Georg Cantor

Death is not the end, but a transition to another state of being.

The universe is a manifestation of divine thought, and mathematics is the key to deciphering it.

The pursuit of beauty in mathematics is a pursuit of divine harmony.

The human condition is a paradox of finite existence and infinite aspirations.

I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a façon de parler, the true meaning being a limit which certain ratios approach indefinitely, while others increase indefinitely.

A set is a Many that allows itself to be thought of as a One.

The actual infinite, which I introduced into mathematics, has been until now considered by many as a forbidden fruit.

I entertain no doubts as to the truth of the transfinite numbers, which I introduced into mathematics, in the face of the opposition which they have encountered.

The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it is only a step away from us.

My theory of transfinite numbers has been attacked by some as being dangerous to religion. But I believe that it is not only harmless, but even beneficial to religion.

The transfinite numbers are in a certain sense nothing but a generalization of the finite numbers.

Every infinite set contains a denumerable subset.

The power of the continuum is greater than the power of the set of natural numbers.

I am so in love with the transfinite that I cannot give it up.

The transfinite numbers are not arbitrary creations of my mind, but rather they are the necessary consequences of the concepts of number and order.

The theory of transfinite numbers is an organic whole, which has grown out of the concept of the actual infinite.

The transfinite numbers are in a certain sense more real than the finite numbers, because they are not subject to the limitations of our intuition.

The actual infinite exists in three forms: in the absolute God, in the created world, and in the mathematical concepts.

The continuum is not a mere collection of points, but a whole, which is more than the sum of its parts.

The theory of sets is the foundation of all mathematics.