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List Of Second-generation Mathematicians
Math ability is passed from parent to child with the most famous example being the Bernoulli family. This List of second-generation physicists, second generation phenomenon also holds in physics but in that field the Nobel Prize in Physics gives a tool for tracking it, since it has been given out for more than 120 years, and there are on average more than two Nobel Prizes in Physics given each year. There is no comparable award in mathematics but perusing (for example) the MacTutor History of Mathematics Archive list of biographies enables the construction of a similar list of notable two-generation pairs of mathematicians. The following is a list of parent-child pairs who both made contributions to mathematics significant enough to be noted in the citation for a prestigious prize, in an obituary in a major math journal, or in a similarly authoritative source. All are father-son except for Emmy Noether and Cathleen Morawetz. The list is in chronological order by birth date o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernoulli Family
The Bernoulli family ( ; ; ) of Basel was a Patrician (post-Roman Europe), patrician family, notable for having produced eight mathematically gifted academics who, among them, contributed substantially to the development of mathematics and physics during the Early Modern Switzerland, early modern period. History Originally from Antwerp, a branch of the family relocated to Basel in 1620. While their origin in Antwerp is certain, proposed earlier connections with the Dutch family of Italian ancestry called ''Bornouilla'' (''Bernoullie''), or with the Castilian family ''de Bernuy'' (''Bernoille'', ''Bernouille''), are uncertain. The first known member of the family was Leon Bernoulli (d. 1561), a doctor in Antwerp, at that time part of the Spanish Netherlands. His son, Jacob, emigrated to Frankfurt am Main in 1570 to escape from the Inquisition in the Netherlands, Spanish persecution of the Protestants. Jacob's grandson, a spice trader, also named Jacob, moved to Basel, Switzerlan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elie Cartan
Elie may refer to: People * Elie (given name) * Elie (surname) Places *Elie, Fife, a village in Scotland, now part of the town of Elie and Earlsferry *Elie, Manitoba, Canada **Elie, Manitoba tornado See also *Elie Hall, Grenada *Elie House, country house in Elie, Fife, Scotland * *Eli (other) *Elia (other) *Élie, the French equivalent of "Elias" or "Elijah" *Ellie (other) Ellie or Elly is a given name and nickname. It may also refer to: __NOTOC__ Arts and entertainment * ''Ellie'' (film), a 1984 comedy * "Ellie" (''CSI''), an episode of the American crime drama ''CSI'' * "Ellie" (''The West Wing''), an episode of ... * Ely (surname) {{disambiguation, given name, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether's Theorem
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This is the first of two theorems (see Noether's second theorem) published by the mathematician Emmy Noether in 1918. The action of a physical system is the integral over time of a Lagrangian function, from which the system's behavior can be determined by the principle of least action. This theorem applies to continuous and smooth symmetries of physical space. Noether's formulation is quite general and has been applied across classical mechanics, high energy physics, and recently statistical mechanics. Noether's theorem is used in theoretical physics and the calculus of variations. It reveals the fundamental relation between the symmetries of a physical system and the conservation laws. It also made modern theoretical physicists much more focused on symmetries of physical systems. A generalization of the formulations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether Inequality
In mathematics, the Noether inequality, named after Max Noether, is a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4-manifold. It holds more generally for minimal projective surfaces of general type over an algebraically closed field. Formulation of the inequality Let ''X'' be a smooth minimal projective surface of general type defined over an algebraically closed field (or a smooth minimal compact complex surface of general type) with canonical divisor ''K'' = −''c''1(''X''), and let ''p''g = ''h''0(''K'') be the dimension of the space of holomorphic two forms, then : p_g \le \frac c_1(X)^2 + 2. For complex surfaces, an alternative formulation expresses this inequality in terms of topological invariants of the underlying real oriented four manifold. Since a surface of general type is a Kähler surface, the dimension of the maximal positive subspace in intersection form on the second cohomology is given by ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann–Roch Theorem For Surfaces
In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was first given by , after preliminary versions of it were found by and . The sheaf-theoretic version is due to Hirzebruch. Statement One form of the Riemann–Roch theorem states that if ''D'' is a divisor on a non-singular projective surface then :\chi(D) = \chi(0) +\tfrac D . (D - K) \, where χ is the holomorphic Euler characteristic, the dot . is the intersection number, and ''K'' is the canonical divisor. The constant χ(0) is the holomorphic Euler characteristic of the trivial bundle, and is equal to 1 + ''p''''a'', where ''p''''a'' is the arithmetic genus of the surface. For comparison, the Riemann–Roch theorem for a curve states that χ(''D'') = χ(0) + deg(''D''). Noether's formula Noether's formula states that :\chi = \frac = \frac where χ=χ(0) is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brill–Noether Theory
