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George David Birkhoff, March 21, 1884 — November 12, 1944 | By Oswald Veblen | Biographical Memoirs Birkhoff studied at the Lewis Institute, Chicago, from 1896 to 1902, and at the University of Chicago for a year. Birkhoff returned to the University of Chicago in the fall of 1905 and received his Ph.D. summa cum laude in 1907 at the age of twenty-three. Birkhoff shared in the exploratory studies then being made of analysis situs, as it was called before being formalized into "topology," and saw their close relation to the class of dynamical problems which were at this time taking definite form in his mind. www.nap.edu /html/biomems/gbirkhoff.html   (2416 words)

Math Trek: A Measure of Beauty, Science News Online, May 22, 2004 Birkhoff's formula and its potential applications—to such creations as vases, architectural designs, melodies, and even poetry—were intriguing enough to be the subject of an article in the March 17, 1934, issue of Science News Letter (now known as Science News). Birkhoff himself attempted to apply the principles embedded in his formula to the composition of a poem. Birkhoff himself conceded that an intuitive appreciation is better than any attempt to analyze the source of one's delight in a beautiful object. www.sciencenews.org /articles/20040522/mathtrek.asp   (1179 words)

Birkhoff, George David   (Site not responding. Last check: 2007-10-16) Birkhoff was born at Overisel, Michigan, and studied at the University of Chicago and at Harvard. With John Von Neumann, Birkhoff was chiefly responsible for establishing, in the 1930s, the modern science of ergodics. Birkhoff also transformed the Maxwell-Boltzmann hypothesis of the kinetic theory of gases, which was undermined by the number of exceptions found to it, into a vigorous principle. www.cartage.org.lb /en/themes/Biographies/MainBiographies/B/Birkhoff/1.html   (222 words)

Garrett Birkhoff - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-10-16) Garrett Birkhoff (January 19, 1911 - November 22, 1996) was an American mathematician who was born in Princeton, New Jersey, USA and died on November 22,1996 inWater Mill, New York, USA. He is the son of the mathematician George David Birkhoff. Birkhoff is most famous for the creation of a new branch of mathematics, universal algebra, with his 1935 paper, On the Structure of Abstract Algebras. encyclopedia.worldsearch.com /garrett_birkhoff.htm   (199 words)

Birkhoff Birkhoff taught at the University of Wisconsin at Madison as an instructor from 1907 to 1909. Because Birkhoff worked on so many different mathematical topics it is difficult to do justice to the range of his contributions in a biography of this length. Mac Lane [11], defends Birkhoff by saying that whatever "diffuse and varied versions of anti-Semitism" Birkhoff may have had, they were undoubtedly shared by many of his contemporaries. www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Birkhoff.html   (1484 words)

Birkhoff_Garrett   (Site not responding. Last check: 2007-10-16) Birkhoff graduated from Harvard in 1932 and was awarded a Henry Fellowship to study at Cambridge University in England. From Cambridge Birkhoff went to Munich for a month in July 1933 and worked on his own on group theory, but while he was there he visited Carathéodory who pointed him towards van der Waerden's algebra text and Speiser's group theory book. Returning to the United States, Birkhoff was a member of the Society of Fellows at Harvard from 1933 to 1936, and then he was appointed as an instructor at Harvard in 1936. www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Birkhoff_Garrett.html   (1068 words)

Harvard Gazette: Memorial Minute It is a testament to Garrett Birkhoff's strength of character that he entered a field dominated by his father and was able to have such a brilliant and varied career. Birkhoff served as assistant professor from 1938 to 1941, associate professor from 1941 to 1946, and full professor from 1946 to 1981. In 1969 Birkhoff was appointed George Putnam Professor of Pure and Applied Mathematics, a post he held until his retirement in 1981. www.news.harvard.edu /gazette/2002/12.12/24-mm.html   (954 words)

Blind Spot Birkhoff kept tabs on his monitor, using the remote camera outside the van to keep an eye on the lighted wing of the building. Birkhoff reached for an oreo cookie and was about to bite into it when a beep issued from his com unit. Birkhoff was responsible for the deaths of twelve innocents. www.geocities.com /TelevisionCity/5932/blind_spot01.html   (2062 words)

