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Hilbert's Sixth Problem
Hilbert's sixth problem is to axiomatize those branches of physics in which mathematics is prevalent. It occurs on the widely cited list of Hilbert's problems in mathematics that he presented in the year 1900. In its common English translation, the explicit statement reads: :6. Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: ''To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics.'' Hilbert gave the further explanation of this problem and its possible specific forms: :"As to the axioms of the theory of probabilities, it seems to me desirable that their logical investigation should be accompanied by a rigorous and satisfactory development of the method of mean values in mathematical physics, and in particular in the kinetic theory of gases. ... Boltzmann's work on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is a premise or starting point for reasoning. As used in mathematics, the term ''axiom'' is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (''A'' and ''B'') implies ''A''), while non-logical axioms (e.g., ) are actually ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by Carl Friedrich Gauss, David Hilbert and Hermann Minkowski. His research has had major significance for theoretical physics as well as purely mathematical disciplines such as number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years. Weyl contributed to an exceptionally wide range of mathematical fields, including works on space, time, matter, philosophy, logic, symmetry and the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. Freeman Dyson wrote that Weyl alone bore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of Symposia In Pure Mathematics
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiomatic System
In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system. A formal theory is an axiomatic system (usually formulated within model theory) that describes a set of sentences that is closed under logical implication. A formal proof is a complete rendition of a mathematical proof within a formal system. Properties An axiomatic system is said to be ''consistent'' if it lacks contradiction. That is, it is impossible to derive both a statement and its negation from the system's axioms. Consistency is a key requirement for most axiomatic systems, as the presence of contradiction would allow any statement to be proven (principle of explosion). In an axiomatic syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ilya Karlin
Ilya, Iliya, Ilia, Ilja, or Ilija (russian: Илья́, Il'ja, , or russian: Илия́, Ilija, ; uk, Ілля́, Illia, ; be, Ілья́, Iĺja ) is the East Slavic form of the male Hebrew name Eliyahu (Eliahu), meaning "My God is Yahu/ Jah." It comes from the Byzantine Greek pronunciation of the vocative (Ilía) of the Greek Elias (Ηλίας, Ilías). It is pronounced with stress on the second syllable. The diminutive form is Iliusha or Iliushen'ka. The Russian patronymic for a son of Ilya is " Ilyich", and a daughter is "Ilyinichna". People with the name Real people *Ilya (Archbishop of Novgorod), 12th-century Russian Orthodox cleric and saint * Ilya Ivanovitch Alekseyev (1772–1830), commander of the Russian Imperial Army *Ilya Borok (born 1993), Russian jiujitsu fighter *Ilya Bryzgalov (born 1980), Russian ice hockey goalie *Ilya Ehrenburg (1891–1967), Russian writer and Soviet cultural ambassador *Ilya Glazunov (1930–2017), Russian painter *Ilya Gringolts (born 1982 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Nikolaevich Gorban
Alexander Nikolaevich Gorban (russian: Александр Николаевич Горба́нь) is a scientist of Russian origin, working in the United Kingdom. He is a professor at the University of Leicester, and director of its Mathematical Modeling Centre. Gorban has contributed to many areas of fundamental and applied science, including statistical physics, non-equilibrium thermodynamics, machine learning and mathematical biology. Gorban is the author of about 20 books and 300 scientific publications. He has founded several scientific schools in the areas of physical and chemical kinetics, dynamical systems theory and artificial neural networks, and is ranked as one of the 1000 most cited researchers of Russian origin.According to http://www.scientific.ru/ , 2012 Gorban has supervised 6 habilitations and more than 30 PhD theses. Biography Alexander N. Gorban was born in Omsk on 19 April 1952. His father Nikolai Vasilievich Gorban was a historian and writer exiled to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laure Saint-Raymond
Laure Saint-Raymond (born 1975) is a French mathematician, and a professor of mathematics at Institut des Hautes Études Scientifiques (IHES). She was previously a professor at École Normale Supérieure de Lyon. She is known for her work in partial differential equations, and in particular for her contributions to the mathematically rigorous study of the connections between interacting particle systems, the Boltzmann equation, and fluid mechanics. In 2008 she was awarded the European Mathematical Society, European Mathematical Society Prize, with her citation reading: Biography Laure Saint-Raymond studied in Paris, entering École Normale Supérieure in 1994. In 1996, she received a Master's degrees in plasma physics from Versailles Saint-Quentin-en-Yvelines University and in applied mathematics from Pierre and Marie Curie University. In 2000 she finished her Ph.D. in applied mathematics at Paris Diderot University, under the supervision of François Golse. She worked for tw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rudolf Haag
Rudolf Haag (17 August 1922 – 5 January 2016) was a German theoretical physicist, who mainly dealt with fundamental questions of quantum field theory. He was one of the founders of the modern formulation of quantum field theory and he identified the formal structure in terms of the principle of locality and local observables. He also made important advances in the foundations of quantum statistical mechanics. Biography Rudolf Haag was born on 17 August 1922, in Tübingen, a university town in the middle of Baden-Württemberg. His family belonged to the cultured middle class. Haag's mother was the writer and politician Anna Haag. His father, Albert Haag, was a teacher of mathematics at a Gymnasium. After finishing high-school in 1939, he visited his sister in London shortly before the beginning of World War II. He was interned as an enemy alien and spent the war in a camp of German civilians in Manitoba. There he used his spare-time after the daily compulsory labour to study p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Wightman
Arthur Strong Wightman (March 30, 1922 – January 13, 2013) was an American mathematical physicist. He was one of the founders of the axiomatic approach to quantum field theory, and originated the set of Wightman axioms. With his rigorous treatment of quantum field theories, he promoted research on various aspects of modern mathematical physics. Biography Arthur Wightman was born on March 30, 1922, in Rochester, in New York. He studied at the Yale University and in 1942 he earned a bachelor's degree in physics. In 1949 he received his doctorate at the Princeton University under the supervision of John Wheeler. He intended to graduate with Eugene Wigner, but he was spending most of his time at the Oak Ridge National Laboratory. In the early 1950s, he started as a young instructor in the Princeton Physics department and later became the Thomas D. Jones Professor of Mathematical Physics, in 1971. He retired in 1992 as professor emeritus. In the years 1951-1952 and 1956-1957 he wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measure Theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general. The intuition behind this concept dates back to ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile Borel, Henri Lebesgue, Nikolai Luzin, Johann Radon, Const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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