"One cannot escape the feeling that these mathematical formulae have an independent existence and intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than we originally put into them."

"It is positively spooky how the physicist finds the mathematician has been there before him or her."

"I find it quite amazing that it is possible to predict what will happen by mathematics, which is simply following rules which really have nothing to do with the original [physical] thing."

"What matters in mathematics, and to a very great extent in physical science, is not the intrinsic nature of our terms, but the logical nature of their inter-relations."

"…only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple"

"The word 'existence' has not the same meaning when it refers to a mathematical entity as when it refers to a material object. A mathematical entity exists provided there is no contradiction implied in its definition..."

‏¹ http://www.tau.ac.il/~cohn/seminar/2009-10/week10Coh...
‏² http://space.mit.edu/home/tegmark/crazy.html

‏⁴ http://arxiv.org/pdf/0704.0646v2

‏⁶ http://arxiv.org/pdf/0905.1283
‏⁷ http://arxiv.org/pdf/astro-ph/0511774