Mathematicians Stand On Each Other's Shoulders.

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.

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.

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.

That This Subject [of Imaginary Magnitudes] Has Hitherto Been Considered From The Wrong Point Of View And Surrounded By A Mysterious Obscurity, Is To Be Attributed Largely To An Ill-adapted Notation. If, For Example, +1, -1, And The Square Root Of -1 Had Been Called Direct, Inverse And Lateral Units, Instead Of Positive, Negative And Imaginary (or Even Impossible), Such An Obscurity Would Have Been Out Of The Question.

Mathematics Is The Queen Of The Sciences.