There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.

This view [of the infinite], which I consider to be the sole correct one, is held by only a few. While possibly I am the very first in history to take this position so explicitly, with all of its logical consequences, I know for sure that I shall not be the last!

I entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.

In mathematics the art of proposing a question must be held of higher value than solving it.

Great innovation only happens when people aren't afraid to do things differently.

The essence of mathematics lies precisely in its freedom.

In mathematics, the art of asking questions is more valuable than solving problems.