# Carl Størmer : biography

**Fredrik Carl Mülertz Størmer** (3 September 1874 – 13 August 1957) was a Norwegian mathematician and physicist, known both for his work in number theory and for studying the movement of charged particles in the magnetosphere and the formation of aurorae.

## Personal life and career

Størmer was born on 3 September 1874 in Skien, the only child of a pharmacist Georg Ludvig Størmer (1842–1930) and Elisabeth Amalie Johanne Henriette Mülertz (1844–1916). He was a nephew of Henrik Christian Fredrik Størmer.

He studied mathematics at the Royal Frederick University (now: University of Oslo) from 1892 to 1897, earning the rank of candidatus realium in 1898. He then studied with Picard, Poincaré, Painlevé, Jordan, Darboux, and Goursat at the Sorbonne in Paris from 1898 to 1900. On his return to Kristiania in 1900 as a research fellow in mathematics, he married Ada Clauson, with whom he eventually had five children. He visited the University of Göttingen in 1902, and returned to Kristiania in 1903, where he was appointed as a professor of mathematics, a position he held for 43 years. After he received a permanent position in Kristiania, Størmer published his subsequent writings under a shortened version of his name, Carl Størmer. In 1918, he was elected as the first president of the newly-formed Norwegian Mathematical Society. He participated regularly in Scandinavian mathematical congresses, and was president of the 1936 International Congress of Mathematicians in Oslo (from 1924 the new name of Kristiania). Størmer was also affiliated with the Institute of Theoretical Astrophysics at the University of Oslo, which was founded in 1934. He died on 13 August 1957, at Blindern.

Størmer was also an amateur street photographer, beginning in his student days, and near the age of 70 he put on an exhibition in Oslo of the photographs of celebrities that he had taken over the years. He was also a supervisory council member of the insurance company Forsikringsselskapet Norden.

In February 1900 he married consul's daughter Ada Clauson (1877–1973). They had the son Leif Størmer, who became a professor of historical geology at the University of Oslo. His daughter Henny married landowner Carl Otto Løvenskiold. Carl Størmer is also the grandfather of the mathematician Erling Størmer.

## Awards and honors

Størmer was a foreign member of the Royal Society and a corresponding member of the French Academy of Sciences. He was also a member of the Norwegian Academy of Science and Letters from 1900. He was given honorary degrees by Oxford University (in 1947), the University of Copenhagen (1951), and the Sorbonne (1953), and in 1922 the French Academy awarded him their Janssen Medal. In 1971, the crater Störmer on the far side of the Moon was named after him.

In 1902, Størmer was decorated with King Oscar II's Medal of Merit in gold. He was also decorated as a Knight, First Order of the Order of St. Olav in 1939. He was upgraded to Grand Cross of the Order of St. Olav in 1954.

## Mathematical research

Størmer's first mathematical publication, published when he was a beginning student at the age of 18, concerned trigonometric series generalizing the Taylor expansion of the arcsine function, a problem he revisited again a few years later. Next, he systematically investigated Machin-like formula by which the number π may be represented as a rational combination of the so-called "Gregory numbers" of the form tan−1(1/*n*). Machin's original formula,

- \textstyle\pi = 16\arctan \frac15 - 4\arctan\frac1{239},

is of this type, and Størmer showed that there were three other ways of representing π as a rational combination of two Gregory numbers. He then investigated combinations of three Gregory numbers, and found 102 representations of π of this form, but was unable to determine whether there might be additional solutions of this type. These representations led to fast algorithms for computing numerical approximations of π; a four-term representation found by Størmer,