When The Physicists Ask Us For The

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.

It May Be Appropriate To Quote A Statement Of Poincare, Who Said (partly In Jest No Doubt) That There Must Be Something Mysterious About The Normal Law Since Mathematicians Think It Is A Law Of Nature Whereas Physicists Are Convinced That It Is A Mathematical Theorem.

Doubt Everything Or Believe Everything: These Are Two Equally Convenient Strategies. With Either We Dispense With The Need For Reflection.

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.

It Is By Logic We Prove. It Is By Intuition We Discover.