Geometry, Like Arithmetic, Requires For Its Logical

Who Of Us Would Not Be Glad To Lift The Veil Behind Which The Future Lies Hidden; To Cast A Glance At The Next Advances Of Our Science And At The Secrets Of Its Development During Future Centuries? What Particular Goals Will There Be Toward Which The Leading Mathematical Spirits Of Coming Generations Will Strive? What New Methods And New Facts In The Wide And Rich Field Of Mathematical Thought Will The New Centuries Disclose?

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.

If One Were To Bring Ten Of The Wisest Men In The World Together And Ask Them What Was The Most Stupid Thing In Existence, They Would Not Be Able To Discover Anything So Stupid As Astrology.

The Further A Mathematical Theory Is Developed, The More Harmoniously And Uniformly Does Its Construction Proceed, And Unsuspected Relations Are Disclosed Between Hitherto Separated Branches Of The Science.

No One Shall Expel Us From The Paradise Which Cantor Has Created For Us. Expressing The Importance Of Cantor's Set Theory In The Development Of Mathematics.