Chapter 10 Insider, Turing(2/2)
As long as you master metamathematics, you have mastered all mathematics.
The core of metamathematics is three topics - about completeness, consistency and computability.
Completeness, all mathematical problems can be proved or falsified.
Consistency, all mathematical assertions, are either true or not true, and there is no proof of contradiction that is both true and false.
Computability, all mathematical proofs, can be obtained through a feasible process and a finite number of operations.
As long as these three questions are answered, humans can solve all mathematical problems with machines - the "ultimate answer" to mathematics will fall into the hands of humans.
All mathematicians in the world are crazy about these three problems.
The Turing machine is an artifact that can overcome these three problems.
This is a structure full of "wisdom".
Youki applauded. The applause was partly polite and partly sincere: "But Xiangshan, what does this have to do with what we call 'internal strength'..."
***The author has something to say***
Chapter completed!