Stephen Cole Kleene

“The first step in making a branch of science autonomous is to fix its language.”

“By a theory, we shall mean a body of knowledge which is expressed in a fixed language.”

“A formal system is determined by a list of symbols and a list of rules.”

“Intuitionism is based on the idea that mathematics is a creation of the mind. Mathematics is not a source of timeless truths that exist in some platonic realm, but a free activity of the mind. So the basis of mathematics lies in the mathematician's intuition.”

“Logic is the art of going wrong with confidence.”

“We must be able to say, at any moment, what has already been accomplished.”

“The study of the properties of formal systems is metamathematics.”