It Is With Logic That One Proves;

A Small Error In The Former Will Produce An Enormous Error In The Latter.

...the Feeling Of Mathematical Beauty, Of The Harmony Of Numbers And Of Forms, Of Geometric Elegance. It Is A Genuinely Aesthetic Feeling, Which All Mathematicians Know

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 Happen That Small Differences In The Initial Conditions Produce Very Great Ones In The Final Phenomena. A Small Error In The Former Will Produce An Enormous Error In The Later. Prediction Becomes Impossible, And We Have The Fortuitous Phenomena.

Pure Logic Could Never Lead Us To Anything But Tautologies; It Can Create Nothing New; Not From It Alone Can Any Science Issue.