cosmological redshift that motivates the expanding universe theory is due to curvature of the cosmos, according to Segal. He portrayed the spatial part of the cosmos as a large 3-sphere. Spacetime cannot turn back on itself. At each point in the cosmos there is a convex future direction, meaning, "the future can never merge into the past", no spacetime curvature can close or loop. Building on common symmetry expressed by the Lorentz group, Poincare group, and conformal group of spacetime, Segal saw the closing up of the universe as consistent with compactification of spacetime used to define the conformal group. Segal reviewed redshift data to verify his cosmology. He claimed confirmation, but generally his chronometric cosmology has not found favor. For instance, Abraham H. Taub reviewed Mathematical Cosmology and Extragalactic Astronomy, saying As for the cosmic microwave background, in the chronometric view, "The observed blackbody... is simply the most likely disposition of remnants of light on a purely random basis... and is not at all uniquely indicative of a Big Bang." In 2005 A. Daigneault spoke on "Irving Segal's Axiomitization of Spacetime and it Cosmological Consequences" in Budapest. He concedes at the outset that Segal's cosmology is "generally ignored by astrophysicists", and that the model was first proposed by Einstein in 1917 and is "supposedly discredited". Selected publications For a list of 227 articles and 10 books to which Segal contributed, see the MIT external link below. 1951: 1962: Lectures at the Boulder Summer Seminar, American Mathematical Society 1963: 1968: (with Ray Kunze) 1976: 1992: (with John C. Baez and Zhengfang Zhou) 1993: (with Nicoll, J.F., Wu, P., Zhou, Z.) Statistically Efficient Testing of the Hubble and Lundmark Laws on IRAS Galaxy Samples, The Astrophysical Journal 465–484 1995: (with Zhou, Z.) Maxwell's Equations in the Einstein Universe and Chronometric Cosmology, ApJS. Ser. 100, 307–324 1997: "Cosmic time dilation", The Astrophysical Journal 482:L115–17 See also Commutation theorem for traces Metaplectic group Symplectic group Symplectic spinor bundle References External links John C. Baez (1999) Memories of Irving Segal Leonard Gross and William Segal, "Irving E. Segal", Biographical Memoirs of the National Academy of Sciences (2022) 1918 births 1998 deaths Princeton University alumni Yale University alumni Harvard University faculty 20th-century American mathematicians Massachusetts Institute of Technology School of Science faculty Members of the United States National Academy of Sciences 20th-century American Jews