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Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was developed by Kurt Gödel for the proof of his incompleteness theorems.
Frank Plumpton Ramsey was a British philosopher, mathematician, and economist who made major contributions to all three fields before his death at the age of 26. He was a close friend of Ludwig Wittgenstein and, as an undergraduate, translated Wittgenstein's Tractatus Logico-Philosophicus into English. He was also influential in persuading Wittgenstein to return to philosophy and Cambridge. Like Wittgenstein, he was a member of the Cambridge Apostles, the secret intellectual society, from 1921.
Angie Dickinson is an American retired actress. She began her career on television, appearing in many anthology series during the 1950s, before gaining her breakthrough role in Gun the Man Down (1956) with James Arness and the Western film Rio Bravo (1959) with John Wayne and Dean Martin, for which she received the Golden Globe Award for New Star of the Year.
Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that "arithmetical truth cannot be defined in arithmetic".
Kent School is a private, co-educational, college preparatory boarding school in Kent, Connecticut. Frederick Herbert Sill established the school in 1906. It is affiliated with the Episcopal Church of the United States. It has a long history as an "elite school, not a school for elites," and innovated the sliding-scale tuition model in the early 20th century.
Dickinson State University (DSU) is a public university in Dickinson, North Dakota. It is part of the North Dakota University System. It was founded in 1918 as Dickinson State Normal School and granted full university status in 1987.
The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who served the Society for 25 years. The Cole Prize in algebra was funded by Cole himself, from funds given to him as a retirement gift; the prize fund was later augmented by his son, leading to the double award.
Lester Jesse Dickinson was a Republican United States Representative and Senator from Iowa. He was, in the words of Time magazine, "a big, friendly, white-thatched Iowa lawyer." In early 1936, he dreamed of winning the presidency. However, the only race he would enter that year would be for his own seat in the Senate which he lost.
The Dickinson System was a mathematical point formula that awarded national championships in college football. Devised by University of Illinois economics professor Frank G. Dickinson, the system ranked national teams from 1924 to 1940.
The 1930 college football season saw Notre Dame repeat as national champion under the Dickinson System, as well as claim the No. 1 position from each of the other three contemporary major selectors,. The post-season Rose Bowl matchup featured two unbeaten (9–0) teams, Washington State and Alabama, ranked No. 2 and No. 3, respectively. Alabama won the Pasadena contest, 24–0.
The 1931 college football season saw the USC Trojans win the Knute Rockne Memorial Trophy as national champion under the Dickinson System, as well as the No. 1 position from each of the other three contemporary major selectors. Rockne, who had coached Notre Dame to a championship in 1930, had been killed in a plane crash on March 31, 1931. For the first time, the champion under the Dickinson System also played in a postseason game. The 1932 Rose Bowl, promoted as a national championship game between the best teams of East and West, matched USC and Tulane, No. 1 and No. 2 in the Dickinson ratings. USC won, 21–12, and was awarded the Albert Russel Erskine Trophy.
The 1931 USC Trojans football team was an American football team that represented the University of Southern California (USC) in the Pacific Coast Conference (PCC) during the 1931 college football season. In their seventh season under head coach Howard Jones, the Trojans lost the opening game to Saint Mary's and then won the remaining ten games of the season. They finished the season with a 10–1 record, shut out six of eleven opponents, outscored all opponents by a total of 363 to 52, and won the PCC and national championships.
Frank Ayres, Jr. was a mathematics professor, best known as an author for the popular Schaum's Outlines.
The 1938 United States Senate election in Iowa took place on November 8, 1938. Incumbent Democratic Senator Guy M. Gillette, who won a special election to complete the unexpired term of Richard Louis Murphy, won a full term in office by defeating Republican former Senator Lester J. Dickinson. Gillette and Dickinson had briefly served together in the final months of 1936.
The 1936 United States Senate election in Iowa took place on November 3, 1936. Incumbent Republican Senator Lester J. Dickinson ran for re-election to a second term but was defeated by Democratic Governor Clyde Herring.
David S. Richeson is an American mathematician whose interests include the topology of dynamical systems, recreational mathematics, and the history of mathematics. He is a professor of mathematics at Dickinson College, where he holds the John J. & Ann Curley Faculty Chair in the Liberal Arts.
The 1934 college football season rankings included a poll of leading newspapers conducted by the Associated Press (AP), a poll of 250 sports writers conducted by the committee responsible for awarding the Toledo Cup to the nation's top college football team, and the Boand and Dickinson Systems, mathematical systems operated by William F. Boand and Frank G. Dickinson. The four ranking systems were unanimous in selecting the undefeated Minnesota Golden Gophers as the national champion. Professor Dickinson gave the nod to Minnesota even though one-loss Pittsburgh received a higher mathematical score.
The 1933 college football season rankings included mathematical systems operated by William F. Boand and Frank G. Dickinson. Both systems selected the undefeated Michigan Wolverines as the national champion.
References
- ↑ "Dickinson Gives Title to Trojans". Monroe Morning World. December 13, 1931. p. 8 – via Newspapers.com.