Mathematicians Stand On Each Other's Shoulders.

Mathematics Is The Queen Of Sciences And Number Theory Is The Queen Of Mathematics. She Often Condescends To Render Service To Astronomy And Other Natural Sciences, But In All Relations She Is Entitled To The First Rank.

There Are Problems To Whose Solution I Would Attach An Infinitely Greater Importance Than To Those Of Mathematics, For Example Touching Ethics, Or Our Relation To God, Or Concerning Our Destiny And Our Future; But Their Solution Lies Wholly Beyond Us And Completely Outside The Province Of Science.

Complete Knowledge Of The Nature Of An Analytic Function Must Also Include Insight Into Its Behavior For Imaginary Values Of The Arguments. Often The Latter Is Indispensable Even For A Proper Appreciation Of The Behavior Of The Function For Real Arguments. It Is Therefore Essential That The Original Determination Of The Function Concept Be Broadened To A Domain Of Magnitudes Which Includes Both The Real And The Imaginary Quantities, On An Equal Footing, Under The Single Designation Complex Numbers.

To Praise It Would Amount To Praising Myself. For The Entire Content Of The Work... Coincides Almost Exactly With My Own Meditations Which Have Occupied My Mind For The Past Thirty Or Thirty-five Years.

It Is Always Noteworthy That All Those Who Seriously Study This Science [the Theory Of Numbers] Conceive A Sort Of Passion For It.