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Jules Richard (mathematician)
Jules Richard (12 August 1862 – 14 October 1956) was a French mathematician who worked mainly in geometry but his name is most commonly associated with Richard's paradox. Life and works Richard was born in Blet, in the Cher ''département''. He taught at the lycées of Tours, Dijon and Châteauroux. He obtained his doctorate, at age of 39, from the Faculté des Sciences in Paris. His thesis of 126 pages concerns Fresnel's wave-surface. Richard worked mainly on the foundations of mathematics and geometry, relating to works by Hilbert, von Staudt and Méray. In a more philosophical treatise about the nature of axioms of geometry Richard discusses and rejects the following basic principles: # Geometry is founded on arbitrarily chosen axioms - there are infinitely many equally true geometries. # Experience provides the axioms of geometry, the basis is experimental, the development deductive. # The axioms of geometry are definitions (in contrast to (1)). # Axioms are neither ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French People
The French people (french: Français) are an ethnic group and nation primarily located in Western Europe that share a common French culture, history, and language, identified with the country of France. The French people, especially the native speakers of langues d'oïl from northern and central France, are primarily the descendants of Gauls (including the Belgae) and Romans (or Gallo-Romans, western European Celtic and Italic peoples), as well as Germanic peoples such as the Franks, the Visigoths, the Suebi and the Burgundians who settled in Gaul from east of the Rhine after the fall of the Roman Empire, as well as various later waves of lower-level irregular migration that have continued to the present day. The Norse also settled in Normandy in the 10th century and contributed significantly to the ancestry of the Normans. Furthermore, regional ethnic minorities also exist within France that have distinct lineages, languages and cultures such as Bretons in Brittany, Occi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred North Whitehead
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy, which today has found application to a wide variety of disciplines, including ecology, theology, education, physics, biology, economics, and psychology, among other areas. In his early career Whitehead wrote primarily on mathematics, logic, and physics. His most notable work in these fields is the three-volume ''Principia Mathematica'' (1910–1913), which he wrote with former student Bertrand Russell. ''Principia Mathematica'' is considered one of the twentieth century's most important works in mathematical logic, and placed 23rd in a list of the top 100 English-language nonfiction books of the twentieth century by Modern Library. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century French Mathematicians
The 19th (nineteenth) century began on 1 January 1801 ( MDCCCI), and ended on 31 December 1900 ( MCM). The 19th century was the ninth century of the 2nd millennium. The 19th century was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The 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 Islamic gunpowder empires fell into decline and European imperialism brought much of South Asia, Southeast Asia, and almost all of Africa under colonial rule. It was also marked by the collapse of the large ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1956 Deaths
Events January * January 1 – The Anglo-Egyptian Sudan, Anglo-Egyptian Condominium ends in Sudan. * January 8 – Operation Auca: Five U.S. evangelical Christian Missionary, missionaries, Nate Saint, Roger Youderian, Ed McCully, Jim Elliot and Pete Fleming, are killed for trespassing by the Huaorani people of Ecuador, shortly after making contact with them. * January 16 – Egyptian leader Gamal Abdel Nasser vows to reconquer Palestine (region), Palestine. * January 25–January 26, 26 – Finnish troops reoccupy Porkkala, after Soviet Union, Soviet troops vacate its military base. Civilians can return February 4. * January 26 – The 1956 Winter Olympics open in Cortina d'Ampezzo, Italy. February * February 11 – British Espionage, spies Guy Burgess and Donald Maclean (spy), Donald Maclean resurface in the Soviet Union, after being missing for 5 years. * February 14–February 25, 25 – The 20th Congress of the Communist Party of the Soviet Union is held in Mosc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1862 Births
Year 186 ( CLXXXVI) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Aurelius and Glabrio (or, less frequently, year 939 ''Ab urbe condita''). The denomination 186 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Peasants in Gaul stage an anti-tax uprising under Maternus. * Roman governor Pertinax escapes an assassination attempt, by British usurpers. New Zealand * The Hatepe volcanic eruption extends Lake Taupō and makes skies red across the world. However, recent radiocarbon dating by R. Sparks has put the date at 233 AD ± 13 (95% confidence). Births * Ma Liang, Chinese official of the Shu Han state (d. 222) Deaths * April 21 – Apollonius the Apologist, Christian martyr * Bian Zhang, Chinese official and gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Of Impossibility
