I Didn't Work Especially Hard At Mathematics

A Mathematical Problem Should Be Difficult In Order To Entice Us, Yet Not Completely Inaccessible, Lest It Mock At Our Efforts. It Should Be To Us A Guide Post On The Mazy Paths To Hidden Truths, And Ultimately A Reminder Of Our Pleasure In The Successful Solution.

[on Cantor's Work:] The Finest Product Of Mathematical Genius And One Of The Supreme Achievements Of Purely Intellectual Human Activity.

Some People Have Got A Mental Horizon Of Radius Zero And Call It Their Point Of View.

However Unapproachable These Problems May Seem To Us And However Helpless We Stand Before Them, We Have, Nevertheless, The Firm Conviction That Their Solution Must Follow By A Finite Number Of Purely Logical Processes.

Besides It Is An Error To Believe That Rigour Is The Enemy Of Simplicity. On The Contrary We Find It Confirmed By Numerous Examples That The Rigorous Method Is At The Same Time The Simpler And The More Easily Comprehended. The Very Effort For Rigor Forces Us To Find Out Simpler Methods Of Proof.