[t]he Different Branches Of Arithmetic - Ambition

The Mathematical Facts Worthy Of Being Studied Are Those Which, By Their Analogy With Other Facts, Are Capable Of Leading Us To The Knowledge Of A Physical Law. They Reveal The Kinship Between Other Facts, Long Known, But Wrongly Believed To Be Strangers To One Another.

Zero Is The Number Of Objects That Satisfy A Condition That Is Never Satisfied. But As Never Means "in No Case", I Do Not See That Any Progress Has Been Made.

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.

For A Long Time The Objects That Mathematicians Dealt With Were Mostly Ill-defined; One Believed One Knew Them, But One Represented Them With The Senses And Imagination; But One Had But A Rough Picture And Not A Precise Idea On Which Reasoning Could Take Hold.

If Nature Were Not Beautiful, It Would Not Be Worth Knowing, And If Nature Were Not Worth Knowing, Life Would Not Be Worth Living