The 48+ David Hilbert Quotes

[on Cantor's Work:] The Finest Product Of Mathematical Genius And One Of The Supreme Achievements Of Purely Intellectual Human Activity.

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.

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.

The Arithmetical Symbols Are Written Diagrams And The Geometrical Figures Are Graphic Formulas.

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.

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

Who Of Us Would Not Be Glad To Lift The Veil Behind Which The Future Lies Hidden; To Cast A Glance At The Next Advances Of Our Science And At The Secrets Of Its Development During Future Centuries? What Particular Goals Will There Be Toward Which The Leading Mathematical Spirits Of Coming Generations Will Strive? What New Methods And New Facts In The Wide And Rich Field Of Mathematical Thought Will The New Centuries Disclose?

I Have Tried To Avoid Long Numerical Computations, Thereby Following Riemann's Postulate That Proofs Should Be Given Through Ideas And Not Voluminous Computations.

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.

Geometry Is The Most Complete Science.

Physics Is Much Too Hard For Physicists.

The Further A Mathematical Theory Is Developed, The More Harmoniously And Uniformly Does Its Construction Proceed, And Unsuspected Relations Are Disclosed Between Hitherto Separated Branches Of The Science.