George David Birkhoff | |
|---|---|
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| Born | (1884-03-21)March 21, 1884 |
| Died | November 12, 1944(1944-11-12) (aged 60) Cambridge, Massachusetts, U.S. |
| Alma mater | Harvard University (AB,AM) University of Chicago (PhD) |
| Known for | Ergodic theorem Birkhoff's axioms |
| Awards | Bôcher Memorial Prize(1923) Newcomb Cleveland Prize(1926) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Harvard University Yale University Princeton University Radcliffe College |
| Thesis | Asymptotic Properties of Certain Ordinary Differential Equations with Applications to Boundary Value and Expansion Problems (1907) |
| Doctoral advisor | E. H. Moore |
| Doctoral students | Clarence Adams Raymond Brink Robert D. Carmichael Bernard Koopman Rudolph Langer Charles Morrey Marston Morse G. Baley Price I. M. Sheffer Marshall H. Stone Joseph L. Walsh Hassler Whitney David Widder Kenneth Williams |
| Signature | |
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George David Birkhoff (March 21, 1884 – November 12, 1944) was one of the top American mathematicians of his generation. He made valuable contributions to the theory ofdifferential equations,dynamical systems, thefour-color problem, thethree-body problem, andgeneral relativity. Today, Birkhoff is best remembered for theergodic theorem.[1] TheGeorge D. Birkhoff House, his residence inCambridge, Massachusetts, has been designated aNational Historic Landmark.
He was born inOverisel Township, Michigan,[2] the son of two Dutch immigrants, David Birkhoff, who arrived in the United States in 1870, and Jane Gertrude Droppers.[3][4] Birkhoff's father worked as aphysician in Chicago while he was a child.[4] From 1896 to 1902, he would attend theLewis Institute as a teenager.[4]
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.[5] Following his time at theLewis Institute, Birkhoff would spend a year at theUniversity of Chicago.[4] He then obtained his A.B. and A.M. fromHarvard University, returned to the University of Chicago in 1905, and at the age of twenty-three, graduatedsumma cum laude with hisPh.D. in 1907 indifferential equations.[4] WhileE. H. Moore was his supervisor,[6] he was most influenced by the writings ofHenri Poincaré. After teaching at theUniversity of Wisconsin–Madison from 1907 to 1909 and atPrinceton University from 1909 to 1912, he taught at Harvard from 1912 until his death.[4] Being the only American familiar with the three main mathematical institutions within the United States—Chicago, Harvard and Princeton—he was held in high regard by his colleagues.[5]
During his membership in theAmerican Mathematical Society, Birkhoff served multiple positions in the organization. In 1919, he served as vice president of the society. He was editor ofTransactions of the American Mathematical Society from 1920 to 1924.
From 1925 to 1926, he was President of the American Mathematical Society. During his tenure as president of the society, Birkhoff sought to create a lectureship program to travel the United States to promote mathematics.[7] In 1926, he travelled Europe to serve as an unofficial representative of theRockefeller Foundation's International Education Board.[5] During his time in Europe, Birkhoff attempted to create links between American and French institutions, especially due to his affection for Paris.[8]
In 1937, he served as president of theAmerican Association for the Advancement of Science, a rare occurrence for mathematicians and was proof of his respect amongst the scientific community.[9]
In 1912, attempting to solve thefour color problem, Birkhoff introduced thechromatic polynomial. Even though this line of attack did not prove fruitful, thepolynomial itself became an important object of study inalgebraic graph theory.
In 1913, he proved Poincaré's "Last Geometric Theorem,"[10] a special case of thethree-body problem, a result that made him world-famous and improved the international recognition of American mathematics.[5]
Birkhoff was also acontributor to the development ofgeneral relativity. He wrote on the foundations of relativity andquantum mechanics, publishing (withR. E. Langer) the monographRelativity and Modern Physics in 1923. In 1923, Birkhoff alsoproved that theSchwarzschild geometry is the unique spherically symmetric solution of theEinstein field equations. A consequence is thatblack holes are not merely a mathematical curiosity, but could result from any spherical star having sufficient mass. His theorem was later used to develop theOppenheimer–Snyder model. In 1927, he published hisDynamical Systems.
