Practical importance of Turing machines?

I am an electrical engineer, and only had one CS course in college 26 years ago. However, I am also a devoted Mathematica user.

I have the sense that Turing Machines are very important in computer science. Is the importance only in the theory of computer science? If there are practical implications/applications what are some of them?

The importance of Turing machines is twofold. First, Turing machines were one of the first (if not the first) theoretical models for computers, dating from 1936. Second, a lot of theoretical computer science has been developed with Turing machines in mind, and so a lot of the basic results are in the language of Turing machines. One reason for this is that Turing machines are simple, and so amenable to analysis.

That said, Turing machines are not a practical model for computing. As an engineer and a Mathematica user, they shouldn't concern you at all. Even in the theoretical computer science community, the more realistic RAM machines are used in the areas of algorithms and data structures.

In fact, from the point of view of complexity theory, Turing machines are polynomially equivalent to many other machine models, and so complexity classes like P and NP can equivalently be defined in terms of these models. (Other complexity classes are more delicate.)

StackExchange Computer Science Q#9341, answer score: 25