The Infinite! No Other Question Has Ever

The Arithmetical Symbols Are Written Diagrams And The Geometrical Figures Are Graphic Formulas.

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 Art Of Doing Mathematics Consists In Finding That Special Case Which Contains All The Germs Of Generality.

The Tool Which Serves As Intermediary Between Theory And Practice, Between Thought And Observation, Is Mathematics; It Is Mathematics Which Builds The Linking Bridges And Gives The Ever More Reliable Forms.

Every Mathematical Discipline Goes Through Three Periods Of Development: The Naive, The Formal, And The Critical.