I'm only a layman therefore only discuss stuff naïvely.
I read some introductory articles about halting problems with a scenario that if there were such a decider accessible to us, we should be able to solve some unsolved mathematical problems. We could write some brute-force programs to check Goldbach conjecture, say, and then throw it into the decider to see what happens. Then he refers to halting problem to say that such kind of dream is not possible.
However I notice that there's difference between halting problem and his scenario. Such a brute-force checking program has nothing to do with input data, but for halting problem, we assume the decider to check for every input. So I wonder whether halting problem without input is also undecidable?
I googled and found this. Personally I think it's wrong and couldn't be corrected because of self-reference.
Thanks for your help!