Geometry Is Not True, It Is Advantageous.

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?

In The Old Days When People Invented A New Function They Had Something Useful In Mind. Now, They Invent Them Deliberately Just To Invalidate Our Ancestors' Reasoning, And That Is All They Are Ever Going To Get Out Of Them.

The Scientist Does Not Study Nature Because It Is Useful To Do So. He Studies It Because He Takes Pleasure In It, And He Takes Pleasure In It Because It Is Beautiful. If Nature Were Not Beautiful It Would Not Be Worth Knowing, And Life Would Not Be Worth Living. I Am Not Speaking, Of Course, Of The Beauty Which Strikes The Senses, Of The Beauty Of Qualities And Appearances. I Am Far From Despising This, But It Has Nothing To Do With Science. What I Mean Is That More Intimate Beauty Which Comes From The Harmonious Order Of Its Parts, And Which A Pure Intelligence Can Grasp.

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.

Thought Must Never Submit, Neither To A Dogma, Nor To A Party, Nor To A Passion, Nor To An Interest, Nor To A Preconceived Idea, Nor To Whatever It May Be, Save To The Facts Themselves, Because, For Thought, Submission Would Mean Ceasing To Be.