Harald Cramér
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Harald Cramér (; 25 September 1893 – 5 October 1985) was a
Swedish Swedish or ' may refer to: Anything from or related to Sweden, a country in Northern Europe. Or, specifically: * Swedish language, a North Germanic language spoken primarily in Sweden and Finland ** Swedish alphabet, the official alphabet used by ...
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 ...
, actuary, and
statistician A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may wor ...
, specializing in
mathematical statistics Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical ...
and probabilistic number theory. John Kingman described him as "one of the giants of statistical theory".Kingman 1986, p. 186.


Biography


Early life

Harald Cramér was born in Stockholm, Sweden on 25 September 1893. Cramér remained close to Stockholm for most of his life. He entered the University of Stockholm as an undergraduate in 1912, where he studied mathematics and chemistry. During this period, he was a research assistant under the famous chemist, Hans von Euler-Chelpin, with whom he published his first five articles from 1913 to 1914. Following his lab experience, he began to focus solely on mathematics. He eventually began his work on his doctoral studies in mathematics which were supervised by Marcel Riesz at the University of Stockholm. Also influenced by G. H. Hardy, Cramér's research led to a PhD in 1917 for his thesis "On a class of Dirichlet series".


Academic professional career

Following his PhD, he served as an Assistant Professor of Mathematics at Stockholm University from 1917 to 1929. Early on, Cramér was highly involved in analytic number theory. He also made some important statistical contributions to the distribution of primes and
twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
s. His most famous paper on this subject is entitled "On the order of magnitude of the difference between consecutive prime numbers", which provided a rigorous account of the constructive role in which
probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
applied to
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...
Kendall 1986, p. 211. and included an estimate for prime gaps that became known as Cramér's conjecture. In the late 1920s, Cramér became interested in the field of probability, which at the time was not an accepted branch of mathematics. Cramér knew that a radical change was needed in this field, and in a paper in 1926 said, "The probability concept should be introduced by a purely mathematical definition, from which its fundamental properties and the classical theorems are deduced by purely mathematical operations."Blom 1987, p. 1340. Cramér took an interest in the rigorous mathematical formulation of probability in the work of
French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...
and Russian mathematicians such as Kolmogorov, Lévy, Bernstein, and Khinchin in the early 1930s. Cramér also made significant development to the revolution in probability theory. Cramér later wrote his careful study of the field in his Cambridge publication ''Random variables and probability distributions'' which appeared in 1937 (with a 2nd edition in 1962 and a 3rd edition in 1970). Shortly after World War II, Cramér went on to publish the influential ''Mathematical Methods of Statistics'' in 1946. This text was one that "showed the way in which statistical practice depended on a body of rigorous mathematical analysis as well as Fisherian intuition." His 1955 book ''Elements of Probability Theory and Some of its Applications'' introduces probability theory at a more elementary level than ''Mathematical Methods of Statistics''. In 1929, Cramér was appointed to a newly created chair in Stockholm University, becoming the first Swedish professor of Actuarial Mathematics and Mathematical Statistics. Cramér retained this position up until 1958. During his tenure at Stockholm University, Cramér was a PhD advisor for 10 students, most notably
Herman Wold Herman Ole Andreas Wold (25 December 1908 – 16 February 1992) was a Norwegian-born econometrician and statistician who had a long career in Sweden. Wold was known for his work in mathematical economics, in time series analysis, and in econometric ...
and Kai Lai Chung. In 1950 he was elected as a Fellow of the American Statistical Association. Starting in 1950, Cramér took on the additional responsibility of becoming the President of Stockholm University. In 1958, he was also appointed to be Chancellor of the entire Swedish university system. Cramér retired from the Swedish university system in 1961.


Actuarial career

A large portion of Cramér's work concerned the field of actuarial science and insurance mathematics. During the period from 1920 to 1929, he was an actuary for the life insurance company Svenska livförsäkringsbolaget. His actuarial work during this time led him to study probability and statistics which became the main area of his research. In 1927 he published an elementary text in Swedish Probability theory and some of its applications. Following his work for Svenska livförsäkringsbolaget, he went on to work for Återförsäkringsaktiebolaget Sverige, a
reinsurance Reinsurance is insurance that an insurance company purchases from another insurance company to insulate itself (at least in part) from the risk of a major claims event. With reinsurance, the company passes on ("cedes") some part of its own ins ...
company, up until 1948. He was also known for his pioneering efforts in insurance
risk theory In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probab ...
. After this period, he remained as a consultant actuary to Sverige from 1949 to 1961. Later in his life, he was elected to be the Honorary President of the Swedish Actuarial Society.


Later years

Cramér remained an active contributor to his professional career for an additional 20 years. Following his retirement in 1961, he became extremely active in research, which had been slowed due to his Chancellorship. During the years from 1961 to 1983, Cramér traveled throughout the United States and Europe to continue his research, making significant stops at Berkeley, Princeton, and at the Research Triangle Institute of North Carolina. Cramér received an Honorary Doctorate from
Heriot-Watt University Heriot-Watt University ( gd, Oilthigh Heriot-Watt) is a public research university based in Edinburgh, Scotland. It was established in 1821 as the School of Arts of Edinburgh, the world's first mechanics' institute, and subsequently granted uni ...
in 1972. His academic career spanned over seven decades, from 1913 to 1982.Blom 1987, p. 1338. Harald Cramér married Marta Hansson in 1918, and they remained together up until her death in 1973. He had often referred to her as his "Beloved Marta". Together they had one daughter, Marie-Louise, and two sons, Tomas and Kim.


Notes


References

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External links

*
photographs of Harald Cramér
at th
Oberwolfach Photo CollectionPhotograph
with C. R. Rao from th
PORTRAITS OF STATISTICIANS
* {{DEFAULTSORT:Cramer, Harald 1893 births 1985 deaths Swedish statisticians Swedish actuaries Probability theorists 20th-century Swedish mathematicians Scientists from Stockholm Fellows of the American Statistical Association Foreign associates of the National Academy of Sciences Members of the Royal Society of Sciences in Uppsala