NationMaster - Encyclopedia: George David Birkhoff

George David Birkhoff (21 March 1884, Overisel, Michigan - 12 November 1944, Cambridge, Massachusetts) was an American mathematician, best known for what is now called the ergodic theorem. Birkhoff was one of the most important leaders in American mathematics in his generation, and during his prime he was considered by many to be the preeminent American mathematician. Image File history File links George_Birkhoff. ... Image File history File links George_Birkhoff. ... March 21 is the 80th day of the year in the Gregorian Calendar (81st in leap years). ... 1884 (MDCCCLXXXIV) is a leap year starting on Tuesday (click on link to calendar) of the Gregorian calendar (or a leap year starting on Thursday of the 12-day-slower Julian calendar). ... November 12 is the 316th day of the year (317th in leap years) in the Gregorian Calendar, with 49 days remaining. ... 1944 (MCMXLIV) was a leap year starting on Saturday (the link is to a full 1944 calendar). ... Settled: 1630 â€“ Incorporated: 1636 Zip Code(s): 02138, 02139, 02140, 02141, 02142 â€“ Area Code(s): 617 / 857 Official website: http://www. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... In mathematics, a measure-preserving transformation T on a probability space is said to be ergodic if the only measurable sets invariant under T have measure 0 or 1. ...

The mathematician Garrett Birkhoff (1911-1996) was his son. Garrett Birkhoff (January 19, 1911, Princeton, New Jersey, USA - November 22, 1996, Water Mill, New York, USA) was an American mathematician. ...

Career

Birkhoff obtained his A.B. and A.M. from Harvard. He completed his Ph.D. in 1907, on differential equations, at the University of Chicago. While Eliakim Hastings Moore was his supervisor, he was most influenced by the writings of Henri Poincaré. After teaching at the University of Wisconsin and Princeton University, he taught at Harvard University from 1912 until his death. In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... The University of Chicago is a private university located principally in the Hyde Park neighborhood of Chicago. ... Eliakim Hastings Moore (born January 26, 1862, died December 30, 1932) was an American mathematician. ... Jules Henri PoincarÃ© (April 29, 1854 â€“ July 17, 1912) (IPA: [][1]), was one of Frances greatest mathematicians and theoretical physicists, and a philosopher of science. ... The University of Wisconsinâ€“Madison is a public university located in Madison, Wisconsin. ... Princeton University is a coeducational private university located in Princeton, New Jersey in the United States of America. ... Harvard University (incorporated as The President and Fellows of Harvard College) is a private university in Cambridge, Massachusetts. ...

Awards and honors

In 1923, he was awarded the inaugural Bôcher Memorial Prize by the American Mathematical Society for his paper Birkhoff (1917) containing, among other things, what is now called the Birkhoff curve shortening flow. 1923 (MCMXXIII) was a common year starting on Monday (link will take you to calendar). ... The BÃ´cher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime BÃ´cher with an initial endowment of $1,450 (contributed by members of that society). ... The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ...

He was elected to the National Academy of Sciences, the American Philosophical Society, the American Academy of Arts and Sciences, the Académie des Sciences in Paris, the Pontifical Academy, and the London and Edinburg Mathematical Societies. President Harding and the National Academy of Sciences at the White House, Washington, DC, April 1921 The National Academy of Sciences (NAS) is a corporation in the United States whose members serve pro bono as advisers to the nation on science, engineering, and medicine. ... The American Philosophical Society is a discussion group founded as the Junto in 1743 by Benjamin Franklin. ... The House of the Academy, Cambridge, Massachusetts. ... The French Academy of Sciences (AcadÃ©mie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. ... A Pontifical university is a Roman Catholic university established by and directly under the authority of the Holy See. ...

Service

The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ... The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ... Transactions of the American Mathematical Society is a monthly mathematics journal published by the American Mathematical Society. ...

