A Turing machine is just a computer program.<p>The Goldbach Conjecture example is just a program to loop through and test that each successive even integer can be reached as the sum of two prime numbers.  If there is a counterexample to the conjecture, then theoretically this program will eventually find it.  For these purposes, the authors don&#x27;t care if the program calculates efficiently, but are interested in the length of the program.  So brute force is fine.<p>The Riemann Hypothesis and ZFC programs similarly are just brute force searching for counterexamples.<p>The existence of programs to search for counterexamples is not new or surprising.  I am not so sure what part of this work is new.  I guess it is the discussion of philisophical implications.