There Have Been Only Three Epoch-making Mathematicians,

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.

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.

Finally, Two Days Ago, I Succeeded - Not On Account Of My Hard Efforts, But By The Grace Of The Lord. Like A Sudden Flash Of Lightning, The Riddle Was Solved. I Am Unable To Say What Was The Conducting Thread That Connected What I Previously Knew With What Made My Success Possible.

When I Have Clarified And Exhausted A Subject, Then I Turn Away From It, In Order To Go Into Darkness Again.

The Higher Arithmetic Presents Us With An Inexhaustible Store Of Interesting Truths - Of Truths, Too, Which Are Not Isolated, But Stand In A Close Internal Connection, And Between Which, As Our Knowledge Increases, We Are Continually Discovering New And Sometimes Wholly Unexpected Ties.