Mathematicians Are Born, Not Made.

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

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.

For A Long Time The Objects That Mathematicians Dealt With Were Mostly Ill-defined; One Believed One Knew Them, But One Represented Them With The Senses And Imagination; But One Had But A Rough Picture And Not A Precise Idea On Which Reasoning Could Take Hold.

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

It May Happen That Small Differences In The Initial Conditions Produce Very Great Ones In The Final Phenomena.