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George David Birkhoff

May 18, 2023

George David Birkhoff (March 21, 1884 – November 12, 1944) 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 time he was considered by many to be the preeminent American mathematician.[1]

The George D. Birkhoff House, his residence in Cambridge, Massachusetts, has been designated a National Historic Landmark.

Personal life

He was born in Overisel Township, Michigan,[2] the son of David Birkhoff and Jane Gertrude Droppers.[3] The mathematician Garrett Birkhoff (1911–1996) was his son.

Career

Birkhoff obtained his A.B. and A.M. from Harvard University. He completed his Ph.D. in 1907, on differential equations, at the University of Chicago. While E. H. Moore was his supervisor, he was most influenced by the writings of Henri Poincaré. After teaching at the University of Wisconsin–Madison and Princeton University, he taught at Harvard from 1912 until his death.

Awards and honors

In 1923, he was awarded the inaugural Bôcher Memorial Prize by the American Mathematical Society for his paper in 1917 containing, among other things, what is now called the Birkhoff curve shortening process.[4]

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 of Sciences,[5] and the London and Edinburgh Mathematical Societies.

The George David Birkhoff Prize in applied mathematics is awarded jointly by the American Mathematical Society and the Society for Industrial and Applied Mathematics in his honor.

Service

Work

In 1912, attempting to solve the four color problem, Birkhoff introduced the chromatic polynomial. Even though this line of attack did not prove fruitful, the polynomial itself became an important object of study in algebraic graph theory.

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 1927, he published his . 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.

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 Euclidean geometry different from Hilbert's (see Birkhoff's axioms); this work culminated in his text Basic Geometry (1941).

His 1933 Aesthetic Measure proposed a mathematical theory of aesthetics.[6] 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.

Influence on hiring practices

Albert Einstein and Norbert Wiener, among others, accused[7][8][9] 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. Birkhoff's anti-Semitic views and remarks are well-documented,[10] but Saunders Mac Lane has argued that Birkhoff's efforts were motivated less by animus towards Jews than by a desire to find jobs for home-grown American mathematicians.[11]

However, Birkhoff took a particular liking to certain Jewish mathematicians, including Stanislaw 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."[12]

Selected publications

  • Birkhoff, George David (1912). "A determinant formula for the number of ways of coloring a map". Ann. Math. 14 (1/4): 42–46. doi:10.2307/1967597. JSTOR 1967597.
  • Birkhoff, George David (1913). "Proof of Poincaré's geometric theorem". Trans. Amer. Math. Soc. 14: 14–22. doi:10.1090/s0002-9947-1913-1500933-9.
  • Birkhoff, George David (1917). "Dynamical Systems with Two Degrees of Freedom". Trans. Amer. Math. Soc. 18 (2): 199–300. doi:10.1090/s0002-9947-1917-1501070-3. PMC 1091243. PMID 16586726.
  • Birkhoff, George David and Ralph Beatley. 1959. Basic Geometry, 3rd ed. Chelsea Publishing Co. [Reprint: American Mathematical Society, 2000. ISBN 978-0-8218-2101-5]

See also

Notes

  1. ^ Morse, Marston (1946). "George David Birkhoff and his mathematical work". Bulletin of the American Mathematical Society. 52 (5, Part 1): 357–391. doi:10.1090/s0002-9904-1946-08553-5. MR 0016341.
  2. ^ (PDF). Archived from the original (PDF) on September 19, 2015. Retrieved April 12, 2015.
  3. ^ Hockey, Thomas (2009). The Biographical Encyclopedia of Astronomers. Springer Publishing. ISBN 978-0-387-31022-0. Retrieved August 22, 2012.
  4. ^ Birkhoff, George D. (1917). "Dynamical systems with two degrees of freedom". Transactions of the American Mathematical Society. American Mathematical Society. 18 (2): 199–300. doi:10.2307/1988861. JSTOR 1988861.
  5. ^ "George David Birkhoff". Casinapioiv.va. Retrieved August 17, 2012.
  6. ^ Cucker, Felipe (2013). Manifold Mirrors: The Crossing Paths of the Arts and Mathematics. Cambridge University Press. pp. 116–120. ISBN 978-0-521-72876-8.
  7. ^ Nadis, Steve; Yau, Shing-Tung (2014). A History in Sum. Harvard University Press.
  8. ^ . Archived from the original on January 12, 2014. Retrieved January 12, 2014. [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.
  9. ^ Feuer, Lewis (1976). "Recollections of Harry Austryn Wolfson" (PDF). American Jewish Archives. 28 (1): 25–50.
  10. ^ Siegmund-Schultze, Reinhard (2001), Rockefeller and the Internationalization of Mathematics Between the Two Worlds Wars: Documents and Studies for the Social History of Mathematics in the 20th Century, Progress in Mathematics, vol. 25, Springer, p. 200, ISBN 9783764364687, The most blatant utterances of anti-semitism among mathematicians came from George David Birkhoff.
  11. ^ Eisenberg, Ted (2008), "Reaction to the reactors", The Montana Mathematics Enthusiast, 5 (1): 37–44, doi:10.54870/1551-3440.1083, ISBN 9787774566574, S2CID 117640225.
  12. ^ From cardinals to chaos: reflections on the life and legacy of Stanislaw Ulam, Necia Grant Cooper, Roger Eckhardt, Nancy Shera, CUP Archive, 1989, Chapter: The Lost Cafe by Gian-Carlo Rota, page 26

