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Shiing-Shen Chern Quotes (1911-2004)
Poet, Leader, Mathematician
About Shiing-Shen Chern
Shiing-Shen Chern (ι³ηθΊ« October 26, 1911 β December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geometry" and is widely regarded as a leader in geometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including the Wolf Prize and the inaugural Shaw Prize.
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βIntegral geometry, started by the English geometer M. W. Crofton, has received recently important developments through the works of W. Blaschke, L. A. SantalΓ³, and others. Generally speaking, its principal aim is to study the relations between the measures which can be attached to a given variety.β
βThe main object of study in differential geometry is, at least for the moment, the differential manifolds, structures on the manifolds (Riemannian, complex, or other), and their admissible mappings. On a manifold the coordinates are valid only locally and do not have a geometric meaning themselves.β
βIn 1917 Levi-Civita discovered his celebrated parallelism which is an infinitesimal transportation of tangent vectors preserving the scalar product and is the first example of a connection. The salient fact about the Levi-Civita parallelism is the result that it is the parallelism, and not the Riemannian metric, which accounts for most of the properties concerning curvature.β
βNot all the geometrical structures are "equal". It would seem that the riemannian and complex structures, with their contacts with other fields of mathematics and with their richness in results, should occupy a central position in differential geometry. A unifying idea is the notion of a G-structure, which is the modern version of an equivalence problem first emphasized and exploited in its various special cases by Elie Cartan.β
βThe treatises of Darboux (1842β1917) and Bianchi (1856β1928) on surface theory are among the great works in the mathematical literature. They are: G. Darboux, ThΓ©orie gΓ©nΓ©rale des surfaces, Tome 1 (1887), 2 (1888), 3 (1894), 4 (1896), and later editions and reprints. L. Bianchi. Lezioni di Geometria Differenziale, Pisa 1894; German translation by Lukat, Lehrbuch der Differentialgeometrie, 1899. The subject is basically local surface theory.β
βIt is well known that in three-dimensional elliptic or spherical geometry the so-called Clifford's parallelism or parataxy has many interesting properties. A group-theoretical reason for the most important of these properties is the fact that the universal covering group of the proper orthogonal group in four variables is the direct product of the universal covering groups of two proper orthogonal groups in three variables. This last-mentioned property has no analogue for orthogonal groups in n (>4) variables. On the other hand, a knowledge of three-dimensional elliptic or spherical geometry is useful for the study of orientable Riemannian manifols of four dimensions, because their tangent spaces possess a geometry of this kind.β
Quotes About Shiing-Shen Chern
Gain deeper perspective through quotes about Shiing-Shen Chern from others.
AndrΓ© Weil as quoted on Shiing-Shen Chern
βI have no doubt that future historians of differential geometry will rank Chern as the worthly successor of Elie Cartan in that field.β
Amir D. Aczel on Shiing-Shen Chern
βRecently, having refreshed my understanding of the mathematics of relativity theory, I called one of my old Berkeley professors to ask him some questions about the geometry of general relativity. S. S. Chern is arguably the greatest living geometer. We spoke on the phone for a long time, and he patiently answered all my questions. When I told him I was contemplating writing a book about relativity, cosmology, and geometry and how they interconnect to explain the universe, he said, "It's a wonderful idea for a book, but writing it will surely take too many years of your life ... I wouldn't do it." Then he hung up.β
Andrew Locascio on Shiing-Shen Chern
βS. S. Chern revolutionized differential geometry with the use of moving frames, the invention of characteristic classes, the modern concept of a connection and so much more, but heβll probably always be most remembered for the yellowing University of Chicago mimeographed lecture notes from the 1950s. An entire generation of geometers learned the elements of differentiable manifolds from those notes.β
About Shiing-Shen Chern
Shiing-Shen Chern (ι³ηθΊ« October 26, 1911 β December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geometry" and is widely regarded as a leader in geometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including the Wolf Prize and the inaugural Shaw Prize.