AMS Prize - George David Birkhoff Prize in Applied Mathematics This prize was established in 1967 in honor of Professor George David Birkhoff. The initial endowment was contributed by the Birkhoff family and there have been subsequent additions by others. Eleventh award, 2003: To John Mather for being a mathematician of exceptional depth, power, and originality; and to Charles S. Peskin for devoting much of his career to understanding the dynamics of the human heart and bringing an extraordinarily broad range of expertise to bear on this problem. www.ams.org /prizes/birkhoff-prize.html   (422 words)

JACKAL Birkhoff's fear was that Nikita might lose control if something were to go wrong and her team was in distress. Madeline was to his left, Birkhoff and Walter were at the center of the table, and Michael was seated at the end. Birkhoff and Walter were deep in debate as they headed out, but Michael glided out silently. www.geocities.com /TelevisionCity/5932/jackal01.html   (1175 words)

Computational Esthetics Birkhoff, however, was not making an artistic statement or propounding a normative theory; he viewed his model as an empirical theory, and was interested in its validity. This betrays a weak point in Birkhoff's "theory": for every genre of input objects, new rules must be formulated, and the notion of beauty embodied by Birkhoff's formula may therefore shift a little in each case. We mentioned already that Birkhoff's "Esthetic Measure" is in fact merely an "orderliness-coefficient", and this characterization also applies to the the information-theoretic versions of this notion based on Bense or Leeuwenberg. iaaa.nl /rs/compestE.html   (4000 words)

Search Results for Birkhoff   (Site not responding. Last check: 2007-10-16) Birkhoff was awarded his A.B. Birkhoff returned to the University of Chicago in 1905 to study for his doctorate. Birkhoff read Poincare's works on differential equations and celestial mechanics and he learnt more, and was more strongly influenced in the direction his research was taking, by Poincare than from his supervisor. Birkhoff's work on linear differential equations, difference equations and the generalised Riemann problem mostly all arose from the basis he laid in his thesis. www-gap.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?BIOGINDEX=Birkhoff   (1774 words)

AllRefer.com - George David Birkhoff (Mathematics, Biography) - Encyclopedia The son of a physician, he was educated at Harvard (B.A., 1905) and the Univ. of Chicago (Ph.D., 1907) After teaching shortly at Chicago and Princeton, he joined the faculty at Harvard (1912) where he taught until his death. Birkhoff, perhaps the first American mathematician of international repute, is known for his work on linear differential equations and difference equations. He was also deeply interested in and made contributions to the analysis of dynamical systems, celestial mechanics, the four-color map problem, and function spaces. reference.allrefer.com /encyclopedia/B/BirkhoffGD.html   (218 words)

The Ehrhart polynomial of the Birkhoff polytope   (Site not responding. Last check: 2007-10-16) Birkhoff polytope is the set of all doubly stochastic n-by-n matrices, that is, those matrices with nonnegative real coefficients in which every row and column sums to one. We present a new, complex-analytic way to compute the Ehrhart polynomial of the Birkhoff polytope, that is, the function counting the integer points in the dilated polytope. The leading term of the Ehrhart polynomial is--up to a trivial factor--the volume of the polytope, which is one reason why we are interested in this counting function. www.math.binghamton.edu /dennis/Papers/birkhoff.html   (180 words)

Miller   (Site not responding. Last check: 2007-10-16) Using George Birkhoff's concept of beauty applying order, complexity, and aesthetic measure, this paper will show that, in fact, hockey is more beautiful and structured than ever before. Aesthetic measure is determined by the fraction M=O/C. Birkhoff's concept of beauty is useful in determining the overall aesthetic measure of a chaotic sport, because it expresses how complexity is not beautiful without order and structure. To apply Birkhoff's theory to hockey, the positional and material parameters of the game must be defined. opim.wharton.upenn.edu /aesthetic/Papers/Miller.htm   (1201 words)

References for Birkhoff_Garrett   (Site not responding. Last check: 2007-10-16) Garrett Birkhoff : on the occasion of his 70th birthday, Algebra Universalis 17 (3) (1983), 223-226. Garrett Birkhoff, in Albers and G L Alexanderson (eds.), Mathematical People : Profiles and Interviews (Cambridge, MA, 1985), 3-15. S Mac Lane, Garrett Birkhoff and the "Survey of modern algebra", Notices Amer. www-history.mcs.st-and.ac.uk /Printref/Birkhoff_Garrett.html   (131 words)

