in Christiania a job as a mathematics teacher, as this spot became vacant end of 1817 suddenly in dramatic circumstances. The Rector initially turned to the younger brother Christopher Andrew, who had been students at the Cathedral School and had also begun his studies in 1814. Both had distinguished themselves in mathematics, but the rector held Christopher Andrew for the better. However, this had become a language study started, so that the offer now went to Bernt Michael, who took up the post at the New Year 1818 as an adjunct.

In the same year he already was given responsibility for the entire teaching of mathematics at the cathedral. He made suggestions to the curriculum in the various grade levels and invited to events one in which the teacher could take turns to present their respective compartment at the annual examinations. He was convinced that the reason for the complaints of students, mathematics is " mind-numbing and boring stuff ," was that you can not used it enough time to become familiar with the mathematical signs. There are these characters that distinguish mathematics from other sciences. The use of this sign must therefore be practiced, and the teachers would have to show by constant repetition in the use of the marks to students their importance. Such an introduction to the mathematics required a systematic presentation by the teacher. With so many horror of mathematics empfänden and could not recognize the internal relation of cause and effect in a mathematical formula, the lie on a piecemeal lecture.

He insisted that students expressed in words, which includes a formula, and vice versa, if you presented them the contents of a formula in words, they would have this text can play in mathematical characters. If the student so the formula (a b) - c = (a - c ) saw b , he had to be able to say immediately: instead of abstracting a number of a sum of two other numbers, they can also abstract from one of the summands and to the result add the other summands. His model was the self-taught mathematical Joseph -Louis Lagrange. However, this was because he was self-taught, careful with definitions, how they should convey best mathematics. In addition, it was totally new to that time, to give the students tasks to be solved independently.

Between 1825 and 1827 he wrote textbooks in arithmetic and geometry. They were in the following decade in common use, and appeared in several editions. They were very abstract and theoretical. In his textbook on geometry, there were only a very few examples, and constructing he held for a visualization of a concept and not for use by ruler and compass. Teaching should educate the students, especially in the formal sense, by his thinking should enable reasoning closing after strict order.

## The fundamental dispute with Hansteen

This led to a sharp confrontation with Christopher Hansteen, who followed a completely different approach. It was the first public debate on a textbook in Norway - apart from earlier arguments about different catechisms. The significant public interest in this dispute lay in the very general discussion 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 ( Neuhumanisten against realists ).

The occasion was a book review Holmboe to a 1835 published textbook Hansteen. This was from his teaching practice that students indeed had some knowledge crammed, but were not able to apply it. They would have learned by rote ready, but do not understand what they have learned. Many are not in a position to ruler and compass to bisect an angle, because they did not master the use of ruler and compass. They drew circles freehand, " so that they rather resembled a potato ." So one could run no geometry. One reason he saw in Holboes purely theoretical textbook, and his own textbook for the plane trigonometry should counteract this. He used watch glasses, stove pipes and corkscrew in his examples and explained in detail the use of ruler and compass. Holmboe said Hansteen's textbook in his book review for unsuitable for use in Norwegian schools and made his criticism noted in particular on the definition of the parallel, which is why the dispute between the two professors was named as " dispute about parallels ". This dispute, however, shows that both opponents were not at the level of scientific knowledge of the time: The geometric works Lobatschewskis or Bolyai them were not clearly known. But the discussion soon went away from the parallels to the basic upper secondary school education. Counter Hansteen criticism, with freihänig drawn circles one could operate no geometry, he argued that his student Niels Henrik Abel had at least learned from him as mathematics and one can not say that its geometry is useless.

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

## Career

1826 Holmboe lecturer at the University and in 1834 Professor of Pure Mathematics. He also was a teacher of mathematics at the Military College since its founding in 1826 until his death. 1832 to 1848 he was a member of the Supervisory Committee for the supply and support companies, which was the first public control authority for the entire insurance industry of the country. In 1844 he was among the founders of " The norske Livrenteforening " (Norwegian life insurance company ) and 1847 member of the directorate of the life insurance company " Gjensidige ", which was founded this year by his pupil Ole Jacob Broch.

After Holmboe a prize is named, " Holmboeprisen ", which is every spring by the Norwegian Mathematikrat mathematics teachers who have excelled in their field of mediation, awarded and funded by the Abel Fund. The price is 100,000 NKr. doped and is divided between the award winner and his school.

## Works

- Forsøg paa en fremstilling af Mathematikens Principer, including af denne Videnskabs Committed til philosophies. ( Attempt at a presentation of the principles of mathematics, including its relationship to philosophy ) Invitation font of Christiania Cathedral School. 1822.
- Lærebog i Mathematiken. Første Deel. Indeholdende Indledning til Mathematiken including Begyndelsesgrundene til Arithmetikken ( textbook of mathematics. First Part, containing an introduction to the mathematics with a foundation of arithmetic). In 1825.
- Lærebog i Mathematiken. Andes Deel. Indeholdende Begyndelsesgrundene til geometries. ( Textbook of Matemetik. Bridegroom part, including the foundations of geometry) in 1827.
- " Kort fremstilling af Niels Henrik Abel Liv og videnskabelige virksomhed ". (Brief description of the life of Niels Henrik Abel and his scientific achievements ) in: Magazine for Naturvidenskaberne. , 1829.
- Stereometry. In 1833.
- Plan- og sfärisk trigonometry. ( Plane and spherical trigonometry ) 1834.
- "Om Prof. Hansteen nye nye Parallellære i hans Lærebog i plan geometries. " Book review in Morgenbladet 1835 No. 339
- Gjenmæle fremkaldt ved Hr. prof. Hansteen Belysning af min Anmeldelse af hans Lærebog i geometries. (Reply to Prof. Hansteen's discussion of my book review of his textbook on geometry ) in 1836.
- Table over Solens declination for Aarene 1819-1831, og for Aarene 1835-1848. Table of declination of the sun for the years 1819-1831 and the years 1835-1848.
- De evolutione functionum cos. nx et sin. nx, dissertatio. , 1836. University program to hard on the occasion of the 25th anniversary of the founding of the university.

He also gave Abel out mathematical works, which is why he is also known mainly.