The Further A Mathematical Theory Is Developed,

Wir Mussen Wissen. Wir Werden Wissen. We Must Know. We Will Know. Inscribed On His Tomb In Gilttingen.

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.

How Thoroughly It Is Ingrained In Mathematical Science That Every Real Advance Goes Hand In Hand With The Invention Of Sharper Tools And Simpler Methods Which, At The Same Time, Assist In Understanding Earlier Theories And In Casting Aside Some More Complicated Developments.

I Didn't Work Especially Hard At Mathematics At School, Because I Knew That's What I'd Be Doing Later.

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.