Roger Penrose discusses his family background; influence of older brother Oliver; career of father; early interest in mathematics, particularly geometry; building 3-d models out of cardboard; influence of Fred Hoyle's radio talks in the late 1940s; questioning of some of the statements by Hoyle in his radio talks; meeting Dennis Sciama; early sympathy toward the steady state model; importance of aesthetics in scientific theories; early preference for closed universes; history of Penrose's ideas on the application of the second law of thermodynamics to cosmology; preference for a very mathematical structure of the origin of the universe; work with Hodge at Cambridge in pure mathematics; influence of Sciama in turning to physics and cosmology; history of work on the singularity theorems; influence of a lecture by David Finkelstein; early work on spinors; work on first singularity theorem for black holes; Penrose's preference for working on problems for which he has a different angle from everyone else; belief in a quantum era in the early universe; influence of Sciama in abandoning the steady state model; work with Stephen Hawking on the singularity theorems for cosmology; view of twistor theory; beauty of complex analytic structure; inseparability of mathematics and physics; importance of complex numbers; importance of visual images; reaction to the horizon problem; pre-eminence of the entropy problem; inadequacy of the inflationary universe model to solve the entropy problem; reasons why the inflationary universe model has been so influential; dislike for the inflationary universe model; particle physicists' lack of appreciation of the problems of general relativity; attitude toward the flatness problem; importance of quantum gravity in solving all these problems; the anthropic principle; reaction to de Lapparent, Geller, and Huchra's work on large-scale inhomogeneities; outstanding problems in cosmology: physics in the very early universe, galaxy formation, missing mass, nature of dark matter; ideal design for the universe and the unity of mathematics and physics; question of whether the universe has a purpose.