The Higher Arithmetic Presents Us With An

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

...as Our Friend Zach Has Often Noted, In Our Days Those Who Do The Best For Astronomy Are Not The Salaried University Professors, But So-called Dillettanti, Physicians, Jurists, And So Forth.lamenting The Fragmentary Time Left To A Professor Has Remaining After Fulfilling His Teaching Duties.

In The Last Two Months I Have Been Very Busy With My Own Mathematical Speculations, Which Have Cost Me Much Time, Without My Having Reached My Original Goal. Again And Again I Was Enticed By The Frequently Interesting Prospects From One Direction To The Other, Sometimes Even By Will-o'-the-wisps, As Is Not Rare In Mathematic Speculations.

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.

To The Distracting Occupations Belong Especially My Lecture Courses Which I Am Holding This Winter For The First Time, And Which Now Cost Much More Of My Time Than I Like. Meanwhile I Hope That The Second Time This Expenditure Of Time Will Be Much Less, Otherwise I Would Never Be Able To Reconcile Myself To It, Even Practical (astronomical) Work Must Give Far More Satisfaction Than If One Brings Up To B A Couple More Mediocre Heads Which Otherwise Would Have Stopped At A.