Mathematicians Stand On Each Other's Shoulders.

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.

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.

In My Opinion Instruction Is Very Purposeless For Such Individuals Who Do No Want Merely To Collect A Mass Of Knowledge, But Are Mainly Interested In Exercising (training) Their Own Powers. One Doesn't Need To Grasp Such A One By The Hand And Lead Him To The Goal, But Only From Time To Time Give Him Suggestions, In Order That He May Reach It Himself In The Shortest Way.

You Know That I Write Slowly. This Is Chiefly Because I Am Never Satisfied Until I Have Said As Much As Possible In A Few Words, And Writing Briefly Takes Far More Time Than Writing At Length.

It May Be True That People Who Are Merely Mathematicians Have Certain Specific Shortcomings; However That Is Not The Fault Of Mathematics, But Is True Of Every Exclusive Occupation. Likewise A Mere Linguist, A Mere Jurist, A Mere Soldier, A Mere Merchant, And So Forth. One Could Add Such Idle Chatter That When A Certain Exclusive Occupation Is Often Connected With Certain Specific Shortcomings, It Is On The Other Hand Always Free Of Certain Other Shortcomings.