One Must Be Able To

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.

Besides It Is An Error To Believe That Rigour Is The Enemy Of Simplicity. On The Contrary We Find It Confirmed By Numerous Examples That The Rigorous Method Is At The Same Time The Simpler And The More Easily Comprehended. The Very Effort For Rigor Forces Us To Find Out Simpler Methods Of Proof.

We Do Not Master A Scientific Theory Until We Have Shelled And Completely Prised Free Its Mathematical Kernel.

If I Were To Awaken After Having Slept For A Thousand Years, My First Question Would Be: Has The Riemann Hypothesis Been Proven?

In Mathematics ... We Find Two Tendencies Present. On The One Hand, The Tendency Towards Abstraction Seeks To Crystallise The Logical Relations Inherent In The Maze Of Materials ... Being Studied, And To Correlate The Material In A Systematic And Orderly Manner. On The Other Hand, The Tendency Towards Intuitive Understanding Fosters A More Immediate Grasp Of The Objects One Studies, A Live Rapport With Them, So To Speak, Which Stresses The Concrete Meaning Of Their Relations.