A Small Error In The Former Will

All That Is Not Thought Is Pure Nothingness; Since We Can Think Only Thoughts, And All The Words We Use To Speak Of Things Can Express Only Thoughts, To Say There Is Something Other Than Thought Is Therefore An Affirmation Which Can Have No Meaning.

Thus, Be It Understood, To Demonstrate A Theorem, It Is Neither Necessary Nor Even Advantageous To Know What It Means.

I Entered An Omnibus To Go To Some Place Or Other. At That Moment When I Put My Foot On The Step The Idea Came To Me, Without Anything In My Former Thoughts Seeming To Have Paved The Way For It, That The Transformations I Had Used To Define The Fuchsian Functions Were Identical With Non-euclidean Geometry.

But All Of My Efforts Served Only To Make Me Better Acquainted With The Difficulty, Which In Itself Was Something.

If We Wish To Foresee The Future Of Mathematics, Our Proper Course Is To Study The History And Present Condition Of The Science.