I was told I lack mathematical rigour. But how do I go on improving on it? Is it only a matter of being very careful? Do I have to always support everything with a clear Euclidean succession of logical steps? Is it only a matter of 'believing' in the validity of the supporting tools? Then it's an oxymoron that while some people consider rigorous to firmly step on past tools, they mainly do it via respect to the mathematicians that invented them, rather than on a clear understanding of them. Concerning my personal case, I think I don't lack knowledge so much on the process but rather on discipline. e.g. I was taught from a very young age the elegance of Geometrical axioms leading to a whole science but when it gets to other concepts, my mind usually flies to places that should really have a more solid basis behind them before going there.