"Number rules the universe."
"For travelers by land there are royal roads and roads for ordinary citizens: but in geometry there is only one road for everyone."
"There was more imagination in Archimedes' head than in that of Homer."
"Mathematics is the science of the infinite; its goal is the symbolic grasping of the infinite with human, i.e., finite means."
"Mathematicians are a kind of Frenchman; if one says something to them, they translate it into their own language, and it immediately becomes something completely different."
"Our poems are written in a quite special language, the language of mathematics,... and unfortunately these poems can only be understood in the original language."
"he infinite has always moved the human mind as deeply as no other question has; the infinite has had an energizing and fruitful effect on the understanding as hardly any other idea has; but the infinite is also in need of clarification as hardly any other concept is."
"Mathematics is a profound conversation of the human spirit with itself."
"To the extent that the theorems of mathematics have to do with reality, they are not certain, and to the extend that they are certain, they do not have to do with reality."
"There are questions on whose answers I would place an infinitely higher value than on those of mathematics, e.g. about ethics, about our relationship to God, about our purpose and about our future: but their solution lies completely unattainably above us and completely outside the domain of science."
"The genuine mathematician is an enthusiast per se. Without enthusiasm, no mathematics."
"Everything that happens in mathematics serves solely the glory of the human spirit."
"Reality is finite and therefore always unmathematical. If one wants to use mathematics to understand reality, one must idealize reality according to mathematics.."
"Theory should be the friend of practice, but not its slave."