The Tool Which Serves As

Every Kind Of Science, If It Has Only Reached A Certain Degree Of Maturity, Automatically Becomes A Part Of Mathematics.

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.

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

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.

Before Beginning [to Try To Prove Fermat's Last Theorem] I Should Have To Put In Three Years Of Intensive Study, And I Haven't That Much Time To Squander On A Probable Failure.