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Cesare Burali-Forti
Cesare Burali-Forti (13 August 1861 – 21 January 1931) was an Italian mathematician, after whom the Burali-Forti paradox is named. Biography Burali-Forti was born in Arezzo, and was an assistant of Giuseppe Peano in Turin from 1894 to 1896, during which time he discovered a theorem which Bertrand Russell later realised contradicted a previously proved result by Georg Cantor. The contradiction came to be called the Burali-Forti paradox of Cantorian set theory. He died in Turin. Books by C. Burali-Forti Analyse vectorielle générale: Applications à la mécanique et à la physique.with Roberto Marcolongo (Mattéi & co., Pavia, 1913). Corso di geometria analitico-proiettiva per gli allievi della R. Accademia Militare(G. B. Petrini di G. Gallizio, Torino, 1912). Geometria descrittiva(S. Lattes & c., Torino, 1921). Introduction à la géométrie différentielle, suivant la méthode de H. Grassmann(Gauthier-Villars, 1897). Lezioni Di Geometria Metrico-Proiettiva(Fratelli Boc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arezzo
Arezzo ( , , ) , also ; ett, 𐌀𐌓𐌉𐌕𐌉𐌌, Aritim. is a city and ''comune'' in Italy and the capital of the province of the same name located in Tuscany. Arezzo is about southeast of Florence at an elevation of above sea level. As of 2022, the population was about 97,000. Known as the city of gold and of the high fashion, Arezzo was home to artists and poets such as Giorgio Vasari, Guido of Arezzo and Guittone d'Arezzo and in its province to Renaissance artist Michelangelo. In the artistic field, the city is famous for the frescoes by Piero della Francesca inside the Basilica of San Francesco, and the crucifix by Cimabue inside the Basilica of San Domenico. The city is also known for the important Giostra del Saracino, a game of chivalry that dates back to the Middle Ages. History Described by Livy as one of the ''Capita Etruriae'' (Etruscan capitals), Arezzo (''Aritim'' in Etruscan) is believed to have been one of the twelve most important Etruscan cities ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turin
Turin ( , Piedmontese language, Piedmontese: ; it, Torino ) is a city and an important business and cultural centre in Northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital from 1861 to 1865. The city is mainly on the western bank of the Po (river), Po River, below its Susa Valley, and is surrounded by the western Alps, Alpine arch and Superga Hill. The population of the city proper is 847,287 (31 January 2022) while the population of the urban area is estimated by Larger Urban Zones, Eurostat to be 1.7 million inhabitants. The Turin metropolitan area is estimated by the Organisation for Economic Co-operation and Development, OECD to have a population of 2.2 million. The city used to be a major European political centre. From 1563, it was the capital of the Duchy of Savoy, then of the Kingdom of Sardinia ruled by the House of Savoy, and the first capital of the Kingdom of Italy from 1861 to 1865. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burali-Forti Paradox
In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system that allows its construction. It is named after Cesare Burali-Forti, who, in 1897, published a paper proving a theorem which, unknown to him, contradicted a previously proved result by Cantor. Bertrand Russell subsequently noticed the contradiction, and when he published it in his 1903 book ''Principles of Mathematics'', he stated that it had been suggested to him by Burali-Forti's paper, with the result that it came to be known by Burali-Forti's name. Stated in terms of von Neumann ordinals We will prove this by a deliberational deconstruction. # Let be a set consisting of all ordinal numbers. # is transitive because for every element of (which is an ordinal number and can be any ordinal number) and every element of (i.e. under the definition of Von Neumann ordinals, for every ... [...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, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) 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 mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giuseppe Peano
Giuseppe Peano (; ; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction. He spent most of his career teaching mathematics at the University of Turin. He also wrote an international auxiliary language, Latino sine flexione ("Latin without inflections"), which is a simplified version of Classical Latin. Most of his books and papers are in Latino sine flexione, others are in Italian. Biography Peano was born and raised on a farm at Spinetta, a hamlet now belonging to Cuneo, Piedmont, Italy. He attended the Liceo classico Cavour in Turin, and enrolled at the University of Turin in 1876, graduatin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, artificial intelligence, cognitive science, computer science and various areas of analytic philosophy, especially philosophy of mathematics, philosophy of language, epistemology, and metaphysics.Stanford Encyclopedia