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Padoa
Alessandro Padoa (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano. He is remembered for a method for deciding whether, given some formal theory, a new primitive notion is truly independent of the other primitive notions. There is an analogous problem in axiomatic theories, namely deciding whether a given axiom is independent of the other axioms. The following description of Padoa's career is included in a biography of Peano: :He attended secondary school in Venice, engineering school in Padua, and the University of Turin, from which he received a degree in mathematics in 1895. Although he was never a student of Peano, he was an ardent disciple and, from 1896 on, a collaborator and friend. He taught in secondary schools in Pinerolo, Rome, Cagliari, and (from 1909) at the Technical Institute in Genoa. He also held positions at the Normal School in Aquila and the Naval School in Genoa, and, beginning in 189 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mario Pieri
Mario Pieri (22 June 1860 – 1 March 1913) was an Italian mathematician who is known for his work on foundations of geometry. Biography Pieri was born in Lucca, Italy, the son of Pellegrino Pieri and Ermina Luporini. Pellegrino was a lawyer. Pieri began his higher education at University of Bologna where he drew the attention of Salvatore Pincherle. Obtaining a scholarship, Pieri transferred to '' Scuola Normale Superiore'' in Pisa. There he took his degree in 1884 and worked first at a technical secondary school in Pisa. When an opportunity arose at the military academy in Turin to teach projective geometry, Pieri moved there and, by 1888, he was also an assistant instructor in the same subject at the University of Turin. By 1891, he had become ''libero docente'' at the university, teaching elective courses. Pieri continued to teach in Turin until 1900 when, through competition, he was awarded the position of ''extraordinary professor'' at University of Catania on the island o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line (geometry)
In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher dimension spaces. The word ''line'' may also refer to a line segment in everyday life, which has two points to denote its ends. Lines can be referred by two points that lay on it (e.g., \overleftrightarrow) or by a single letter (e.g., \ell). Euclid described a line as "breadthless length" which "lies evenly with respect to the points on itself"; he introduced several postulates as basic unprovable properties from which he constructed all of geometry, which is now called Euclidean geometry to avoid confusion with other geometries which have been introduced since the end of the 19th century (such as non-Euclidean, projective and affine geometry). In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analy ... [...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, gradua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primitive Notion
In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory, relations between primitive notions are restricted by axioms. Some authors refer to the latter as "defining" primitive notions by one or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of infinite regress (per the regress problem). For example, in contemporary geometry, ''point'', ''line'', and ''contains'' are some primitive notions. Instead of attempting to define them, their interplay is ruled (in Hilbert's axiom system) by axioms like "For every two points there exists a line that contains them both". Details Alfred Tarski explained the role of primitive notions as follows: :When we set out to construct a given discipline, we distinguish, first of all, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1937 Deaths
Events January * January 1 – Anastasio Somoza García becomes President of Nicaragua. * January 5 – Water levels begin to rise in the Ohio River in the United States, leading to the Ohio River flood of 1937, which continues into February, leaving 1 million people homeless and 385 people dead. * January 15 – Spanish Civil War: Second Battle of the Corunna Road ends inconclusively. * January 20 – Second inauguration of Franklin D. Roosevelt: Franklin D. Roosevelt is sworn in for a second term as President of the United States. This is the first time that the United States presidential inauguration occurs on this date; the change is due to the ratification in 1933 of the Twentieth Amendment to the United States Constitution. * January 23 – Moscow Trials: Trial of the Anti-Soviet Trotskyist Center – In the Soviet Union 17 leading Communists go on trial, accused of participating in a plot led by Leon Trotsky to overthrow Joseph Stalin's regime, and assassinate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moritz Pasch
Moritz Pasch (8 November 1843, Breslau, Prussia (now Wrocław, Poland) – 20 September 1930, Bad Homburg, Germany) was a German mathematician of Jewish ancestry specializing in the foundations of geometry. He completed his Ph.D. at the University of Breslau at only 22 years of age. He taught at the University of Giessen, where he is known to have supervised 30 doctorates. In 1882, Pasch published a book, ''Vorlesungen über neuere Geometrie'', calling for the grounding of Euclidean geometry in more precise primitive notions and axioms, and for greater care in the deductive methods employed to develop the subject. He drew attention to a number of heretofore unnoted tacit assumptions in Euclid's ''Elements''. He then argued that mathematical reasoning should not invoke the physical interpretation of the primitive terms, but should instead rely solely on formal manipulations justified by axioms. This book is the point of departure for: *Similarly concerned Italians: Peano, Mario ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometers
A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * Manava (c. 750 BC–690 BC) – Euclidean geometry * Thales of Miletus (c. 624 BC – c. 546 BC) – Euclidean geometry * Pythagoras (c. 570 BC – c. 495 BC) – Euclidean geometry, Pythagorean theorem * Zeno of Elea (c. 490 BC – c. 430 BC) – Euclidean geometry * Hippocrates of Chios (born c. 470 – 410 BC) – first systematically organized '' Stoicheia – Elements'' (geometry textbook) * Mozi (c. 468 BC – c. 391 BC) * Plato (427–347 BC) * Theaetetus (c. 417 BC – 369 BC) * Autolycus of Pitane (360–c. 290 BC) – astronomy, spherical geometry * Euclid (fl. 300 BC) – ''Elements'', Euclidean geometry (sometimes called the "father of geometry") * Apollonius of Perga (c. 262 BC – c. 190 BC) – Euclidean geometry, conic s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theorists
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations ( Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century Italian Mathematicians
The 19th (nineteenth) century began on 1 January 1801 (Roman numerals, MDCCCI), and ended on 31 December 1900 (Roman numerals, MCM). The 19th century was the ninth century of the 2nd millennium. The 19th century was characterized by vast social upheaval. Slavery was abolitionism, abolished in much of Europe and the Americas. The Industrial Revolution, First Industrial Revolution, though it began in the late 18th century, expanding beyond its British homeland for the first time during this century, particularly remaking the economies and societies of the Low Countries, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Gunpowder empires, Islamic gunpowder empires fell into decline and European imperialism brought much of South Asia, Southeast Asia, and almost ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1868 Births
Events January–March * January 2 – British Expedition to Abyssinia: Robert Napier leads an expedition to free captive British officials and missionaries. * January 3 – The 15-year-old Mutsuhito, Emperor Meiji of Japan, declares the '' Meiji Restoration'', his own restoration to full power, under the influence of supporters from the Chōshū and Satsuma Domains, and against the supporters of the Tokugawa shogunate, triggering the Boshin War. * January 5 – Paraguayan War: Brazilian Army commander Luís Alves de Lima e Silva, Duke of Caxias enters Asunción, Paraguay's capital. Some days later he declares the war is over. Nevertheless, Francisco Solano López, Paraguay's president, prepares guerrillas to fight in the countryside. * January 7 – The Arkansas constitutional convention meets in Little Rock. * January 9 – Penal transportation from Britain to Australia ends, with arrival of the convict ship '' Hougoumont'' in Weste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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