My question is pretty much what i wrote in the title, i'm wondering how hard a phd in mathematics from mit or an ivy league univ would be.
Getting INTO a PhD program in mathematics at MIT, on the other hand, is significantly harder than many math PhD programs in US.
you are ignoring the gist of my comment about vetting. namely schools take people that seem likely to succeed. hence by making yourself more qualified, you increase the likelihood of admission.
I remember it going the other way in that particular fight actually. Just saiyan.