Work

In 1913, he proved Poincaré's "Last Geometric Theorem," a special case of the three body problem, a result that made him world famous. In 1928, he published his Dynamical Systems. He wrote on the foundations of relativity and quantum mechanics, publishing (with R E Langer) the monograph Relativity and Modern Physics in 1923. In 1923, Birkhoff also proved that the Schwarzschild geometry is the unique spherically symmetric solution of the Einstein field equations. A consequence is that black holes are not merely a mathematical curiosity, but could result from any spherical star having sufficient mass. The n-body problem is the problem of finding, given the initial positions, masses, and velocities of n bodies, their subsequent motions as determined by classical mechanics, i. ... This article needs cleanup. ... This article or section is in need of attention from an expert on the subject. ... A black hole is an object predicted by general relativity[1] with a gravitational field so strong that nothing can escape it â€” not even light. ...

Birkhoff's most durable result has been his 1931 discovery of what is now called the ergodic theorem. Combining insights from physics on the ergodic hypothesis with measure theory, this theorem solved, at least in principle, a fundamental problem of statistical mechanics. The ergodic theorem has also had repercussions for dynamics, probability theory, group theory, and functional analysis. He also worked on number theory, the Riemann-Hilbert problem, and the four colour problem. He proposed an axiomatization of Euclidian geometry different from Hilbert's; this work culminated in his text Basic Geometry (1941). In mathematics, a measure-preserving transformation T on a probability space is said to be ergodic if the only measurable sets invariant under T have measure 0 or 1. ... The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... In physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i. ... In mathematics, a measure is a function that assigns a number, e. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Probability theory is the mathematical study of phenomena characterized by randomness or uncertainty. ... In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. ... Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... The twenty-first problem of the 23 Hilbert problems, from the celebrated list put forth in 1900 by David Hilbert, was phrased like this (English translation from 1902). ... Example of a four color map The four color theorem states that every possible geographical map can be colored with at most four colors in such a way that no two adjacent regions receive the same colour. ... In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry sometimes referred to as Birkhoffs axioms. ...

In his later years, Birkhoff published two curious speculative works. His 1933 Aesthetic Measure proposed a mathematical theory of aesthetics. While writing this book, he spent a year studying the art, music and poetry of various cultures around the world. His 1938 Electricity as a Fluid combined his ideas on philosophy and science. His 1943 theory of gravitation is also puzzling, since Birkhoff knew (but didn't seem to mind) that his theory allows as sources only matter which is a perfect fluid in which the speed of sound must equal the speed of light (which, needless to say, is quite inconsistent with experiment!).^{[citation needed]} The Parthenons facade showing an interpretation of golden rectangles in its proportions. ... In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame energy density Ï and isotropic pressure p. ... The speed of sound is a term used to describe the speed of sound waves passing through an elastic medium. ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation in a vacuum, not just visible light. ...

Influence on hiring practices

Albert Einstein, among others, accused Birkhoff of advocating anti-Semitic hiring practices. During the 1930s, when many Jewish mathematicians fled Europe and tried to obtain jobs in the USA, Birkhoff is alleged to have influenced the hiring process at American institutions to exclude Jews. While Birkhoff may have held anti-Semitic views, it was also the case that he had always been outspoken in his promotion of American mathematics and mathematicians. Until Hitler's 1933 ascension, Americans often did their Ph.Ds in Europe, and American mathematics was not well-regarded by European mathematicians. It has been argued that Birkhoff's actions were in good part motivated by a desire to assure jobs for home-grown American mathematicians. Saunders Mac Lane (1994), a close friend and collaborator of Birkhoff's son, argued that any anti-Semitic tendencies Birkhoff may have had were not unusual for his time. Einstein redirects here. ... The Eternal Jew: 1937 German poster. ... Adolf Hitler Adolf Hitler (April 20, 1889 – April 30, 1945, standard German pronunciation in the IPA) was the Führer (leader) of the National Socialist German Workers Party (Nazi Party) and of Nazi Germany from 1933 to 1945. ... Saunders Mac Lane (4 August 1909, Taftville, Connecticut - 14 April 2005, San Francisco) was an American mathematician who cofounded category theory with Samuel Eilenberg. ...

Selected publications

References

Saunders Mac Lane (4 August 1909, Taftville, Connecticut - 14 April 2005, San Francisco) was an American mathematician who cofounded category theory with Samuel Eilenberg. ... Kip S. Thorne Professor Kip Stephen Thorne, Ph. ...

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