Aubry-Mather sets and the invariant circle The passage of Birkhoff periodic sets of a given rotation number p/q is in general a complicated sequence of possibly simultaneous bifurcations. , an isolated hyperbolic Birkhoff periodic orbit of index -1 approaches the caustic, hits the caustic as a parabolic orbit of index -1 and leaves the caustic as an isolated elliptic orbit with index 1. Thus, the sum of the indices of Birkhoff periodic orbits passing through the caustic curve is equal to zero. www.math.harvard.edu /~knill/oldinterests/string/node5.html   (1301 words)

PlanetCerec  /  The Birkhoff Effect   (Site not responding. Last check: 2007-10-16) This is known as "The Birkhoff Effect" (so named by Dr. David Lawler). This second image, showing the double-clicks high up on the walls, is a more accurate representation of Dr. Birkhoff's method. These are Dr. Krieger's latest drawings (he may have work as a graphic artist if he ever gives up his handpiece...!). www.planetcerec.com /birkhoff_effect.shtml   (255 words)

Alibris: Birkhoff by MacLane, Saunders, and Birkhoff, Garrett D. This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses. An understanding of the developments in classical analysis during the nineteenth century is vital to a full appreciation of the history of twentieth-century mathematical thought. by Birkhoff, Garrett D. This volume describes the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering. www.alibris.com /search/books/author/Birkhoff   (514 words)

Atlas: The Homoclinic Birkhoff "Remarkable Curves" in Euclidean Spaces by Dmitry W. Serow   (Site not responding. Last check: 2007-10-16) In 1932, Birkhoff discovered his ``remarkable curve'', which is actually a strange set and not an arc or topological circle. ) the Birkhoff curve is either indecomposable continuum or the union of two indecomposable continua, and furthemore it is a compact being common boundary of the infinite number of regions. It is clear that the Birkhoff curves there subsist in n-dimensional Eucliadean spaces. atlas-conferences.com /cgi-bin/abstract/cady-62   (270 words)

The Officer Down Memorial Page Remembers . . . Patrolman Birkhoff was killed in an automobile accident while pursuing a youth who was fleeing on foot. Patrolman Birkhoff had commandeered a car and was riding on the running board. Patrolman Birkhoff had served with the Passaic Police Department for 10 years and was survived by his wife and three young children. www.odmp.org /officer.php?oid=1871   (81 words)

Active Skim View of: George David Birkhoff This correspondence resulted in the publication in 1904 of their joint paper in the Annals of Mathematics “On the integral devisors of an-bn.” So far as I know this was Birkhoff’s only publication in the theory of numbers, Reprinted with permission from the Proceedings of the American Philosophical Society (Yearbook 1946, pp. comments on his own work and revelations of his point of view toward that of his contemporaries, in Birkhoff’s address on “Fifty years of American mathematics” which was published in 1938 in a volume celebrating the semicentennial of the American Mathematical Society. The third phase of Birkhoff’s scientific career was that in which he sought to extend mathematical methods into other fields of thought, —physics, aesthetics, and even ethics. www.nap.edu /nap-cgi/skimit.cgi?isbn=0309082811&chap=44-57   (535 words)

The Hutchinson Dictionary of Scientific Biography: Birkhoff, George David (1884-1944)@ HighBeam Research   (Site not responding. Last check: 2007-10-16) The Hutchinson Dictionary of Scientific Biography: Birkhoff, George David (1884-1944)@ HighBeam Research US mathematician who made fundamental contributions to the study of dynamics and formulated the 'weak form' of the ergodic theorem. Birkhoff was born in Overisel, Michigan, on 21 March 1884. www.highbeam.com /library/doc0.asp?DOCID=1P1:99915795&refid=ip_encyclopedia_hf   (177 words)

