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23-687: [REDACTED] Look up Harald  or Haraldr in Wiktionary, the free dictionary. Harald or Haraldr is the Old Norse form of the given name Harold . It may refer to: Medieval [ edit ] Kings of Denmark [ edit ] Harald Bluetooth (935–985/986) Kings of Norway [ edit ] Harald Fairhair (c. 850–c. 933) Harald Greycloak (died 970) Harald Hardrada (1015–1066) Harald Gille (reigned 1130–1136) Grand Dukes of Kiev [ edit ] Mstislav

46-404: A PhD in 1917 for his thesis "On a class of Dirichlet series ". 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

69-462: 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

92-470: 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

115-688: Is different from Wikidata All article disambiguation pages All disambiguation pages Harald [REDACTED] Look up Harald  or Haraldr in Wiktionary, the free dictionary. Harald or Haraldr is the Old Norse form of the given name Harold . It may refer to: Medieval [ edit ] Kings of Denmark [ edit ] Harald Bluetooth (935–985/986) Kings of Norway [ edit ] Harald Fairhair (c. 850–c. 933) Harald Greycloak (died 970) Harald Hardrada (1015–1066) Harald Gille (reigned 1130–1136) Grand Dukes of Kiev [ edit ] Mstislav

138-513: Is different from Wikidata All article disambiguation pages All disambiguation pages Harald Cram%C3%A9r 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

161-3055: The First World War Harald Freiherr von Elverfeldt (1900–1945), German general of the Second World War Harald Hægermark (1894–1965), Swedish Army lieutenant general Harald Nugiseks (1921–2014), Estonian army sergeant Harald Öhquist (1891–1971), Finnish general of the Second World War Harald Riipalu (1912–1961), Estonian military commander Harald Sunde (general) (born 1954), Norwegian military officer, Chief of Defence of Norway Harald Turner (1891–1947), German Nazi SS commander executed for war crimes Harald Nicolai Storm Wergeland (1814–1893), Norwegian military officer, politician and mountaineer Harald Åkermark (1873–1963), Swedish Navy vice admiral Sport [ edit ] Harald Aabrekk (born 1956), Norwegian footballer and coach Harald Andersson (1907–1985), Swedish athlete Harald Baker (1882–1962), Australian rugby union footballer Harald Berg (born 1941), Norwegian footballer Harald Bohr (1887–1951), Danish Olympic football player and mathematician, and brother of Niels Bohr Harald Brattbakk (born 1971), Norwegian footballer Harald Cerny (born 1973), Austrian footballer Harald Grohs (born 1944), German racing driver Harald Grønningen (1934–2016), Norwegian skier Harald Hasselbach (1967-2023), Dutch football player Harald Kaarmann (1901–1942), Estonian footballer Harald Koch (born 1969), Austrian badminton player Harald Lechner (born 1982), Austrian professional football referee Harald Maartmann (1926–2021), Norwegian cross-country skier Harald Nielsen (1941–2015), Danish footballer Harald Nielsen (boxer) (1902–1983), Danish boxer Harald Økern (1898–1977), Norwegian skier Harald Schmid (born 1957), German athlete Harald Schumacher (born 1954), German footballer Harald Strøm (1897–1977), Norwegian speed skater Harald Sunde (footballer) (born 1944), Norwegian footballer Harald Tammer (1899–1942), Estonian journalist, athlete and weightlifter Harald Nilsen Tangen (born 2001), Norwegian footballer Harald Winkler (born 1962), Austrian bobsledder Other people [ edit ] Harald T. Friis (1893–1976), Danish-American radio engineer Harald Glööckler (born 1965), German fashion designer Harald Keres (1912–2010), Estonian physicist Harald Johan Løbak (1904–1985), Norwegian politician Harald Løvenskiold (1926–1994), Norwegian businessman Harald T. Nesvik (born 1966), Norwegian politician Harald Petersen (1893–1970), Danish politician Harald Sandberg (born 1950), Swedish diplomat Harald Servus (born 1965), Austrian politician Harald Sverdrup (disambiguation) Fictional [ edit ] Harald Hilding Markurell,