References

  • Aubin, David, 2005, "Dynamical systems" in Grattan-Guinness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 871–81.
  • Mac Lane, Saunders (1994). "Jobs in the 1930s and the views of George D. Birkhoff". Math. Intelligencer. 16 (3): 9–10. doi:10.1007/bf03024350. S2CID 189887142.
  • Kip Thorne, 19nn. Black Holes and Time Warps. W. W. Norton. ISBN 0-393-31276-3.
  • Vandiver, H. S. (1963). "Some of my recollections of George David Birkhoff". J. Math. Anal. Appl. 7 (2): 271–83. doi:10.1016/0022-247x(63)90052-0.
  • Norbert Wiener, 1956. I am a Mathematician. MIT Press. Especially pp. 27–28.
  • George D. Birkhoff, Proc Natl Acad Sci U S A. 1943 August; 29(8): 231–239, "Matter, Electricity and Gravitation in Flat Space-Time".

Further reading

External links

May 18, 2023
george, david, birkhoff, march, 1884, november, 1944, american, mathematician, best, known, what, called, ergodic, theorem, birkhoff, most, important, leaders, american, mathematics, generation, during, time, considered, many, preeminent, american, mathematici. George David Birkhoff March 21 1884 November 12 1944 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 time he was considered by many to be the preeminent American mathematician 1 George David BirkhoffBorn 1884 03 21 March 21 1884Overisel Township MichiganDiedNovember 12 1944 1944 11 12 aged 60 Cambridge MassachusettsNationalityAmericanAlma materHarvard UniversityUniversity of ChicagoKnown forErgodic theoremBirkhoff s axiomsAwardsBocher Memorial Prize 1923 Newcomb Cleveland Prize 1926 Scientific careerFieldsMathematicsInstitutionsHarvard UniversityYale UniversityPrinceton UniversityRadcliffe CollegeDoctoral advisorE H MooreDoctoral studentsClarence AdamsRaymond BrinkRobert D CarmichaelBernard KoopmanRudolph LangerCharles MorreyMarston MorseG Baley PriceI M ShefferMarshall H StoneJoseph L WalshHassler WhitneyDavid WidderKenneth WilliamsThe George D Birkhoff House his residence in Cambridge Massachusetts has been designated a National Historic Landmark Contents 1 Personal life 2 Career 2 1 Awards and honors 2 2 Service 3 Work 4 Influence on hiring practices 5 Selected publications 6 See also 7 Notes 8 References 9 Further reading 10 External linksPersonal life EditHe was born in Overisel Township Michigan 2 the son of David Birkhoff and Jane Gertrude Droppers 3 The mathematician Garrett Birkhoff 1911 1996 was his son Career EditBirkhoff obtained his A B and A M from Harvard University He completed his Ph D in 1907 on differential equations at the University of Chicago While E H Moore was his supervisor he was most influenced by the writings of Henri Poincare After teaching at the University of Wisconsin Madison and Princeton University he taught at Harvard from 1912 until his death Awards and honors Edit In 1923 he was awarded the inaugural Bocher Memorial Prize by the American Mathematical Society for his paper in 1917 containing among other things what is now called the Birkhoff curve shortening process 4 He was elected to the National Academy of Sciences the American Philosophical Society the American Academy of Arts and Sciences the Academie des Sciences in Paris the Pontifical Academy of Sciences 5 and the London and Edinburgh Mathematical Societies The George David Birkhoff Prize in applied mathematics is awarded jointly by the American Mathematical Society and the Society for Industrial and Applied Mathematics in his honor Service Edit Vice president of the American Mathematical Society 1919 President of the American Mathematical Society 1925 1926 Editor of Transactions of the American Mathematical Society 1920 1924 Work EditIn 1912 attempting to solve the four color problem Birkhoff introduced the chromatic polynomial Even though this line of attack did not prove fruitful the polynomial itself became an important object of study in algebraic graph theory In 1913 he proved Poincare s Last Geometric Theorem a special case of the three body problem a result that made him world famous In 1927 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 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 Euclidean geometry different from Hilbert s see Birkhoff s axioms this work culminated in his text Basic Geometry 1941 His 1933 Aesthetic Measure proposed a mathematical theory of aesthetics 6 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 Influence on hiring practices EditAlbert Einstein and Norbert Wiener among others accused 7 8 9 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 Birkhoff s anti Semitic views and remarks are well documented 10 but Saunders Mac Lane has argued that Birkhoff s efforts were motivated less by animus towards Jews than by a desire to find jobs