Fredrik Carl Mülertz Størmer () (3 September 1874 – 13 August 1957) was a
Norwegian mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and
astrophysicist. In mathematics, he is known for his work in
number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
, including the calculation of
and
Størmer's theorem on consecutive smooth numbers. In physics, he is known for studying the movement of charged particles in the
magnetosphere
In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body with an active interior Dynamo ...
and the formation of
aurorae, and for his book on these subjects, ''From the Depths of Space to the Heart of the Atom''. He worked for many years as a professor of mathematics at the
University of Oslo
The University of Oslo (; ) is a public university, public research university located in Oslo, Norway. It is the List of oldest universities in continuous operation#Europe, oldest university in Norway. Originally named the Royal Frederick Univ ...
in Norway. A
crater on the far side of the Moon is named after him.
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).
His uncle was the entrepreneur and inventor
Henrik Christian Fredrik Størmer.
[
Størmer studied mathematics at the Royal Frederick University in Kristiania, Norway (now the University of Oslo, in Oslo) from 1892 to 1897, earning the rank of candidatus realium in 1898. He then studied with Picard, ]Poincaré
Poincaré is a French surname. Notable people with the surname include:
* Henri Poincaré
Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philos ...
, Painlevé, Jordan
Jordan, officially the Hashemite Kingdom of Jordan, is a country in the Southern Levant region of West Asia. Jordan is bordered by Syria to the north, Iraq to the east, Saudi Arabia to the south, and Israel and the occupied Palestinian ter ...
, Darboux, and Goursat at the Sorbonne in Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
from 1898 to 1900. He returned to Kristiania in 1900 as a research fellow in mathematics, visited the University of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...
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
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the IMU Abacus Medal (known before ...
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
Blindern is the main campus of the University of Oslo, located in Nordre Aker in Oslo, Norway.
Campus
Most of the departments of the University of Oslo are located at Blindern; other, smaller campuses include Sentrum, Oslo, Sentrum (law), Gaust ...
.
He was also an amateur street photographer, beginning in his student days. In the years 1893-1897, he documented daily life on the streets of Oslo using a miniature CP Stirn spy camera. Between 1942 and 1943, he shared a small portion of his works with the public. However, it was not until he was 70 years old that he organized an exhibition showcasing all his historical photographs of celebrities that he had taken over the years. For instance it included one of Henrik Ibsen strolling down Karl Johans gate, the main road in Oslo. Most of these can now be viewed in Norway's Digitalt Museum.
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), with whom he eventually had five children. Their son Leif Størmer became a professor of historical geology at the University of Oslo
The University of Oslo (; ) is a public university, public research university located in Oslo, Norway. It is the List of oldest universities in continuous operation#Europe, oldest university in Norway. Originally named the Royal Frederick Univ ...
.[ His daughter Henny married landowner Carl Otto Løvenskiold. Carl Størmer is also the grandfather of the mathematician Erling Størmer.
]
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. He revisited this problem a few years later. Next, he systematically investigated Machin-like formula by which the number may be represented as a rational combination of the so-called " Gregory numbers" of the form . Machin's original formula,
:
is of this type, and Størmer showed that there were three other ways of representing 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 . In particular, a four-term representation found by Størmer,
:
was used in a record-setting calculation of to 1,241,100,000,000 decimal digits in 2002 by Yasumasa Kanada. Størmer is also noted for the Størmer numbers, which arose from the decomposition of Gregory numbers in Størmer's work.
Størmer's theorem, which he proved in 1897, shows that, for any finite set of prime numbers, there are only finitely many pairs of consecutive integers
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
having only the numbers from as their prime factor
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
s. In addition, Størmer describes an algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...
for finding all such pairs. The superparticular ratios generated by these consecutive pairs are of particular importance in music theory. Størmer proves this theorem by reducing the problem to a finite set of Pell equations, and the theorem itself can also be interpreted as describing the possible factorizations of solutions to Pell's equation. Chapman quotes Louis Mordell as saying "His result is very pretty, and there are many applications of it."
Additional subjects of Størmer's mathematical research included Lie group
In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
A manifold is a space that locally resembles Eucli ...
s, the gamma function
In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined ...
, and Diophantine approximation
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria.
The first problem was to know how well a real number can be approximated ...
of algebraic numbers and of the transcendental numbers arising from elliptic functions. From 1905 Størmer was an editor of the journal '' Acta Mathematica'', and he was also an editor of the posthumously-published mathematical works of Niels Henrik Abel and Sophus Lie
Marius Sophus Lie ( ; ; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He also made substantial cont ...
.
Astrophysical research
From 1903, when Størmer first observed Kristian Birkeland
Kristian Olaf Bernhard Birkeland (born 13 December 1867 – 15 June 1917) was a Norway, Norwegian space physics, space physicist, inventor, and professor of physics at the University of Oslo, Royal Fredriks University in Oslo. He is best remembe ...
