To Invent Is To Discern, To Choose.

If We Wish To Foresee The Future Of Mathematics, Our Proper Course Is To Study The History And Present Condition Of The Science.

Chance ... Must Be Something More Than The Name We Give To Our Ignorance.

Thought Must Never Submit, Neither To A Dogma, Nor To A Party, Nor To A Passion, Nor To An Interest, Nor To A Preconceived Idea, Nor To Whatever It May Be, Save To The Facts Themselves, Because, For Thought, Submission Would Mean Ceasing To Be.

All That We Can Hope From These Inspirations, Which Are The Fruits Of Unconscious Work, Is To Obtain Points Of Departure For Such Calculations. As For The Calculations Themselves, They Must Be Made In The Second Period Of Conscious Work Which Follows The Inspiration, And In Which The Results Of The Inspiration Are Verified And The Consequences Deduced.‎

Logic Sometimes Makes Monsters. For Half A Century We Have Seen A Mass Of Bizarre Functions Which Appear To Be Forced To Resemble As Little As Possible Honest Functions Which Serve Some Purpose.