for home grown American mathematicians 11 However Birkhoff took a particular liking to certain Jewish mathematicians including Stanislaw 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 12 Selected publications EditBirkhoff George David 1912 A determinant formula for the number of ways of coloring a map Ann Math 14 1 4 42 46 doi 10 2307 1967597 JSTOR 1967597 Birkhoff George David 1913 Proof of Poincare s geometric theorem Trans Amer Math Soc 14 14 22 doi 10 1090 s0002 9947 1913 1500933 9 Birkhoff George David 1917 Dynamical Systems with Two Degrees of Freedom Trans Amer Math Soc 18 2 199 300 doi 10 1090 s0002 9947 1917 1501070 3 PMC 1091243 PMID 16586726 Birkhoff George David and Ralph Beatley 1959 Basic Geometry 3rd ed Chelsea Publishing Co Reprint American Mathematical Society 2000 ISBN 978 0 8218 2101 5 See also Edit Biography portal Mathematics portal Physics portalBirkhoff factorization Birkhoff Grothendieck theorem Birkhoff s theorem Birkhoff s axioms Birkhoff interpolation Birkhoff Kellogg invariant direction theorem Poincare Birkhoff theorem Equidistribution theorem Chromatic polynomial Recurrent point Topological dynamicsNotes Edit Morse Marston 1946 George David Birkhoff and his mathematical work Bulletin of the American Mathematical Society 52 5 Part 1 357 391 doi 10 1090 s0002 9904 1946 08553 5 MR 0016341 Former Fellows of The Royal Society of Edinburgh PDF Archived from the original PDF on September 19 2015 Retrieved April 12 2015 Hockey Thomas 2009 The Biographical Encyclopedia of Astronomers Springer Publishing ISBN 978 0 387 31022 0 Retrieved August 22 2012 Birkhoff George D 1917 Dynamical systems with two degrees of freedom Transactions of the American Mathematical Society American Mathematical Society 18 2 199 300 doi 10 2307 1988861 JSTOR 1988861 George David Birkhoff Casinapioiv va Retrieved August 17 2012 Cucker Felipe 2013 Manifold Mirrors The Crossing Paths of the Arts and Mathematics Cambridge University Press pp 116 120 ISBN 978 0 521 72876 8 Nadis Steve Yau Shing Tung 2014 A History in Sum Harvard University Press Math and Anti Semitism Went Hand in Hand at Harvard for Decades Note While this may be a tertiary source it clearly mentions in detail by way of reference see the quote a book that is a reliable secondary source A History in Sum a new account of mathematics teaching at Harvard published by Harvard University Press Archived from the original on January 12 2014 Retrieved January 12 2014 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 Feuer Lewis 1976 Recollections of Harry Austryn Wolfson PDF American Jewish Archives 28 1 25 50 Siegmund Schultze Reinhard 2001 Rockefeller and the Internationalization of Mathematics Between the Two Worlds Wars Documents and Studies for the Social History of Mathematics in the 20th Century Progress in Mathematics vol 25 Springer p 200 ISBN 9783764364687 The most blatant utterances of anti semitism among mathematicians came from George David Birkhoff Eisenberg Ted 2008 Reaction to the reactors The Montana Mathematics Enthusiast 5 1 37 44 doi 10 54870 1551 3440 1083 ISBN 9787774566574 S2CID 117640225 From cardinals to chaos reflections on the life and legacy of Stanislaw Ulam Necia Grant Cooper Roger Eckhardt Nancy Shera CUP Archive 1989 Chapter The Lost Cafe by Gian Carlo Rota page 26References EditAubin David 2005 Dynamical systems in Grattan Guinness I ed Landmark Writings in Western Mathematics Elsevier 871 81 Mac Lane Saunders 1994 Jobs in the 1930s and the views of George D Birkhoff Math Intelligencer 16 3 9 10 doi 10 1007 bf03024350 S2CID 189887142 Kip Thorne 19nn Black Holes and Time Warps W W Norton ISBN 0 393 31276 3 Vandiver H S 1963 Some of my recollections of George David Birkhoff J Math Anal Appl 7 2 271 83 doi 10 1016 0022 247x 63 90052 0 Norbert Wiener 1956 I am a Mathematician MIT Press Especially pp 27 28 George D Birkhoff Proc Natl Acad Sci U S A 1943 August 29 8 231 239 Matter Electricity and Gravitation in Flat Space Time Further reading EditMorse Marston 1970 1980 Birkhoff George David Dictionary of Scientific Biography Vol 2 New York Charles Scribner s Sons pp 143 146 ISBN 978 0 684 10114 9 External links Edit Media related to George David Birkhoff at Wikimedia Commons O Connor John J Robertson Edmund F George David Birkhoff MacTutor History of Mathematics archive University of St Andrews George David Birkhoff at the Mathematics Genealogy Project Birkhoff s biography permanent dead link from National Academies Press by Oswald Veblen National Academy of Sciences Biographical Memoir Retrieved from https en wikipedia org w index php title George David Birkhoff amp oldid 1143044610, 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