Just As Houses Are Made Of Stones,

One Geometry Cannot Be More True Than Another; It Can Only Be More Convenient.

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.‎

One Would Have To Have Completely Forgotten The History Of Science So As To Not Remember That The Desire To Know Nature Has Had The Most Constant And The Happiest Influence On The Development Of Mathematics.

Mathematics Has A Threefold Purpose. It Must Provide An Instrument For The Study Of Nature. But This Is Not All: It Has A Philosophical Purpose, And, I Daresay, An Aesthetic Purpose.

Guessing Before Proving! Need I Remind You That It Is So That All Important Discoveries Have Been Made?