It Is By Logic That We Prove,

It Is Through Science That We Prove, But Through Intuition That We Discover.

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.

The Mind Uses Its Faculty For Creativity Only When Experience Forces It To Do So.

Thus, Be It Understood, To Demonstrate A Theorem, It Is Neither Necessary Nor Even Advantageous To Know What It Means.

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.