Birkhoff's most durable result has been his 1931 discovery of what is now called theergodic theorem. Combining insights fromphysics on theergodic hypothesis withmeasure theory, this theorem solved, at least in principle, a fundamental problem ofstatistical mechanics. The ergodic theorem has also had repercussions for dynamics,probability theory,group theory, andfunctional analysis. He also worked onnumber theory, theRiemann–Hilbert problem, and thefour colour problem. He proposed an axiomatization ofEuclidean geometry different from Hilbert's (seeBirkhoff's axioms); this work culminated in his textBasic Geometry (1941).
His 1933Aesthetic Measure proposed amathematical theory of aesthetics.[11] While writing this book, he spent a year studying the art, music and poetry of various cultures around the world. His 1938Electricity 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 aperfect fluid in which thespeed of sound must equal thespeed of light.
Birkhoff believed that fellowships from foreign nations would improve the mathematic standards in the United States,[12] though he wanted to raise the standards for fellowships, believing that the qualifications in less-developed countries were different and that access should be limited.[13] He also was adamant that foreign fellows be able to meet language requirements.[14]
Albert Einstein andNorbert Wiener, among others, accused[15][16][17] Birkhoff of advocatinganti-Semitic selection processes. During the 1930s, when many Jewish mathematicians fled Europe and tried to obtain positions in the United States, Birkhoff is alleged to have influenced the selection process at American institutions to exclude Jews.[16]Saunders Mac Lane, who was at Harvard at the time, would call Einstein's allegations "worthless" as he was not familiar with American processes and that the two had competing ideas regarding general relativity while also rebutting the reports of anti-Semitism against Wiener, writing "Birkhoff clearly listened to Norbert's ideas. There could be many reasons why Birkhoff did not take steps to appoint him".[18] Mac Lane also stated that Birkhoff's efforts were motivated less by animus towards Jews than by a desire to find jobs for home-grown American mathematicians.[19]
Birkhoff was also close to Jewish mathematicianStanislaw Ulam.Gian-Carlo Rota writes: "Like other persons rumored to be anti-Semitic, he would occasionally feel the urge to shower his protective instincts on some good-looking young Jew. Ulam's sparkling manners were diametrically opposite to Birkhoff's hard-working, aggressive, touchy personality. Birkhoff tried to keep Ulam at Harvard, but his colleagues balked at the idea."[20]
Summarizing Birkhoff's selection process, fellow mathematicianOswald Veblen would write:[4]
While Birkhoff was subject to as many prejudices as most of us, he kept always what most of us lose as we grow older, the power to see people and events simply and naively rather than with reference to current opinion.
In 1923, he was awarded the inauguralBôcher Memorial Prize by theAmerican Mathematical Society for his paper in 1917 containing, among other things, what is now called theBirkhoff curve shortening process.[21]
He was elected to theNational Academy of Sciences, theAmerican Philosophical Society, theAmerican Academy of Arts and Sciences, theAcadémie des Sciences in Paris, thePontifical Academy of Sciences,[22] and the London and Edinburgh Mathematical Societies.
TheGeorge David Birkhoff Prize in applied mathematics is awarded jointly by theAmerican Mathematical Society and theSociety for Industrial and Applied Mathematics in his honor.
Birkhoff married Margaret Elizabeth Graftus in 1908.[4] They two had three children, Barbara, mathematicianGarrett Birkhoff (1911–1996) and Rodney.[4]
[QUOTE:] For over three decades, the math department at Harvard was ruled by a man whom Albert Einstein called "one of the world's great anti-Semites." This is one of the key revelations in "A History in Sum," a new account of mathematics teaching at Harvard published by Harvard University Press. Co-authored by science journalist Steve Nadis and current Harvard math professor Shing-Tung Yau, "A History in Sum" describes how George Birkhoff reigned over the Harvard department from 1912 to 1944. Birkhoff, an American of Dutch origin, was instrumental in preventing Jewish mathematicians from being hired. It may seem counterintuitive that a Harvard professor would shed light on this shameful legacy in a book published by the university's own press, but Yau is a veteran whistle-blower who has frequently criticized academic corruption and educational abuses in his native China.
This reference is worthless: Einstein did not then carefully follow the American academic scene Birkhoff had a (then well-known) competing theory of relativity ... Wiener attended Harvard's colloquia; Birkhoff clearly listened to Norbert's ideas. There could be many reasons why Birkhoff did not take steps to appoint him
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