The Essence Of Mathematics Lies Precisely In

My Beautiful Proof Lies All In Ruins.

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.

My Theory Stands As Firm As A Rock; Every Arrow Directed Against It Will Return Quickly To Its Archer. How Do I Know This? Because I Have Studied It From All Sides For Many Years; Because I Have Examined All Objections Which Have Ever Been Made Against The Infinite Numbers; And Above All Because I Have Followed Its Roots, So To Speak, To The First Infallible Cause Of All Created Things.

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.

Don't Always Blindly Follow Guidance And Step-by-step Instructions; You Might Run Into Something Interesting.