"The essence of mathematics lies in its freedom."
Freedom
"A set is a Many that allows itself to be thought of as a One."
Knowledge
"The fear of infinity is one form of myopia."
Fear
"In mathematics the art of proposing a question must be held of higher value than solving it."
Education
"God is always geometrizing."
Faith
"The fear of infinity is the beginning of all mathematical knowledge."
Wisdom
"I realize that in the eyes of some I am nothing more than an unpleasant crank and pest."
Perseverance
"It is certain that one cannot understand the most important human and natural phenomena without mathematics."
Science
"Mathematics is the only infinite human activity."
"The actual infinite arises in three contexts: first, when it is realized in the most complete form, a totality, in the absolute, which is God."
Faith
"No one shall expel us from the Paradise that Cantor has created."
Creativity
"The transfinite numbers are just as much at the disposal of the mathematicians as the finite numbers."
Power
"The mathematician is entirely free to construct his abstract beings."
Freedom
"Let no one suppose that the lore of the infinite has been exhausted."
Imagination
"The underlying source and origin of all creation is that which is infinite."
Philosophy
"Every mathematician worthy of the name has experienced the state of direct revelation."
Inspiration
"Time and space are modes by which we think, not conditions in which we live."
Time
"What distinguishes the mathematician is the ability to think abstractly."
Knowledge
"I entertain no doubt as to the absolute certitude and truth of the transfinite numbers."
Truth
"The fear of the infinite is the source of all our misunderstandings."
Fear
"The true spirit of delight, the exaltation, the sense of being more than Man, is the touchstone of the highest excellence."
Happiness
"In mathematics you don't understand things. You just get used to them."
Education
"God is in the details."
Philosophy
"The deeper principle is that each mathematical truth is absolute."
Truth
"Infinity! No other question has ever moved so profoundly the spirit of man."
"Pure mathematics is the judge of its own creations."
Knowledge
"Where the element of infinity presents itself, we must be especially careful."
Patience
"Mathematics takes us into the region of absolute necessity."
Science
"The infinite is not to be feared, but embraced."
Courage
"I regret that I cannot make my work as understandable as I should like."
Perseverance