Turing machines and counter programs are not the only mathematical models of algorithms; there are several others.

Surprisingly enough,
**all** known models can be shown to be equivalent
in terms of the problems they are capable of solving.

Turing machines == counter programs == lambda calculus == Macintosh computers == Cray computers

The Church/Turing Thesis states that not only are these models all
alike, but each captures the essence of *computing*
or algorithmic problem solving (ie, *effective computability*))
which is by nature an intuitive notion.

- The Church/Turing thesis is a thesis, and not a theorem.
- All the evidence points to it being true.

In other words, if a problem can be solved by computer, it can be solved by a Turing machine; if it can't be solved by a Turing machine, it can't be solved by any computer.