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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 of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lucca
Lucca ( , ) is a city and ''comune'' in Tuscany, Central Italy, on the Serchio River, in a fertile plain near the Ligurian Sea. The city has a population of about 89,000, while its province has a population of 383,957. Lucca is known as one of the Italian's "Città d'arte" (Arts town), thanks to its intact Renaissance-era city walls and its very well preserved historic center, where, among other buildings and monuments, are located the Piazza dell'Anfiteatro, which has its origins in the second half of the 1st century A.D. and the Guinigi Tower, a tower that dates from the 1300s. The city is also the birthplace of numerous world-class composers, including Giacomo Puccini, Alfredo Catalani, and Luigi Boccherini. Toponymy By the Romans, Lucca was known as ''Luca''. From more recent and concrete toponymic studies, the name Lucca has references that lead to "sacred wood" (Latin: ''lucus''), "to cut" (Latin: ''lucare'') and "luminous space" (''leuk'', a term used by the f ... [...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, graduat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred Tarski
Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician and mathematician. A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy. Educated in Poland at the University of Warsaw, and a member of the Lwów–Warsaw school of logic and the Warsaw school of mathematics, he immigrated to the United States in 1939 where he became a naturalized citizen in 1945. Tarski taught and carried out research in mathematics at the University of California, Berkeley, from 1942 until his death in 1983. Feferman A. His biographers Anita Burdman Feferman and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he changed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Language
Polish (Polish: ''język polski'', , ''polszczyzna'' or simply ''polski'', ) is a West Slavic language of the Lechitic group written in the Latin script. It is spoken primarily in Poland and serves as the native language of the Poles. In addition to being the official language of Poland, it is also used by the Polish diaspora. There are over 50 million Polish speakers around the world. It ranks as the sixth most-spoken among languages of the European Union. Polish is subdivided into regional dialects The term dialect (from Latin , , from the Ancient Greek word , 'discourse', from , 'through' and , 'I speak') can refer to either of two distinctly different types of linguistic phenomena: One usage refers to a variety of a language that is a ... and maintains strict T–V distinction pronouns, Honorifics (linguistics), honorifics, and various forms of formalities when addressing individuals. The traditional 32-letter Polish alphabet has nine additions (''ą'', ''ć'', ... [...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, Mari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Motion (geometry)
In geometry, a motion is an isometry of a metric space. For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion. More generally, the term ''motion'' is a synonym for surjective isometry in metric geometry, including elliptic geometry and hyperbolic geometry. In the latter case, hyperbolic motions provide an approach to the subject for beginners. Motions can be divided into direct and indirect motions. Direct, proper or rigid motions are motions like translations and rotations that preserve the orientation of a chiral shape. Indirect, or improper motions are motions like reflections, glide reflections and Improper rotations that invert the orientation of a chiral shape. Some geometers define motion in such a way that only direct motions are motions. In differential geometry In differential geometry, a diffeomorphism is called a motion if it induces an isometry between the tangent space at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point (geometry)
In classical Euclidean geometry, a point is a primitive notion that models an exact location in space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space. Being a primitive notion means that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms, that it must satisfy; for example, ''"there is exactly one line that passes through two different points"''. Points in Euclidean geometry Points, considered within the framework of Euclidean geometry, are one of the most fundamental objects. Euclid originally defined the point as "that which has no part". In two-dimensional Euclidean space, a point is represented by an ordered pair (, ) of numbers, where the first number conventionally represents the horizontal and is often denoted by , and the second number conventionally represents the vertical and is often denoted b ... [...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 c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999, pp. 3-5 The University of Chicago, which had opened in 1892, organized an International Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alessandro 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] |
Louis Couturat
Louis Couturat (; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido. Life and education Born in Ris-Orangis, Essonne, France. In 1887 he entered École Normale Supérieure to study philosophy and mathematics. In 1895 he lectured in philosophy at the University of Toulouse and 1897 lectured in philosophy of mathematics at the University of Caen Normandy, taking a stand in favor of transfinite numbers. After a time in Hanover studying the writings of Leibniz, he became an assistant to Henri-Louis Bergson at the Collège de France in 1905. Career He was ''the'' French advocate of the symbolic logic that emerged in the years before World War I, thanks to the writings of Charles Sanders Peirce, Giuseppe Peano and his school, and especially to '' The Principles of Mathematics'' by Couturat's friend and correspondent Bertrand Russell. Like Russell, Couturat saw symbolic log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the List of cities proper by population density, 30th most densely populated city in the world in 2020. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, Fashion capital, fashion, gastronomy, and science. For its leading role in the arts and sciences, as well as its very early system of street lighting, in the 19th century it became known as "the City of Light". Like London, prior to the Second World War, it was also sometimes called Caput Mundi#Paris, the capital of the world. The City of Paris is the centre of the Île-de-France Regions of France, region, or Paris Region, with an estimated population of 12,262,544 in 2019, or about 19% of the population of France, making the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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