Viggo Brun

Viggo Brun (born October 13, 1885 in Lier , † August 15, 1978 in Drøbak ) was a Norwegian mathematician.

Life

Brun was the youngest of ten children of an artillery captain. He studied mathematics and science at the University of Oslo to become a teacher and passed the teachers' state examination in 1909. He never received a doctorate. In 1910 he traveled a few months at his own expense to the University of Göttingen , where he heard David Hilbert and Edmund Landau . From 1910 to 1915 he received research grants in Oslo. He was unable to take up a travel grant to Paris in 1914 because of the First World War, and instead stayed in Drøbak near Oslo. In between he also did his military service. From 1920 he was Axel Thue's assistant for applied mathematics at the university. In 1923 he was appointed professor at the Norwegian Technical University in Trondheim . He stayed there until 1946, when he became a professor at the University of Oslo, which he remained until his retirement in 1955.

His main achievement was an improvement of the Sieve of Eratosthenes in Legendre's version. This enabled him to make progress in Goldbach's conjecture and in the conjecture of an infinite number of prime twins . Brun is thus the real originator of the sieving methods that are important in analytical number theory .

One of his conclusions was the proof that there are an infinite number of natural numbers n, so that n and n + 1 near prime numbers are at most ninth order, i.e. have a maximum of nine prime factors. Another consequence was the theorem that all sufficiently large even natural numbers can be written as the sum of two near-primes at most ninth order.

His theorem that the sum of the reciprocal of all prime twins converges, that this sum is calculable and that its value, Brun's constant , is known and even very small (1.902160583104 ...) has occasionally been called the Brunscher joke . The mathematical joke lies in the fact that, despite Brun's precise result, the really interesting question of whether there are infinitely many prime twins remains open (and the affirmative conjecture has not yet been proven). The sum of the reciprocal values ​​of all prime numbers is divergent, from which it follows that there are infinitely many ( Leonhard Euler ).

A multi-dimensional generalization of the Euclidean algorithm also comes from Viggo Brun and was used by him in music theory (development of tone scales).

Brun also dealt with the history of mathematics and wrote the books (in Norwegian) “Arithmetic Art in Old Norway”, 1962, and “Everything is Number - Mathematical History from Antiquity to the Renaissance”, 1964. He also found one after submitting it to the Paris Academy der Wissenschaft 1826 lost manuscript by Niels Henrik Abel in Florence.

In 1966 he received an honorary doctorate from the University of Hamburg .

Atle Selberg is one of his students .

literature

• Viggo Brun: Rain art i det gamle Norge. Fra Arilds tid til Abel. Oslo [ua]: Universitätsverlag, 1962.
• Viggo Brun: Old he tall. Matematikkens historie i oldtid and middelalder. Oslo [ua]: Universitätsverlag, 1964. Also under the title Alt er tall. Matematikkens historie fra oldtid til renessanse. Oslo [around 1994].
• H. Halberstam and H.-E. Richert : Sieve methods . Academic Press 1974, ISBN 0-12-318250-6 . (with a depiction of Bruns Sieb)
• CJ Scriba : Viggo Brun . Historia Mathematica 7 (1980) 1-6.

Web links

• CJ Scriba: In memory of Viggo Brun . Mitt. Math. Ges. Hamburg 11 (1985) 271-290.
• CV (Norwegian)

Individual evidence

1. ↑ Brun: About Goldbach's law and the number of prime number pairs , Archive for Math. Og Naturvid. B, Volume 34, 1915, No. 8
2. ↑ Bull. Sci. Math., Volume 43, 1919, pp. 100, 124 (in French)
3. ^ Brun: Euclidean algorithms and musical theory , L'enseignement mathematique, Volume 10, 1964, pp. 125-137