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
Stockholm University 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 Stockholm University. 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 primes. 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 applied to
number theory 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." Cramér took an interest in the rigorous mathematical formulation of probability in the work of
French 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. 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." 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 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 company, up until 1948. He was also known for his pioneering efforts in insurance
risk theory. 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. His academic career spanned over seven decades, from 1913 to 1982. 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==