[grkvlt]

Since each theorem has a Gödel-number, there must be a function f(x) -> {0,1} where, when x is the number of an 'interesting' theorem, f(x) is 1, and otherwise it is 0. So, we just need to find this function (or rather, its Gödel number) and then we can iteratively feed all the integers to it, translating the interesting ones back into theorems.

This job is made much easier by the fact that the proof of this 'interestingness' theorem has a Gödel-number of its own; call it F. And, proving that something is interesting is obviously also interesting. So, just find the situation where:

    f(F) = 1

and we're done!

I'll collect my Fields medal later, thanks.

[JadeNB]

Your condition `f(F) = 1` doesn't seem to do anything to distinguish your meta-theorem `F` from any other interesting theorem.

[digama]

You just defined a subset of the natural numbers, and asserted it has a Godel number. Sorry, there are uncountably many subsets of natural numbers and countably many Godel numbers, so there is no guarantee that this is possible. More subtly, you can consider many "natural" classes of functions, such as computable functions, recursively enumerable functions, etc. and for each such enumeration there will be a "natural" function that escapes the class. Functions to do with definability or (in this case) 'interestingness' are especially susceptible to this. See also "Tarski's theorem on the undefinability of truth".