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Gaisi Takeuti
was a Japanese mathematician, known for his work in proof theory. After graduating from Tokyo University, he went to Princeton to study under Kurt Gödel. He later became a professor at the University of Illinois at Urbana–Champaign. Takeuti was president (2003–2009) of the Kurt Gödel Society, having worked on the book ''Memoirs of a Proof Theorist: Godel and Other Logicians''. His goal was to prove the consistency of the real numbers. To this end, Takeuti's conjecture speculates that a sequent formalisation of second-order logic In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic quantifies on ... has cut-elimination.. An erratum to this article was published in the same journal as . He is also known for his work on ordinal diagrams with Akiko Kino. Publications * * * 2013 Dover ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinal Notation
In mathematical logic and set theory, an ordinal notation is a partial function mapping the set of all finite sequences of symbols, themselves members of a finite alphabet, to a countable set of ordinal number, ordinals. A Gödel numbering is a function mapping the set of well-formed formulae (a finite sequence of symbols on which the ordinal notation function is defined) of some formal language to the natural numbers. This associates each well-formed formula with a unique natural number, called its Gödel number. If a Gödel numbering is fixed, then the subset relation on the ordinals induces an ordering on well-formed formulae which in turn induces a well-ordering on the subset of natural numbers. A recursive ordinal notation must satisfy the following two additional properties: # the subset of natural numbers is a recursive set # the induced well-ordering on the subset of natural numbers is a recursive relation There are many such schemes of ordinal notations, including schemes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Tokyo Alumni
A university () is an educational institution, institution of tertiary education and research which awards academic degrees in several Discipline (academia), academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Universities typically offer both undergraduate education, undergraduate and postgraduate education, postgraduate programs. The first universities in Europe were established by Catholic Church, Catholic monks. The University of Bologna (), Italy, which was founded in 1088, is the first university in the sense of: *being a high degree-awarding institute. *using the word (which was coined at its foundation). *having independence from the ecclesiastic schools and issuing secular as well as non-secular degrees (with teaching conducted by both clergy and non-clergy): grammar, rhetoric, logic, theology, canon law and notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theorists
Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a construct in proof theory * Mathematical proof, a convincing demonstration that some mathematical statement is necessarily true * Proof complexity, computational resources required to prove statements * Proof procedure, method for producing proofs in proof theory * Proof theory, a branch of mathematical logic that represents proofs as formal mathematical objects * Statistical proof, demonstration of degree of certainty for a hypothesis Law and philosophy * Evidence, information which tends to determine or demonstrate the truth of a proposition * Evidence (law), tested evidence or a legal proof * Legal burden of proof, duty to establish the truth of facts in a trial * Philosophic burden of proof, obligation on a party in a dispute to provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Japanese Philosophers
File:1st century collage.png, From top left, clockwise: Jesus is crucified by Roman authorities in Judaea (17th century painting). Four different men (Galba, Otho, Vitellius, and Vespasian) claim the title of Emperor within the span of a year; The Great Fire of Rome (18th-century painting) sees the destruction of two-thirds of the city, precipitating the empire's first persecution against Christians, who are blamed for the disaster; The Roman Colosseum is built and holds its inaugural games; Roman forces besiege Jerusalem during the First Jewish–Roman War (19th-century painting); The Trưng sisters lead a rebellion against the Chinese Han dynasty (anachronistic depiction); Boudica, queen of the British Iceni leads a rebellion against Rome (19th-century statue); Knife-shaped coin of the Xin dynasty., 335px rect 30 30 737 1077 Crucifixion of Jesus rect 767 30 1815 1077 Year of the Four Emperors rect 1846 30 3223 1077 Great Fire of Rome rect 30 1108 1106 2155 Boudican revolt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese Logicians
Japanese may refer to: * Something from or related to Japan, an island country in East Asia * Japanese language, spoken mainly in Japan * Japanese people, the ethnic group that identifies with Japan through ancestry or culture ** Japanese diaspora, Japanese emigrants and their descendants around the world * Japanese citizens, nationals of Japan under Japanese nationality law ** Foreign-born Japanese, naturalized citizens of Japan * Japanese writing system, consisting of kanji and kana * Japanese cuisine, the food and food culture of Japan See also * List of Japanese people * * Japonica (other) * Japanese studies , sometimes known as Japanology in Europe, is a sub-field of area studies or East Asian studies involved in social sciences and humanities research on Japan. It incorporates fields such as the study of Japanese language, history, culture, litera ... {{disambiguation Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2017 Deaths
This is a list of lists of deaths of notable people, organized by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked below. 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 Earlier years ''Deaths in years earlier than this can usually be found in the main articles of the years.'' See also * Lists of deaths by day * Deaths by year (category) {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1926 Births
In Turkey, the year technically contained only 352 days. As Friday, December 18, 1926 ''(Julian Calendar)'' was followed by Saturday, January 1, 1927 '' (Gregorian Calendar)''. 13 days were dropped to make the switch. Turkey thus became the last country to officially adopt the Gregorian Calendar, which ended the 344-year calendrical switch around the world that took place in October, 1582 by virtue of the Papal Bull made by Pope Gregory XIII. Events January * January 3 – Theodoros Pangalos declares himself dictator in Greece. * January 8 **Ibn Saud is crowned ruler of the Kingdom of Hejaz. ** Crown Prince Nguyễn Phúc Vĩnh Thuy ascends the throne as Bảo Đại, the last monarch of the Nguyễn dynasty of the Kingdom of Vietnam. * January 16 – A British Broadcasting Company radio play by Ronald Knox about workers' revolution in London causes a panic among those who have not heard the preliminary announcement that it is a satire on broadcasting. * January 21 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese Journal Of Mathematics
Japanese may refer to: * Something from or related to Japan, an island country in East Asia * Japanese language, spoken mainly in Japan * Japanese people, the ethnic group that identifies with Japan through ancestry or culture ** Japanese diaspora, Japanese emigrants and their descendants around the world * Japanese citizens, nationals of Japan under Japanese nationality law ** Foreign-born Japanese, naturalized citizens of Japan * Japanese writing system, consisting of kanji and kana * Japanese cuisine, the food and food culture of Japan See also * List of Japanese people * * Japonica (other) * Japanese studies , sometimes known as Japanology in Europe, is a sub-field of area studies or East Asian studies involved in social sciences and humanities research on Japan. It incorporates fields such as the study of Japanese language, history, culture, litera ... {{disambiguation Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cut-elimination Theorem
The cut-elimination theorem (or Gentzen's ''Hauptsatz'') is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen in part I of his landmark 1935 paper "Investigations in Logical Deduction" for the systems LJ and LK formalising intuitionistic and classical logic respectively. The cut-elimination theorem states that any judgement that possesses a proof in the sequent calculus making use of the cut rule also possesses a cut-free proof, that is, a proof that does not make use of the cut rule. The Natural Deduction version of cut-elimination, known as ''normalization theorem'', has been first proved for a variety of logics by Dag Prawitz in 1965 (a similar but less general proof was given the same year by Andrès Raggio). The cut rule A sequent is a logical expression relating multiple formulas, in the form , which is to be read as "If all of hold, then at least one of must hold", or (as Gentzen glossed): "If (A_1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theory
Proof theory is a major branchAccording to , proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
