Side note: it is interesting to precise what is the content actually. Besides the obvious definition, like theorems and proofs, I also see hidden content: paradigms and problem solving techniques. What else?
It turns out that those "loose ends" are rather mixed up with the problem of integer factorization, which might be why I couldn't manage to tie them up. :-)
I'm 27 years old, actually...
there aren't groundbreaking works
Ouch. I'd say that my shared caches side channel attack work was groundbreaking (although Shamir and his graduate students were only a few months behind me). I'd say that my projective algorithm for matching with mismatches is groundbreaking. The sqrt(5) \epsilon error bound on complex floating-point multiplication shouldn't have been groundbreaking, but apparently was -- I've never seen numerical analysts get so excited about a ~30% reduction in an error bound.
You're right -- and modern mathematics requires more study than a field like computer science, simply because computer science as a field hasn't had enough time to accumulate very much content. (This is one of the ideas I mentioned as floating around but not fully crystallized earlier.)
But this doesn't contradict what I was saying: My point was not about doing original research, but merely about crossing the threshold to being recognized as a prodigy. A 13 year old attending university is certainly noticed -- but that doesn't mean he's doing original research (I didn't until I was 15).