Stephen Cole Kleene

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

“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.”

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

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

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

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

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