Mathematics Is Concerned Only With The Enumeration

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

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.

A Great Part Of Its Theories Derives An Additional Charm From The Peculiarity That Important Propositions, With The Impress Of Simplicity On Them, Are Often Easily Discovered By Induction, And Yet Are Of So Profound A Character That We Cannot Find The Demonstrations Till After Many Vain Attempts; And Even Then, When We Do Succeed, It Is Often By Some Tedious And Artificial Process, While The Simple Methods May Long Remain Concealed.

In Mathematics There Are No True Controversies.

I Have A True Aversion To Teaching. The Perennial Business Of A Professor Of Mathematics Is Only To Teach The Abc Of His Science; Most Of The Few Pupils Who Go A Step Further, And Usually To Keep The Metaphor, Remain In The Process Of Gathering Information, Become Only Halbwisser [one Who Has Superficial Knowledge Of The Subject], For The Rarer Talents Do Not Want To Have Themselves Educated By Lecture Courses, But Train Themselves. And With This Thankless Work The Professor Loses His Precious Time.