I'm a graduate student in applied math (applied probability, asymptotic etc.). I have written several articles on either solving "small" problems, or developing particular methodology/techniques towards certain type of problems. I'm at a stage where I have lots of ideas and if I want to I may be able to work out the details and write a few papers based off of them.
But none of these things are anywhere near significant much less ground-breaking etc. My advisor said a really good PhD is supposed to make ground-breaking contribution in just one problem/direction, instead of doing petty works in three and put them together to form a "pseudo-thesis". I know what exactly what he is referring to but have no clue where to start to searching for those ground breaking ideas.
My advisor does not like to suggest ideas/problems to me because he said he doesn't know what would be ground-breaking either or else he would do it himself than gift it to me.
As of now, all my ideas do not seem to carry much strength in the sense that they do not withstand much investigation or turn out to be "paraphrasing" classical paradigms. I suspect that I may need to probably read beyond my field because I reckon everyone in my field pretty much is familiar with the same set of literature and has a similar way of thinking. So they have exhausted great ideas that are possible under that mindset over the decades and only leave relatively small "fruits" for me to pick up.
My advisor said it may be good to read quantum physics as he himself is reading that and sees "lots of potential" in cross-disciplinary investigation. It would be a big investment for me because I don't know nothing about physics beyond Newton's law. But I'm in my second year so there is still time for lots of things and I think I'm tempted by the idea of learning physics and do cross-disciplinary research, although I'm keenly aware of the risk. Is learning a completely new field a good pathway towards big discovery? Should I take the risk as a PhD student? How do people stumble upon big discoveries? Is there general guiding principles behind this?