"In the initial stages of research, mathematicians do not seem to function like theorem-proving machines. Instead, they use some sort of mathematical intuition to ‘see’ the universe of mathematics and determine by a sort of empirical process what is true. This alone is not enough, of course. Once one has discovered a mathematical truth, one tries to find a proof for it." (Rudy Rucker, "Infinity and the Mind: The science and philosophy of the infinite", 1982)
"The study of infinity is much more than a dry academic game. The intellectual pursuit of the absolute infinity is, as Georg Cantor realized, a form of the soul's quest for God. Whether or not the goal is ever reached, an awareness of the process brings enlightenment." (Rudy Rucker, "Infinity and the Mind: The science and philosophy of the infinite", 1982)
"At the most elemental level, reality evanesces into something called Schröedinger's Wave Function: a mathematical abstraction which is best represented as a pattern in an infinite-dimensional space, Hilbert Space. Each point of the Hilbert Space represents a possible state of affairs. The wave function for some one physical or mental system takes the form of, let us say, a coloring in of Hilbert Space. The brightly colored parts represent likely states for the system, the dim parts represent less probable states of affairs." (Rudy Rucker, "The Sex Sphere", 1983)
"The space of our universe is the hypersurface of a vast expanding hypersphere." (Rudy Rucker, "The Sex Sphere", 1983)
"What is the shape of space? Is it flat, or is it bent? Is it nicely laid out, or is it warped and shrunken? Is it finite, or is it infinite? Which of the following does space resemble more: (a) a sheet of paper, (b) an endless desert, (c) a soap bubble, (d) a doughnut, (e) an Escher drawing, (f) an ice cream cone, (g) the branches of a tree, or (h) a human body?" (Rudy Rucker, "The Fourth Dimension: Toward a Geometry of Higher Reality", 1984)
"A photon is a wavy yet solid little package that can zip
through empty space without the benefit of any invisible jelly vibrating
underfoot."
"The world is colors and motion, feelings and thought [...] and what does math have to do with it? No much, if "math" means being bored in high school, but in truth mathematics is the one universal science. Mathematics is the study of pure pattern, and everything in the cosmos is a kind of pattern." (Rudy Rucker, "Mind Tools", 1987)
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