In Mathematics There Are No True Controversies.

I Am Coming More And More To The Conviction That The Necessity Of Our Geometry Cannot Be Demonstrated, At Least Neither By, Nor For, The Human Intellect. . . Geometry Should Be Ranked, Not With Arithmetic, Which Is Purely Aprioristic, But With Mechanics.

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

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 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.

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.