In Mathematics, The Art Of Asking Questions

I Entertain No Doubts As To The Truths Of The Tranfinites, Which I Recognized With God's Help And Which, In Their Diversity, I Have Studied For More Than Twenty Years; Every Year, And Almost Every Day Brings Me Further In This Science.

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.

The Transfinite Numbers Are In A Sense The New Irrationalities [ ... They] Stand Or Fall With The Finite Irrational 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.