To Invent Is To Discern, To Choose.

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.

Often When Works At A Hard Question, Nothing Good Is Accomplished At The First Attack. Then One Takes A Rest, Long Or Short, And Sits Down Anew To The Work. During The First Half-hour, As Before, Nothing Is Found, And Then All Of A Sudden The Decisive Idea Presents Itself To The Mind.

This Harmony That Human Intelligence Believes It Discovers In Nature - Does It Exist Apart From That Intelligence? No, Without Doubt, A Reality Completely Independent Of The Spirit Which Conceives It, Sees It Or Feels It, Is An Impossibility. A World So Exterior As That, Even If It Existed, Would Be Forever Inaccessible To Us. But What We Call Objective Reality Is, In The Last Analysis, That Which Is Common To Several Thinking Beings, And Could Be Common To All; This Common Part, We Will See, Can Be Nothing But The Harmony Expressed By Mathematical Laws.

In The Old Days When People Invented A New Function They Had Something Useful In Mind. Now, They Invent Them Deliberately Just To Invalidate Our Ancestors' Reasoning, And That Is All They Are Ever Going To Get Out Of Them.

A First Fact Should Surprise Us, Or Rather Would Surprise Us If We Were Not Used To It. How Does It Happen There Are People Who Do Not Understand Mathematics? If Mathematics Invokes Only The Rules Of Logic, Such As Are Accepted By All Normal Minds...how Does It Come About That So Many Persons Are Here Refractory?