One Does Not Ask Whether A Scientific

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.

The Aim Of Science Is Not Things Themselves, As The Dogmatists In Their Simplicity Imagine, But The Relation Between Things.

A First Fact Should Surprise Us, Or Rather Would Surprise Us If We Were Not Used To It. How Does It Happen There Are People Who Do Not Understand Mathematics? If Mathematics Invokes Only The Rules Of Logic, Such As Are Accepted By All Normal Minds...how Does It Come About That So Many Persons Are Here Refractory?

Doubt Everything Or Believe Everything: These Are Two Equally Convenient Strategies. With Either We Dispense With The Need For Reflection.

Thus, Be It Understood, To Demonstrate A Theorem, It Is Neither Necessary Nor Even Advantageous To Know What It Means. The Geometer Might Be Replaced By The "logic Piano" Imagined By Stanley Jevons; Or, If You Choose, A Machine Might Be Imagined Where The Assumptions Were Put In At One End, While The Theorems Came Out At The Other, Like The Legendary Chicago Machine Where The Pigs Go In Alive And Come Out Transformed Into Hams And Sausages. No More Than These Machines Need The Mathematician Know What He Does.