Solomon Lefschetz

Solomon Lefschetz (3 September 1884 - 5 October 1972) was an American mathematician who did fundamental work on algebraic topology and its applications to algebraic geometry. Quotes The numerical relations existing between ordinary or so-called Plückerian singularities of a plane curve were determined as early as 1834 by PLÜCKER small, but the inverse question has been left almost untouched. It may be stated thus: To show the existence of a curve having assigned Plückerian characters; and is equivalent to the determination of the maximum of cusps κM that a curve of order m and genus p may have. VERONESE ... has solved the question for rational curves. On the existence of loci with given singularities Transactions of the American Mathematical Society 14 1 1913 23–41 0002-9947 10.1090/S0002-9947-1913-1500934-0 (quote from p. 23) In the development of the theory of algebraic functions of one variable the introduction by Riemann of the surfaces that bear his name has played a well-known part. Owing to the partial failure of space intuition with the increase in dimensionality, the introduction of similar ideas into the field of algebraic functions of several variables has been of necessity slow. It was first done by Emile Picard, whose work along this line will remain a classic. A little later came the capital writings of Poincaré in which he laid down the foundations of Analysis Situs, thus providing the needed tools to obviate the failure of space intuition. On certain numerical invariants of algebraic varieties with application to abelian varieties Transactions of the American Mathematical Society 22 3 1921 327–406 0002-9947 10.1090/S0002-9947-1921-1501178-3 (quote from p. 328) It will be remembered that the positions on a Riemann surface are treated by Hensel, Landsberg, and Jung as arithmetical divisors. At bottom the associated symbolical operations are in no sense different from those that occur in connection with the Noether-Brill theory of groups of points, elements being merely multiplied instead of added. Review: Algebraische Flächen, by H. W. E. Jung Bull. Amer. Math. Soc. 1926 32 6 718–719 http://www.ams.org/journals/bull/1926-32-06/S0002-9904-1926-04314-7 10.1090/s0002-9904-1926-04314-7 free As is well known, when one endeavors to pass from one-dimensional birational geometry to the higher dimensions, the difficulties multiply enormously. Many results do not extend at all, or if they do, they are apt to assume a far more complicated aspect or else to demand most difficult proofs. Book Review: Algebraic Surfaces by Oscar Zariski Bulletin of the American Mathematical Society 42 1 1936 13–15 0002-9904 10.1090/S0002-9904-1936-06238-5 It was my lot to plant the harpoon of algebraic topology into the body of the whale of algebraic geometry. Carl C. Gaither Alma E. Cavazos-Gaither Gaither's Dictionary of Scientific Quotations: A Collection of Approximately 27,000 Quotations Pertaining to Archaeology, Architecture, Astronomy, Biology, Botany, Chemistry, Cosmology, Darwinism, Engineering, Geology, Mathematics, Medicine, Nature, Nursing, Paleontology, Philosophy, Physics, Probability, Science, Statistics, Technology, Theory, Universe, and Zoology https://books.google.com/books?id=zQaCSlEM-OEC&pg=PA29 5 January 2012 Springer Science & Business Media 978-1-4614-1114-7 29 (quote from article originally published in 1968) In its early phase (Abel, Riemann, Weierstrass), algebraic geometry was just a chapter in analytic function theory. ... A new current appeared however (1870) under the powerful influence of Max Noether who really put "geometry" and more "birational geometry" into algebraic geometry. In the classical mémoire of Brill-Noether (Math. Ann., 1874), the foundations of "geometry on an algebraic curve" were laid down centered upon the study of linear series cut out by linear systems of curves upon a fixed curve ƒ{x, y) = 0. This produced birational invariance (for example of the genus p) by essentially algebraic methods. A page of mathematical autobiography Bulletin of the American Mathematical Society 74 5 1968 854–880 0002-9904 10.1090/S0002-9904-1968-12059-2 (quote from p. 855) Quotes about Lefschetz It is quite obvious that he was strongly influenced by the similar problems in algebraic geometry, and in particular by the theory of correspondences, studied since the middle of the nineteenth century by Chasles and the school of “enumerative geometry” (de Jonquières, Zeuthen, Schubert), then by Hurwitz in the theory of Riemann surfaces, and which had been thoroughly investigated by Severi in the first years of the twentieth century; this influence explains the rather unusual frame within which Lefschetz developed his theory. Jean Dieudonné A History of Algebraic and Differential Topology, 1900 - 1960 https://books.google.com/books?id=RUV5Dz90rDkC&pg=PA198 1 September 2009 Springer Science & Business Media 978-0-8176-4907-4 198 Solomon Lefschetz had a reputation for “kibitzing” during the lectures of colleagues; at perhaps the first public talk on computing that von Neumann ever gave, von Neumann said, halfway in, “Well, so far so good” — and Lefschetz added, “and so trivial.” (The students passed down an impious faculty song about their elders; the verse for Lefschetz ended, “When he’s at last beneath the sod, he’ll then begin to heckle God.”) Elyse Graham, January 10, 2018 Adventures in Fine Hall Princeton Alumni Weekly https://paw.princeton.edu/article/adventures-fine-hall "Lefschetz made a brief trip to Rome, and I asked Severi what he thought of Lefschetz's work. 'È bravo,' Severi told me, meaning more or less 'he is talented.' The word 'bravo,' as far as I can tell, has no equivalent in other languages. 'He is no Poincaré,' Severi added. Poincaré was an eagle, 'un'aquila'—and at this, he raised his hand high. Lefschetz was a sparrow, 'un passero,' and he lowered his hand halfway. But Lefschetz was talented, 'è bravo però, è bravo.'" André Weil, The Apprenticeship of a Mathematician (1992), p. 49 I would read Lefschetz's book on analysis situs and algebraic geometry - the book about which Hodge used to say that all the important statements were true and all the others false. André Weil, The Apprenticeship of a Mathematician (1992), p. 154 External links Category:Academics from the United States Category:Mathematicians from the United States Category:Jews from Russia Category:Jews from the United States Category:Immigrants to the United States Category:People from Moscow Category:1884 births Category:1972 deaths Category:National Medal of Science laureates Category:Princeton University faculty