's experimental attempts to explain the aurora borealis, he was fascinated by aurorae and related phenomena. His first work on the subject attempted to model mathematically the paths taken by charged particles perturbed by the influence of a magnetized sphere
A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
, and Størmer eventually published over 48 papers on the motion of charged particles. By modeling the problem using differential equations and polar coordinates, Størmer was able to show that the radius of curvature of any particle's path is proportional to the square of its distance from the sphere's center. To solve the resulting differential equations numerically, he used Verlet integration, which is therefore also known as ''Störmer's method''. Ernst Brüche and Willard Harrison Bennett verified experimentally Størmer's predicted particle motions; Bennett called his experimental apparatus "Störmertron" in honor of Størmer. Størmer's calculations showed that small variations in the trajectories of particles approaching the earth would be magnified by the effects of the Earth's magnetic field, explaining the convoluted shapes of aurorae. Størmer also considered the possibility that particles might be trapped within the geomagnetic field, and worked out the orbits of these trapped particles. Størmer's work on this subject applies to what are today called the magnetospheric ring current and Van Allen radiation belts.
As well as modeling these phenomena mathematically, Størmer took many photograph
A photograph (also known as a photo, or more generically referred to as an ''image'' or ''picture'') is an image created by light falling on a photosensitivity, photosensitive surface, usually photographic film or an electronic image sensor. Th ...
s of aurorae, from 20 different observatories across Norway. He measured their heights and latitudes by triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points.
Applications
In surveying
Specifically in surveying, triangulation involves only angle m ...
from multiple observatories, and showed that the aurora are typically as high as 100 kilometers above ground. He classified them by their shapes, and discovered in 1926 the "solar-illuminated aurora", a phenomenon that can occur at twilight when the upper parts of an aurora are lit by the sun; these aurorae can be as high as 1000 km above ground.
Størmer's book, ''From the Depths of Space to the Heart of the Atom'', describing his work in this area, was translated into five different languages from the original Norwegian. A second book, ''The Polar Aurora'' (Oxford Press, 1955), contains both his experimental work on aurorae and his mathematical attempts to model them. In his review of this book, Canadian astronomer John F. Heard calls Størmer "the acknowledged authority" on aurorae.[ Heard writes, "''The Polar Aurora'' will undoubtedly remain for many years a standard reference book; it belongs on the desk of anyone whose work or interest is involved with aurorae."]
Other astrophysical phenomena investigated by Størmer include pulsations of the earth's magnetic field
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from structure of Earth, Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from ...
, echoing in radio
Radio is the technology of communicating using radio waves. Radio waves are electromagnetic waves of frequency between 3 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmitter connec ...
transmissions, nacreous clouds and noctilucent clouds, zodiacal light, meteor
A meteor, known colloquially as a shooting star, is a glowing streak of a small body (usually meteoroid) going through Earth's atmosphere, after being heated to incandescence by collisions with air molecules in the upper atmosphere,
creating a ...
trails, the solar corona
In astronomy, a corona (: coronas or coronae) is the outermost layer of a star's Stellar atmosphere, atmosphere. It is a hot but relatively luminosity, dim region of Plasma (physics), plasma populated by intermittent coronal structures such as so ...
and solar vortices, and cosmic ray
Cosmic rays or astroparticles are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the ...
s.
Awards and honors
Størmer was a Foreign Member of the Royal Society (ForMemRS) and a Corresponding Member of the French Academy of Sciences
The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...
. He was also a member of the Norwegian Academy of Science and Letters from 1900.[ He was given honorary degrees by ]Oxford University
The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the second-oldest continuously operating u ...
(in 1947), the University of Copenhagen
The University of Copenhagen (, KU) is a public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in Scandinavia, after Uppsala University.
...
(1951), and the Sorbonne (1953), and in 1922 the French Academy awarded him their Janssen Medal.[ Three times Størmer was a plenary speaker in the International Congress of Mathematicians (1908 in Rome, 1924 in Toronto, and 1936 in Oslo);][ he was an invited speaker of the ICM in 1920 in Strasbourg and in 1932 in Zurich.] In 1971, the crater Störmer on the far side of the Moon was named after him. The Lie-Størmer Center at UiT - The Arctic University of Norway is 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
Grand Cross is the highest class in many orders, and manifested in its insignia. Exceptionally, the highest class may be referred to as Grand Cordon or equivalent. In other cases, there may exist a rank even higher than Grand Cross, e.g. Gran ...
of the Order of St. Olav in 1954.[
]
References
{{DEFAULTSORT:Stormer, Carl
1874 births
1957 deaths
People from Skien
University of Oslo alumni
University of Paris alumni
Academic staff of the University of Oslo
Norwegian astronomers
Norwegian mathematicians
Norwegian physicists
Number theorists
20th-century astronomers
Members of the Norwegian Academy of Science and Letters
Foreign members of the Royal Society
Members of the French Academy of Sciences
Presidents of the Norwegian Mathematical Society