I Have Tried To Avoid Long Numerical

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

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.

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.

A Mathematical Problem Should Be Difficult In Order To Entice Us, Yet Not Completely Inaccessible, Lest It Mock At Our Efforts. It Should Be To Us A Guide Post On The Mazy Paths To Hidden Truths, And Ultimately A Reminder Of Our Pleasure In The Successful Solution.

Indignant Reply To The Blatent Sex Discrimination Expressed In A Colleague's Opposition When Hilbert Proposed Appointing Emmy Noether As The First Woman Professor At Their University.