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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.

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.

As Long As A Branch Of Science Offers An Abundance Of Problems, So Long It Is Alive; A Lack Of Problems Foreshadows Extinction Or The Cessation Of Independent Development.

Mathematics Knows No Races Or Geographic Boundaries; For Mathematics, The Cultural World Is One Country.

Geometry, Like Arithmetic, Requires For Its Logical Development Only A Small Number Of Simple, Fundamental Principles. These Fundamental Principles Are Called The Axioms Of Geometry.