Mathematical Discoveries, Small Or Great Are Never

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

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

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

So Is Not Mathematical Analysis Then Not Just A Vain Game Of The Mind? To The Physicist It Can Only Give A Convenient Language; But Isn't That A Mediocre Service, Which After All We Could Have Done Without; And, It Is Not Even To Be Feared That This Artificial Language Be A Veil, Interposed Between Reality And The Physicist's Eye? Far From That, Without This Language Most Of The Initimate Analogies Of Things Would Forever Have Remained Unknown To Us; And We Would Never Have Had Knowledge Of The Internal Harmony Of The World, Which Is, As We Shall See, The Only True Objective Reality.

Mathematicians Do Not Study Objects, But The Relations Between Objects.