Rolf Herman Nevanlinna (né Neovius; 22 October 1895 – 28 May 1980) was a Finnish mathematician who made significant contributions to complex analysis. He is the namesake of Nevanlinna theory for meromorphic functions.
Background Nevanlinna was born Rolf Herman Neovius, becoming Nevanlinna in 1906 when his father changed the family name. The Neovius-Nevanlinna family contained many mathematicians: Edvard Engelbert Neovius (Rolf's grandfather) taught mathematics and topography at a military academy; Edvard Rudolf Neovius (an uncle of Rolf's) was a professor of mathematics at the University of Helsinki from 1883 to 1900; Lars Theodor Neovius-Nevanlinna (another uncle of Rolf's) was an author of mathematical textbooks; and Otto Wilhelm Neovius-Nevanlinna (Rolf's father) was a physicist, astronomer and mathematician. After Otto obtained his Ph.D. in physics from the University of Helsinki, he studied at the Pulkovo Observatory with the German astronomer Herman Romberg, whose daughter, Margarete Henriette Louise Romberg, he married in 1892. Otto and Margarete then settled in Joensuu, where Otto taught physics, and there their four children were born: Frithiof (born 1894; also a mathematician), Rolf (born 1895), Anna (born 1896) and Erik (born 1901).
Education Nevanlinna began his formal education at the age of 7. Having already been taught to read and write by his parents, he went straight into the second grade but still found the work boring and soon refused to attend the school. He was then homeschooled before being sent to a grammar school in 1903 when the family moved to Helsinki, where his father took up a new post as a teacher at Helsinki High School. At the new school, Nevanlinna studied French and German in addition to the languages he already spoke: Finnish and Swedish. He also attended an orchestra school and had a love of music, which was encouraged by his mother:
Margarete was an excellent pianist and Frithiof and Rolf would lie under the piano and listen to her playing. At 13 they went to orchestra school and became accomplished musicians – Frithiof on the cello and Rolf on the violin. Through free tickets from the orchestra school they got to know and love the music of the great composers, Bach, Beethoven, Brahms, Schubert, Schumann, Chopin and Liszt, as well as the early symphonies of Sibelius. Rolf first met Sibelius's music in 1907, when he heard his Third Symphony. Although later he met Hilbert, Einstein, Thomas Mann and other famous people, Rolf said that none had had such a strong effect on him as Sibelius. The boys played trios with their mother and their love of music – in particular of chamber music – lasted all their lives. Nevanlinna then progressed onto the Helsinki High School, where his main interests were classics and mathematics. He was taught by a number of teachers during this time but the best of them all was his own father, who taught him physics and mathematics. He graduated in 1913 having performed very well, although he was not the top student of his year. He then went beyond the school syllabus in the summer of 1913 when he read Ernst Leonard Lindelöf's Introduction to Higher Analysis; from that time on, Nevanlinna had an enthusiastic interest in mathematical analysis. (Lindelöf was also a cousin of Nevanlinna's father, and so a part of the Neovius-Nevanlinna mathematical family.) Nevanlinna began his studies at the University of Helsinki in 1913, and received his Master of Philosophy in mathematics in 1917. Lindelöf taught at the university and Nevanlinna was further influenced by him. During his time at the University of Helsinki, World War I was underway and Nevanlinna wanted to join the 27th Jäger Battalion, but his father stopped him, arguing that he would serve his country better as an academic than as a soldier. He did however join the White Guard in the Finnish Civil War, but did not see active military action. In 1919, Nevanlinna presented his thesis, entitled Über beschränkte Funktionen die in gegebenen Punkten vorgeschriebene Werte annehmen ("On limited functions prescribed values at given points"), to Lindelöf, his doctoral advisor. The thesis, which was on complex analysis, was of high quality and Nevanlinna was awarded his Doctor of Philosophy on 2 June 1919.
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