of Philosophy"Bertrand Russell" 1 May 2003. He was one of the early 20th century's most prominent logicians, and a founder of analytic philosophy, along with his predecessor Gottlob Frege, his friend and colleague G. E. Moore and his student and protégé Ludwig Wittgenstein. Russell with Moore led the British "revolt against idealism". Together with his former teacher A. N. Whitehead, Russell wrote ''Principia Mathematica'', a milestone in the development of classical logic, and a major attempt to reduce the whole ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor ( , ; – January 6, 1918) was a German mathematician. He played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact he was well aware of. Originally, Cantor's theory of transfinite numbers was regarded as counter-intuitive – even shocking. This caused it to encounter resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of '' naive set theory''. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox) various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roberto Marcolongo
Roberto Marcolongo (August 28, 1862 in Rome – May 16, 1943 in Rome) was an Italian mathematician, known for his research in vector calculus and theoretical physics. He graduated in 1886, and later he was an assistant of Valentino Cerruti in Rome. In 1895 he became professor of rational mechanics at the University of Messina. In 1908 he moved to the University of Naples, where he remained until retirement in 1935. He worked on vector calculus together with Cesare Burali-Forti, which was then known as "Italian notation". In 1906 he wrote an early work which used the four-dimensional formalism to account for relativistic invariance under Lorentz transformations. In 1921 he published to Messina one of the first treaties on the special relativity and general, where he used the absolute differential calculus without coordinates, developed with Burali-Forti, as opposed to the absolute differential calculus with coordinates of Tullio Levi-Civita and Gregorio Ricci-Curbastro. He was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tommaso Boggio
Tommaso Boggio (22 December 1877 – 25 May 1963) was an Italian mathematician. Boggio worked in mathematical physics, differential geometry, analysis, and financial mathematics. He was an invited speaker in International Congress of Mathematicians 1908 in Rome. He wrote, with Burali-Forti, ''Meccanica Razionale'', published in 1921 by S. Lattes & Compagnia. Notes External links *An Italian short biography of Tommaso Boggioat the University of Turin The University of Turin (Italian: ''Università degli Studi di Torino'', UNITO) is a public research university in the city of Turin, in the Piedmont region of Italy. It is one of the oldest universities in Europe and continues to play an impo ... {{DEFAULTSORT:Boggio, Tommaso 1877 births 1963 deaths 19th-century Italian mathematicians 20th-century Italian mathematicians Mathematical analysts Scientists from Turin University of Turin faculty University of Genoa faculty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Van Heijenoort
Jean Louis Maxime van Heijenoort (; July 23, 1912 – March 29, 1986) was a historian of mathematical logic. He was also a personal secretary to Leon Trotsky from 1932 to 1939, and an American Trotskyist until 1947. Life Van Heijenoort was born in Creil in France. His family's financial situation was difficult as his father, after having immigrated from the Netherlands, died when van Heijenoort was 2. He completed normal education and became fluent in French. He remained attached to his French extended family and friends until his death and visited France twice a year after he became a naturalized American citizen in 1958. He was murdered in Mexico City in 1986 by his 4th spouse. Political views In 1932, Van Heijenoort was recruited by Yvan Craipeau to join the Trotskyist movement. He joined the Communist League in the same year. After Trotsky was exiled, he hired van Heijenoort as a secretary and bodyguard, primarily because of his fluency in French, Russian, German, and Englis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ivor Grattan-Guinness
Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Life Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his bachelor degree as a Mathematics Scholar at Wadham College, Oxford, and an MSc (Econ) in Mathematical Logic and the Philosophy of Science at the London School of Economics in 1966. He gained both the doctorate (PhD) in 1969, and higher doctorate (D.Sc.) in 1978, in the History of Science at the University of London. He was Emeritus Professor of the History of Mathematics and Logic at Middlesex University, and a Visiting Research Associate at the London School of Economics. He was awarded the Kenneth O. May Medal for services to the History of Mathematics by the International Commission on the History of Mathematics (ICHM) on 31 July 2009, at Budapest, on the occasion of the 23rd International Congress for the History of Science. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
