He Who Seeks For Methods Without Having

I Do Not Want To Presuppose Anything As Known. I See In My Explanation In Section 1 The Definition Of The Concepts Point, Straight Line And Plane, If One Adds To These All The Axioms Of Groups I-v As Characteristics. If One Is Looking For Other Definitions Of Point, Perhaps By Means Of Paraphrase In Terms Of Extensionless, Etc., Then, Of Course, I Would Most Decidedly Have To Oppose Such An Enterprise. One Is Then Looking For Something That Can Never Be Found, For There Is Nothing There, And Everything Gets Lost, Becomes Confused And Vague, And Degenerates Into A Game Of Hide And Seek.

The Infinite! No Other Question Has Ever Moved So Profoundly The Spirit Of Man.

[on Cantor's Work:] The Finest Product Of Mathematical Genius And One Of The Supreme Achievements Of Purely Intellectual Human Activity.

Before Beginning [to Try To Prove Fermat's Last Theorem] I Should Have To Put In Three Years Of Intensive Study, And I Haven't That Much Time To Squander On A Probable Failure.

No Other Question Has Ever Moved So Profoundly The Spirit Of Man; No Other Idea Has So Fruitfully Stimulated His Intellect; Yet No Other Concept Stands In Greater Need Of Clarification Than That Of The Infinite.