184-2792: The First World War Harald Freiherr von Elverfeldt (1900–1945), German general of the Second World War Harald Hægermark (1894–1965), Swedish Army lieutenant general Harald Nugiseks (1921–2014), Estonian army sergeant Harald Öhquist (1891–1971), Finnish general of the Second World War Harald Riipalu (1912–1961), Estonian military commander Harald Sunde (general) (born 1954), Norwegian military officer, Chief of Defence of Norway Harald Turner (1891–1947), German Nazi SS commander executed for war crimes Harald Nicolai Storm Wergeland (1814–1893), Norwegian military officer, politician and mountaineer Harald Åkermark (1873–1963), Swedish Navy vice admiral Sport [ edit ] Harald Aabrekk (born 1956), Norwegian footballer and coach Harald Andersson (1907–1985), Swedish athlete Harald Baker (1882–1962), Australian rugby union footballer Harald Berg (born 1941), Norwegian footballer Harald Bohr (1887–1951), Danish Olympic football player and mathematician, and brother of Niels Bohr Harald Brattbakk (born 1971), Norwegian footballer Harald Cerny (born 1973), Austrian footballer Harald Grohs (born 1944), German racing driver Harald Grønningen (1934–2016), Norwegian skier Harald Hasselbach (1967-2023), Dutch football player Harald Kaarmann (1901–1942), Estonian footballer Harald Koch (born 1969), Austrian badminton player Harald Lechner (born 1982), Austrian professional football referee Harald Maartmann (1926–2021), Norwegian cross-country skier Harald Nielsen (1941–2015), Danish footballer Harald Nielsen (boxer) (1902–1983), Danish boxer Harald Økern (1898–1977), Norwegian skier Harald Schmid (born 1957), German athlete Harald Schumacher (born 1954), German footballer Harald Strøm (1897–1977), Norwegian speed skater Harald Sunde (footballer) (born 1944), Norwegian footballer Harald Tammer (1899–1942), Estonian journalist, athlete and weightlifter Harald Nilsen Tangen (born 2001), Norwegian footballer Harald Winkler (born 1962), Austrian bobsledder Other people [ edit ] Harald T. Friis (1893–1976), Danish-American radio engineer Harald Glööckler (born 1965), German fashion designer Harald Keres (1912–2010), Estonian physicist Harald Johan Løbak (1904–1985), Norwegian politician Harald Løvenskiold (1926–1994), Norwegian businessman Harald T. Nesvik (born 1966), Norwegian politician Harald Petersen (1893–1970), Danish politician Harald Sandberg (born 1950), Swedish diplomat Harald Servus (born 1965), Austrian politician Harald Sverdrup (disambiguation) Fictional [ edit ] Harald Hilding Markurell,

207-1056: The Great (1076–1132), known as Harald in Norse sagas King of Mann and the Isles [ edit ] Haraldr Óláfsson (died 1248) Earls of Orkney [ edit ] Harald Haakonsson (died 1131) Harald Maddadsson ( c.  1134 –1206) Harald Eiriksson Others [ edit ] Hagrold (fl. 944–954), also known as Harald, Scandinavian chieftain in Normandy Harald Grenske (10th century), petty king in Vestfold in Norway Harald Klak ( c.  785 – c.  852 ), king in Jutland Harald Wartooth , legendary king of Sweden, Denmark and Norway Harald

230-623: The Great (1076–1132), known as Harald in Norse sagas King of Mann and the Isles [ edit ] Haraldr Óláfsson (died 1248) Earls of Orkney [ edit ] Harald Haakonsson (died 1131) Harald Maddadsson ( c.  1134 –1206) Harald Eiriksson Others [ edit ] Hagrold (fl. 944–954), also known as Harald, Scandinavian chieftain in Normandy Harald Grenske (10th century), petty king in Vestfold in Norway Harald Klak ( c.  785 – c.  852 ), king in Jutland Harald Wartooth , legendary king of Sweden, Denmark and Norway Harald

253-613: 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. 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

