Mathematics, In The Development Of Its Ideas,

I Am So In Favor Of The Actual Infinite That Instead Of Admitting That Nature Abhors It, As Is Commonly Said, I Hold That Nature Makes Frequent Use Of It Everywhere, In Order To Show More Effectively The Perfections Of Its Author. Thus I Believe That There Is No Part Of Matter Which Is Not - I Do Not Say Divisible - But Actually Divisible; And Consequently The Least Particle Ought To Be Considered As A World Full Of An Infinity Of Different Creatures.

A False Conclusion Once Arrived At And Widely Accepted Is Not Easily Dislodged And The Less It Is Understood The More Tenaciously It Is Held.

I Realize That In This Undertaking I Place Myself In A Certain Opposition To Views Widely Held Concerning The Mathematical Infinite And To Opinions Frequently Defended On The Nature Of Numbers.

In Mathematics The Art Of Proposing A Question Must Be Held Of Higher Value Than Solving It.

Mathematics Is Entirely Free In Its Development, And Its Concepts Are Only Linked By The Necessity Of Being Consistent, And Are Co-ordinated With Concepts Introduced Previously By Means Of Precise Definitions.