My Beautiful Proof Lies All In Ruins.

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

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.

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 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.

What I Assert And Believe To Have Demonstrated In This And Earlier Works Is That Following The Finite There Is A Transfinite (which One Could Also Call The Supra-finite), That Is An Unbounded Ascending Lader Of Definite Modes, Which By Their Nature Are Not Finite But Infinite, But Which Just Like The Finite Can Be Determined By Well-defined And Distinguishable Numbers.