A friend of mine usually talks to me about Church's thesis. Some days ago I found a proof and talked about it to him. He said that "it's possible to prove the thesis using an arbitrary definition of algorithm, the problem is that it is a consensus that algorithm is something without mathematical definition and this is why it's a thesis, not a theorem or lemma". But sometimes in my readings, it seems that there is one and other times, it seems that there isn't one.
I've also seen this, but it didn't had anything about mathematical definition of algorithms (or at least, not something I could understand).
So, my questions are:
Is there a mathematical definition for algorithms?
- If not, what would be a mathematical definition for it? What would it need to be in order to be a definition?