The Computability Problem in Algebraic Topology

At first, and this has been immediately noted, this result ensures the durability of the mathematical job, which is not inconsiderable. No finite “system", in the broadest sense of the term, can potentially cover the whole mathematical field. So it can be considered that Church and Turing have proved that mathematicians will always be able to discover new playing fields and their creativitywill never die for lack of study areas.