If I Were To Awaken After Having

The Art Of Doing Mathematics Consists In Finding That Special Case Which Contains All The Germs Of Generality.

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.

Is Mathematics Doomed To Suffer The Same Fate As Other Sciences That Have Split Into Separate Branches?... Mathematics Is, In My Opinion, An Indivisible Whole... May The New Century Bring With It Ingenious Champions And Many Zealous And Enthusiastic Disciples.

Mathematics Is A Presuppositionless Science. To Found It I Do Not Need God, As Does Kronecker, Or The Assumption Of A Special Faculty Of Our Understanding Attuned To The Principle Of Mathematical Induction, As Does Poincaré, Or The Primal Intuition Of Brouwer, Or, Finally, As Do Russell And Whitehead, Axioms Of Infinity, Reducibility, Or Completeness, Which In Fact Are Actual, Contentual Assumptions That Cannot Be Compensated For By Consistency Proofs.

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