Birkhoff   (Site not responding. Last check: 2007-10-16) The volumes of the Birkhoff polytope for n ≤ 10. The calculation of the volume of the Birkhoff polytope when n = 10 requires the evaluation of 4862 integrals. We started the calculation on March 13, 2002, using between 10 and 40 computers (depending on load). www.math.binghamton.edu /dennis/Birkhoff   (161 words)

The Birkhoff Interpolation Problem Abstract: Following the work of Gonzalez-Vega [3], we show how to use recent algorithmic tools of computational real algebraic geometry to solve the Birkhoff Interpolation Problem originally given in [6] and [1]. These algorithms are used to solve the Birkhoff Interpolation Problem in a case which is presented as an open problem in [4]. A subroutine performing a radical equi-dimensional decompoisiton was also implemented using Maple and a file connection with Gb (see [8]). www-calfor.lip6.fr /~safey/applications.html   (829 words)

References for Birkhoff   (Site not responding. Last check: 2007-10-16) L J Butler, George David Birkhoff, American National Biography 2 (Oxford, 1999), 813-814. J Rey Pastor, Professor George D Birkhoff and his influence in Argentina (Spanish), Revista Ci. H S White, Professor George D Birkhoff, president of the American Association for the Advancement of Science, Scientific Mo. 44 (1937), 191-193. www-history.mcs.st-and.ac.uk /Printref/Birkhoff.html   (201 words)

No Title   (Site not responding. Last check: 2007-10-16) and by two-point boundary conditions (1.2) was originated by Birkhoff. Afterwards, continuing up to the present time various questions concerning the spectral theory of differential operators generated by (1.1), (1.2) were studied very intensively, since there are many applications for regular problems (1.1), (1.2). In addition it has been shown by Salaff [14] and Minkin [9] that the boundary conditions of an arbitrary nonsingular selfadjoint eigenvalue problem (1.1), (1.2) are regular in the sense of Birkhoff. www.uni-duisburg.de /FB11/FGS/F7/Publications/ab54/ab54.html   (564 words)

Birkhoff, George David --  Encyclopædia Britannica Birkhoff attended the Lewis Institute (now the Illinois Institute of Technology) in Chicago from 1896 to 1902 and then spent a year at the University of Chicago before switching to Harvard University in 1903 (A.B., 1905; A.M., 1906). "Birkhoff, George David." Encyclopædia Britannica from Encyclopædia Britannica Premium Service. More results on "Birkhoff, George David" when you join. www.britannica.com /eb/article-9015375   (795 words)

Birkhoff's equations and geometrical theory of rotational relativistic system The Birkhoffian and Birkhoff's functions of a rotational relativistic system are constructed, the Pfaff action of rotational relativistic system is defined, the Pfaff-Birkhoff principle of a rotational relativistic system is given and the Pfaff-Birkhoff-D'Alembert principles and Birkhoff's equations of rotational relativistic system are constructed. The geometrical description of a rotational relativistic system is studied and the exact properties of Birkhoff's equations and their forms on The global analysis of Birkhoff's equations for a rotational relativistic system is studied, the global properties of autonomous, semi-autonomous and non-autonomous rotational relativistic Birkhoff's equations and the geometrical properties of energy change for rotational relativistic Birkhoff's equations are given. stacks.iop.org /1009-1963/10/271   (285 words)

Theory of symmetry for a rotational relativistic Birkhoff system The theory of symmetry for a rotational relativistic Birkhoff system is studied. In terms of the invariance of the rotational relativistic Pfaff-Birkhoff-D'Alembert principle under infinitesimal transformations, the Noether symmetries and conserved quantities of a rotational relativistic Birkhoff system are given. In terms of the invariance of rotational relativistic Birkhoff equations under infinitesimal transformations, the Lie symmetries and conserved quantities of the rotational relativistic Birkhoff system are given. stacks.iop.org /1009-1963/11/429   (259 words)

No Title   (Site not responding. Last check: 2007-10-16) H.E. Benzinger, Pointwise and norm convergence of a class of biorthogonal expansions, Trans. G.D. Birkhoff, On the asymptotic character of the solutions of certain linear differential equations containing a parameter, Trans. G.D. Birkhoff, Boundary value and expansion problems of ordinary linear differential equations, Trans. www.uni-duisburg.de /FB11/FGS/F7/Publications/ab55/ab55.html   (654 words)

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