In mathematics, a proof of impossibility is a proof that demonstrates that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general. Such a case is also known as a negative proof, proof of an impossibility theorem, or negative result. Because they show that something cannot be done, proofs of impossibility can be the resolutions to decades or centuries of work attempting to find a solution. Proving that something is impossible is usually much harder than the opposite task, as it is often necessary to develop a proof that works in general, rather than to just show a particular example. Impossibility theorems are usually expressible as negative existential propositions or universal propositions in logic. The irrationality of the square root of 2 is one of the oldest proofs of impossibility. It shows that it is impossible to express the square root of 2 as a ratio of two integers. Another consequential proof of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo (, ; 27 July 187121 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem. Furthermore, his 1929 work on ranking chess players is the first description of a model for pairwise comparison that continues to have a profound impact on various applied fields utilizing this method. Life Ernst Zermelo graduated from Berlin's Luisenstädtisches Gymnasium (now ) in 1889. He then studied mathematics, physics and philosophy at the University of Berlin, the University of Halle, and the University of Freiburg. He finished his doctorate in 1894 at the University of Berlin, awarded for a dissertation on the calculus of variations (''Untersuchungen zur Variationsrechnung''). Zermelo remained at the University of Berlin, where he was appointed assistant to Planck, under whose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinal Number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The ''transfinite'' cardinal numbers, often denoted using the Hebrew symbol \aleph ( aleph) followed by a subscript, describe the sizes of infinite sets. Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets. In the case of finite sets, this agrees with the intuitive notion of size. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for ... [...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] |
Julius König
The gens Julia (''gēns Iūlia'', ) was one of the most prominent patrician families in ancient Rome. Members of the gens attained the highest dignities of the state in the earliest times of the Republic. The first of the family to obtain the consulship was Gaius Julius Iulus in 489 BC. The gens is perhaps best known, however, for Gaius Julius Caesar, the dictator and grand uncle of the emperor Augustus, through whom the name was passed to the so-called Julio-Claudian dynasty of the first century AD. The Julius became very common in imperial times, as the descendants of persons enrolled as citizens under the early emperors began to make their mark in history.''Dictionary of Greek and Roman Biography and Mythology'', vol. II, pp. 642, 643. Origin The Julii were of Alban origin, mentioned as one of the leading Alban houses, which Tullus Hostilius removed to Rome upon the destruction of Alba Longa. The Julii also existed at an early period at Bovillae, evidenced by a very a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incompleteness Theorem
Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies that there are no "holes" in the real numbers * Complete metric space, a metric space in which every Cauchy sequence converges * Complete uniform space, a uniform space where every Cauchy net in converges (or equivalently every Cauchy filter converges) * Complete measure, a measure space where every subset of every null set is measurable * Completion (algebra), at an ideal * Completeness (cryptography) * Completeness (statistics), a statistic that does not allow an unbiased estimator of zero * Complete graph, an undirected graph in which every pair of vertices has exactly one edge connecting them * Complete category, a category ''C'' where every diagram from a small category to ''C'' has a limit; it is ''cocomplete'' if every such functor ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Turing
Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. He is widely considered to be the father of theoretical computer science and artificial intelligence. Born in Maida Vale, London, Turing was raised in southern England. He graduated at King's College, Cambridge, with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation and defined a Turing machine, and went on to prove that the halting problem for Turing machines is undecidable. In 1938, he obtained his PhD from the Department of Mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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