Theory Attracts Practice As The Magnet Attracts

I Am Giving This Winter Two Courses Of Lectures To Three Students, Of Which One Is Only Moderately Prepared, The Other Less Than Moderately, And The Third Lacks Both Preparation And Ability. Such Are The Onera Of A Mathematical Profession.

I Protest Against The Use Of Infinite Magnitude ..., Which Is Never Permissible In Mathematics.

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.

Less Depends Upon The Choice Of Words Than Upon This, That Their Introduction Shall Be Justified By Pregnant Theorems.

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.