In algebraic geometry, Brill–Noether theory, introduced by , is the study of special divisors, certain divisors on a curve that determine more compatible functions than would be predicted. In classical language, special divisors move on the curve in a "larger than expected" linear system of divisors. Throughout, we consider a projective smooth curve over the complex numbers (or over some other algebraically closed field). The condition to be a special divisor can be formulated in sheaf cohomology terms, as the non-vanishing of the cohomology of the sheaf of sections of the invertible sheaf or line bundle associated to . This means that, by the Riemann–Roch theorem, the cohomology or space of holomorphic sections is larger than expected. Alternatively, by Serre duality, the condition is that there exist holomorphic differentials with divisor on the curve. Main theorems of Brill–Noether theory For a given genus , the moduli space for curves of genus should contain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Noether
Max Noether (24 September 1844 – 13 December 1921) was a German mathematician who worked on algebraic geometry and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century". He was the father of Emmy Noether. Biography Max Noether was born in Mannheim in 1844, to a Jewish family of wealthy wholesale hardware dealers. His grandfather, Elias Samuel, had started the business in Bruchsal in 1797. In 1809 the Grand Duchy of Baden established a "Tolerance Edict", which assigned a hereditary surname to the male head of every Jewish family which did not already possess one. Thus the Samuels became the Noether family, and as part of this Christianization of names, their son Hertz (Max's father) became Hermann. Max was the third of five children Hermann had with his wife Amalia Würzburger. At 14, Max contracted polio and was afflicted by its effects for the rest of his life. Through self-study, he learned advanced mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolf Prize
The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for "achievements in the interest of mankind and friendly relations among people ... irrespective of nationality, race, colour, religion, sex or political views". History The prize is awarded in Israel by the Wolf Foundation, founded by Ricardo Wolf, a German-born inventor and former Cuban ambassador to Israel. It is awarded in six fields: Agriculture, Chemistry, Mathematics, Medicine, and Physics, and an Arts The arts or creative arts are a vast range of human practices involving creativity, creative expression, storytelling, and cultural participation. The arts encompass diverse and plural modes of thought, deeds, and existence in an extensive ... prize that rotates between architecture, music, painting, and sculpture. Each prize consists of a diploma and US$100,000. The awards ceremony typically takes place at a session in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Émile Picard Medal
The Émile Picard Medal (or Médaille Émile Picard) is a medal named for Émile Picard awarded every 6 years to an outstanding mathematician by the Institut de France, Académie des sciences. This rewards a mathematician designated by the Academy of Sciences every six years. The first medal was awarded in 1946. Recipients The Émile Picard Medal recipients are * Maurice Fréchet (1946) * Paul Lévy (1953) * Henri Cartan (1959) * Szolem Mandelbrojt (1965), * Jean-Pierre Serre (1971) * Alexandre Grothendieck (1977) * André Néron (1983) * François Bruhat (1989) * Jean-Pierre Kahane (1995) * Jacques Dixmier (2001) * Louis Boutet de Monvel (2007) * Luc Illusie (2012) * Yves Colin de Verdière (2018) See also * List of mathematics awards This list of mathematics awards contains articles about notable awards for mathematics. The list is organized by the region and country of the organization that sponsors the award, but awards may be open to mathematicians from around the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Module
In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, keeping some of the main properties of free modules. Various equivalent characterizations of these modules appear below. Every free module is a projective module, but the converse fails to hold over some rings, such as Dedekind rings that are not principal ideal domains. However, every projective module is a free module if the ring is a principal ideal domain such as the integers, or a (multivariate) polynomial ring over a field (this is the Quillen–Suslin theorem). Projective modules were first introduced in 1956 in the influential book ''Homological Algebra'' by Henri Cartan and Samuel Eilenberg. Definitions Lifting property The usual category theoretical definition is in terms of the property of ''lifting'' that carries over from free to projective modules: a module ''P'' is projective if and only if fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartan's Theorems A And B
In mathematics, Cartan's theorems A and B are two results mathematical proof, proved by Henri Cartan around 1951, concerning a coherent sheaf on a Stein manifold . They are significant both as applied to Function of several complex variables, several complex variables, and in the general development of sheaf cohomology. Theorem B is stated in cohomological terms (a formulation that Cartan (#CITEREFCartan1953, 1953, p. 51) attributes to J.-P. Serre): Analogous properties were established by Jean-Pierre Serre, Serre (#CITEREFSerre1957, 1957) for coherent sheaves in algebraic geometry, when is an affine scheme. The analogue of Theorem B in this context is as follows : These theorems have many important applications. For instance, they imply that a holomorphic function on a closed complex submanifold, , of a Stein manifold can be extended to a holomorphic function on all of . At a deeper level, these theorems were used by Jean-Pierre Serre to prove the GAGA theorem. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henri Cartan
Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of composer , physicist and mathematician , and the son-in-law of physicist Pierre Weiss. Life According to his own words, Henri Cartan was interested in mathematics at a very young age, without being influenced by his family. He moved to Paris with his family after his father's appointment at Sorbonne in 1909 and he attended secondary school at Lycée Hoche in Versailles. available also at In 1923 he started studying mathematics at École Normale Supérieure, receiving an agrégation in 1926 and a doctorate in 1928. His PhD thesis, entitled ''Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications'', was supervised by Paul Montel. Cartan taught at Lycée Malherbe in Caen from 1928 to 1929, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
