Harald August Bohr was Jewish, and was born in 1887 to Christian Bohr, a professor of physiology, and Ellen Adler Bohr, a woman from a wealthy Jewish family of local renown. Harald had a close relationship with his elder brother, which The Times likened to that between Captain Cuttle and Captain Bunsby in Charles Dickens‚ Dombey and Son.
Like his father and brother before him, in 1904 Bohr enrolled at the University of Copenhagen, where he studied mathematics, obtaining his masters in 1909 and his doctorate a year later. Among his tutors were Hieronymus Georg Zeuthen and Thorvald N. Thiele. Bohr worked in mathematical analysis; much of his early work was devoted to Dirichlet series including his doctorate, which was entitled Bidrag til de Dirichletske Rækkers Theori (Contributions to the Theory of Dirichlet Series). A collaboration with Göttingen-based Edmund Landau resulted in the Bohr–Landau theorem, regarding the distribution of zeroes in zeta functions.
In 1915 he became a professor at Polyteknisk Læreanstalt, working there until 1930, when he took a professorship at the University of Copenhagen. He remained in this post for 21 years until his death in 1951. Børge Jessen was one of his students there.
In the 1930s Bohr was a leading critic of the anti-Semitic policies taking root in the German mathematical establishment, publishing an article criticising Ludwig Bieberbach’s ideas in Berlingske Aften in 1934.
Bohr was also an excellent football player. He had a long playing career with Akademisk Boldklub, making his debut as a 16 year old in 1903. During the 1905 season he played alongside his brother Niels, who was a goalkeeper. Harald was selected to play for the Danish national football team in the 1908 Summer Olympics, where football was an official event for the first time. Though a Danish side had played at the 1906 Intercalated Games, the opening match of the 1908 Olympic tournament was Denmark’s first official international football match. Bohr scored two goals as Denmark beat the French „B“ team 9–0. In the next match, the semi-final, Bohr played in a 17–1 win againstFrance, which remains an Olympic record to this day. Denmark faced hosts Great Britain in the final, but lost 2–0, and Bohr won a silver medal. After the Olympics he made one further appearance for the national team, in a 2–1 victory against an England amateur team in 1910. His popularity as a footballer was such that when he defended his doctoral thesis the audience was reported as having more football fans than mathematicians.
Bohr was known as an extremely capable academic teacher and the annual award for outstanding teaching at the University of Copenhagenis called the Harald, in honour of Harald Bohr. With Johannes Mollerup, Bohr wrote an influential four-volume textbook Lærebog i Matematisk Analyse (Textbook in mathematical analysis).
Harald Bohr war der Sohn des dänischen Physiologen Christian Bohr, sein Bruder war der Physiker Niels Bohr. Bohrs Forschungsgebiete lagen im Bereich der analytischen Zahlentheorie und der Analysis. Seine Arbeiten beschäftigen sich mit Dirichletreihen, insbesondere studierte er zusammen mit Edmund Landau die riemannsche ζ-Funktion.
Zunächst verfolgte Bohr eine Karriere als Sportler. Er galt neben seiner Fähigkeiten als Wissenschaftler, als einer der besten Fußballer seiner Zeit, war Spieler der dänischen Nationalmannschaft und gewann bei den Olympischen Sommerspielen 1908 die Silbermedaille.
1914 formulierten die beiden das Bohr-Landau-Theorem, welches Aussagen über die Nullstellenverteilung der riemannschen ζ-Funktion macht. Darüber hinaus untersuchte er ausführlich fastperiodische Funktionen und deren Approximierbarkeitseigenschaften.
1915 wurde Bohr Professor an der Polytechnischen Lehranstalt in Kopenhagen, 1930 wurde er an die Universität Kopenhagen berufen. Von 1926 bis 1951, unterbrochen nur von 1930 bis 1936, war er Präsident der Dänischen Mathematischen Gesellschaft (DMF).
1934 sorgte ein offener Brief von Ludwig Bieberbach an Bohr im Jahresbericht des Deutschen Mathematikervereins (DMV) für einen Skandal, der Bieberbachs Rücktritt von seinen Ämtern im DMV zur Folge hatte. Bieberbach hatte diesen Brief, in dem er auf eine Kritik von Bohr (der jüdische Vorfahren hatte) an seiner Mathematiker-Typisierung einging, ohne Abstimmung im Jahresbericht veröffentlicht.
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