The Infinite Is Only A Manner Of

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

The Problem Of Distinguishing Prime Numbers From Composite Numbers And Of Resolving The Latter Into Their Prime Factors Is Known To Be One Of The Most Important And Useful In Arithmetic. It Has Engaged The Industry And Wisdom Of Ancient And Modern Geometers To Such An Extent That It Would Be Superfluous To Discuss The Problem At Length. ... Further, The Dignity Of The Science Itself Seems To Require That Every Possible Means Be Explored For The Solution Of A Problem So Elegant And So Celebrated.

I Mean The Word Proof Not In The Sense Of The Lawyers, Who Set Two Half Proofs Equal To A Whole One, But In The Sense Of A Mathematician, Where Half Proof = 0, And It Is Demanded For Proof That Every Doubt Becomes Impossible.

There Have Been Only Three Epoch-making Mathematicians, Archimedes, Newton, And Eisenstein.

I Have A True Aversion To Teaching. The Perennial Business Of A Professor Of Mathematics Is Only To Teach The Abc Of His Science; Most Of The Few Pupils Who Go A Step Further, And Usually To Keep The Metaphor, Remain In The Process Of Gathering Information, Become Only Halbwisser [one Who Has Superficial Knowledge Of The Subject], For The Rarer Talents Do Not Want To Have Themselves Educated By Lecture Courses, But Train Themselves. And With This Thankless Work The Professor Loses His Precious Time.