I Entertain No Doubts As To The

The Fear Of Infinity Is A Form Of Myopia That Destroys The Possibility Of Seeing The Actual Infinite, Even Though It In Its Highest Form Has Created And Sustains Us, And In Its Secondary Transfinite Forms Occurs All Around Us And Even Inhabits Our Minds.

The Transfinite Numbers Are In A Certain Sense Themselves New Irrationalities And In Fact In My Opinion The Best Method Of Defining The Finite Irrational Numbers Is Wholly Disimilar To, And I Might Even Say In Priciple The Same As, My Method Described Above Of Introducing Trasfinite Numbers. One Can Say Unconditionally: The Transfinite Numbers Stand Or Fall With The Finite Irrational Numbers; They Are Like Each Other In Their Innermost Being; For The Former Like The Latter Are Definite Delimited Forms Or Modifications Of The Actual Infinite.

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

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.

Great Innovation Only Happens When People Aren't Afraid To Do Things Differently.