Sir Roger Penrose shares his thoughts on mathematics and world reflections. He discusses his “three worlds and three deep mysteries” theory, pure mathematics, the “Impossible Penrose Triangle”, M.C. Escher, Penrose tiling, astrophysics, and consciousness. Sir Roger Penrose is a mathematical physicist and philosopher. He is the Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute of the University of Oxford, as well as an Emeritus Fellow of Wadham College. He is a Nobel laureate for “the discovery that black hole formation is a robust prediction of the general theory of relativity”.