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276-1547: The Younger , 9th-century Viking leader Modern name [ edit ] Royalty [ edit ] Harald V of Norway (born 1937), present King of Norway Prince Harald of Denmark (1876–1949) Arts and entertainment [ edit ] Harald Blüchel (born 1963), German electronic music artist Harald Heide-Steen Jr. (1939–2008), Norwegian actor and comedian Harald Juhnke (1929–2005), German actor and comedian Harald Lander (1905–1971), Danish ballet dancer and choreographer Harald Reinl (1908–1986), Austrian film director Harald Rønneberg (born 1973), Norwegian television personality Harald Sæverud (1897–1992), Norwegian composer Harald Schmidt (born 1957), German actor and comedian Harald Szeemann (1933–2005), Swiss curator and art historian Harald Zwart (born 1965), Norwegian film director Academia [ edit ] Harald Beyer (literary historian) (1891–1960) Harald Bohr (1887–1951), Danish mathematician Harald Cramér (1893–1985), Swedish mathematician, actuary, and statistician Harald Høffding (1843–1931), Danish philosopher and theologian Harald Helfgott (born 1977), Peruvian mathematician Harald Herborg Nielsen (1903–1973), American physicist Harald zur Hausen (1936–2023), German virologist Harald Stümpke , pseudonym of Gerolf Steiner (1908–2009), German zoologist Military [ edit ] Harald Auffarth (1896–1946), German flying ace of

299-1492: The Younger , 9th-century Viking leader Modern name [ edit ] Royalty [ edit ] Harald V of Norway (born 1937), present King of Norway Prince Harald of Denmark (1876–1949) Arts and entertainment [ edit ] Harald Blüchel (born 1963), German electronic music artist Harald Heide-Steen Jr. (1939–2008), Norwegian actor and comedian Harald Juhnke (1929–2005), German actor and comedian Harald Lander (1905–1971), Danish ballet dancer and choreographer Harald Reinl (1908–1986), Austrian film director Harald Rønneberg (born 1973), Norwegian television personality Harald Sæverud (1897–1992), Norwegian composer Harald Schmidt (born 1957), German actor and comedian Harald Szeemann (1933–2005), Swiss curator and art historian Harald Zwart (born 1965), Norwegian film director Academia [ edit ] Harald Beyer (literary historian) (1891–1960) Harald Bohr (1887–1951), Danish mathematician Harald Cramér (1893–1985), Swedish mathematician, actuary, and statistician Harald Høffding (1843–1931), Danish philosopher and theologian Harald Helfgott (born 1977), Peruvian mathematician Harald Herborg Nielsen (1903–1973), American physicist Harald zur Hausen (1936–2023), German virologist Harald Stümpke , pseudonym of Gerolf Steiner (1908–2009), German zoologist Military [ edit ] Harald Auffarth (1896–1946), German flying ace of

322-435: 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

345-502: 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

368-538: 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

391-516: The main character of Swedish novel Markurells of Wadköping (1919) by Hjalmar Bergman Harald Petersen, a playwright in The Group (1963) by Mary McCarthy Other uses [ edit ] Harald (restaurant) , a chain of restaurants in Finland See also [ edit ] Harold (disambiguation) Herald (disambiguation) Herod (disambiguation) Topics referred to by

414-401: The main character of Swedish novel Markurells of Wadköping (1919) by Hjalmar Bergman Harald Petersen, a playwright in The Group (1963) by Mary McCarthy Other uses [ edit ] Harald (restaurant) , a chain of restaurants in Finland See also [ edit ] Harold (disambiguation) Herald (disambiguation) Herod (disambiguation) Topics referred to by

437-426: 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

460-709: The same term [REDACTED] This disambiguation page lists articles associated with the title Harald . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Harald&oldid=1254007942 " Categories : Disambiguation pages Disambiguation pages with given-name-holder lists Scandinavian masculine given names Danish masculine given names Estonian masculine given names German masculine given names Masculine given names Norwegian masculine given names Swedish masculine given names Hidden categories: Short description

483-709: The same term [REDACTED] This disambiguation page lists articles associated with the title Harald . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Harald&oldid=1254007942 " Categories : Disambiguation pages Disambiguation pages with given-name-holder lists Scandinavian masculine given names Danish masculine given names Estonian masculine given names German masculine given names Masculine given names Norwegian masculine given names Swedish masculine given names Hidden categories: Short description

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506-678: Was elected to be the Honorary President of the Swedish Actuarial Society. 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

529-487: 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

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