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George David Birkhoff
George David Birkhoff (March21, 1884November12, 1944) was one of the top American mathematicians of his generation. He made valuable contributions to the theory of differential equations, dynamical systems, the four-color problem, the three-body problem, and general relativity. Today, Birkhoff is best remembered for the ergodic theorem. The George D. Birkhoff House, his residence in Cambridge, Massachusetts, has been designated a National Historic Landmark. Early life He was born in Overisel Township, Michigan, the son of two Dutch immigrants, David Birkhoff, who arrived in the United States in 1870, and Jane Gertrude Droppers. Birkhoff's father worked as a physician in Chicago while he was a child. From 1896 to 1902, he would attend the Lewis Institute as a teenager. Career Birkhoff was part of a generation of American mathematicians who were the first to study entirely within the United States and not participate in academics within Europe. Following his time at the Lewis Insti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overisel Township, Michigan
Overisel Township is a civil township of Allegan County, Michigan, Allegan County in the U.S. state of Michigan. The population was 3,113 at the 2020 United States census, 2020 census. Overisel was named after the Dutch province of Overijssel. Overisel is the birthplace of mathematician George David Birkhoff, best known for what is now called the ergodic theory#Ergodic theorems, ergodic theorem. Communities * Bentheim is a Dutch and German community that was also settled in the mid-1800s. Bentheim is found near the Rabbit River on the far Eastern edge of the Township. * Drenthe is a Dutch community that was first settled by Jan Hulst in 1847. His family's journey from Baltimore took six weeks when made by ox-cart in June 1847.Drenthe Christian Reformed Church Historical Web Page * Overisel is a tightly knit community found in the far western part of Overisel Township and was settled in 1848 by Dutch immigrants consisting of only 12 families at the time. The village consists of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marshall Harvey Stone
Marshall Harvey Stone (April 8, 1903 – January 9, 1989) was an American mathematician who contributed to real analysis, functional analysis, topology and the study of Boolean algebras. Biography Stone was the son of Harlan Fiske Stone, who was the Chief Justice of the United States in 1941–1946. Marshall Stone's family expected him to become a lawyer like his father, but he became enamored of mathematics while he was an undergraduate at Harvard University, where he was a classmate of future judge Henry Friendly. He completed a PhD there in 1926, with a thesis on differential equations that was supervised by George David Birkhoff. Between 1925 and 1937, he taught at Harvard, Yale University, and Columbia University. Stone was promoted to a full professor at Harvard in 1937. During World War II, Stone did classified research as part of the "Office of Naval Operations" and the "Office of the Chief of Staff" of the United States Department of War. In 1946, he became the cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General theory of relativity, relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time in physics, time, or four-dimensional spacetime. In particular, the ''curvature of spacetime'' is directly related to the energy and momentum of whatever is present, including matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations. Newton's law of universal gravitation, which describes gravity in classical mechanics, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three-body Problem
In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses orbiting each other in space and then calculate their subsequent trajectories using Newton's laws of motion and Newton's law of universal gravitation. Unlike the two-body problem, the three-body problem has no general closed-form solution, meaning there is no equation that always solves it. When three bodies orbit each other, the resulting dynamical system is chaotic for most initial conditions. Because there are no solvable equations for most three-body systems, the only way to predict the motions of the bodies is to estimate them using numerical methods. The three-body problem is a special case of the -body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Earth, the Moon, and the Sun. In an extended modern sense, a three-body problem is any problem in cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four-color Problem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions share a common boundary of non-zero length (i.e., not merely a corner where three or more regions meet). It was the first major theorem to be computer-assisted proof#Theorems proved with the help of computer programs, proved using a computer. Initially, this Mathematical proof, proof was not accepted by all mathematicians because the computer-assisted proof was Non-surveyable proof, infeasible for a human to check by hand. The proof has gained wide acceptance since then, although some doubts remain. The theorem is a stronger version of the five color theorem, which can be shown using a significantly simpler argument. Although the weaker five color theorem was proven already in the 1800s, the four color theorem resisted until 1976 when it was p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newcomb Cleveland Prize
The Newcomb Cleveland Prize of the American Association for the Advancement of Science (AAAS) is annually awarded to author(s) of outstanding scientific paper published in the Research Articles or Reports sections of ''Science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...''. Established in 1923, funded by Newcomb Cleveland who remained anonymous until his death in 1951, and for this period it was known as the AAAS Thousand Dollar Prize. "The prize was inspired by Mr. Cleveland's belief that it was the scientist who counted and who needed the encouragement an unexpected monetary award could give." The present rules were instituted in 1975, previously it had gone to the author(s) of noteworthy papers, representing an outstanding contribution to science, presented in a regular sess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bôcher Memorial Prize
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five years) for a notable research work in analysis that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000. There have been forty-one prize recipients. The first woman to win the award, Laure Saint-Raymond, did so in 2020. About eighty percent of the journal articles recognized since 2000 have been from ''Annals of Mathematics'', the ''Journal of the American Mathematical Society'', '' Inventiones Mathematicae'', and '' Acta Mathematica''. Past winners Source: * 1923 George David Birkhoff for ::''Dynamical systems with two degrees of freedom.'' Trans. Amer. Math. Soc. 18 (1917), 119-300. * 1924 Eric Temple Bell for ::''Arithmetical paraphrases. I, II.'' Trans. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birkhoff's Axioms
In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry in the plane, sometimes referred to as Birkhoff's axioms. These postulates are all based on basic geometry that can be confirmed experimentally with a scale and protractor. Since the postulates build upon the real numbers, the approach is similar to a model-based introduction to Euclidean geometry. Birkhoff's axiomatic system was utilized in the secondary-school textbook by Birkhoff and Beatley. These axioms were also modified by the School Mathematics Study Group to provide a new standard for teaching high school geometry, known aSMSG axioms A few other textbooks in the foundations of geometry use variants of Birkhoff's axioms. Birkhoff's Four Postulates The distance between two points and is denoted by , and the angle formed by three points is denoted by . Postulate I: Postulate of line measure. The set of points on any line can be put into a 1:1 correspondence with the real numbers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ergodic Theorem
Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems. The notion of deterministic dynamical systems assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc. Thus, the statistics with which we are concerned are properties of the dynamics. Ergodic theory, like probability theory, is based on general notions of measure theory. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincaré recurrence theorem, which claims that almost all points in any subset of the phase space eventuall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
