and set theory leads to the fact that the axiom of choice is independent and unprovable. But most mathematicians accept that axiom of choice is true. The same

and set theory leads to the fact that the axiom of choice is independent and unprovable. But most mathematicians accept that axiom of choice is true. The same is true for the continuum hypothesis with a smaller majority accepting that as true. Similarly most in comp sci accept that P does not equal NP. One does not need to understand turing machines to understand the concept of time and memory for computers. It is just a way of formalizing the problem. Nice to know that the problem can be formalized but not necessary to be taught. I never said that turing machines where not important. But I am equally sure that you did not formalize your algorithm into a turing machine to show that it was np-complete. The author's point is that the same is true for set theory although he likes to phrase it in a very provoking way that I wholly don't agree with. Mathematicians use the general concepts of set theory not the formal one. Comp sci/programing uses the general concepts of turing machines not the formalizations.