A long gap between BSc and MSc when applying for PhD My BSc was in physics and graduated with GPA 2.46/4.00 about 12 years ago. I am 33 years old now and I have got an admission to a master program in mathematics in Armenia (as an international student). The department didn't care about that my BSc that was in another field, that my GPA is very low and there is a 12-year gap between my BSc and MSc. [my low GPA is mainly due to not being present in the classes and also missing some midterm exams and quizzes; my grades are normally either near 4.0 (when attending was not mandatory with one exam assessment) or between 1.0-2.0 (for otherwise) and rarely between 2.1-3.7.] 

My story is that I loved physics since childhood and even used to study university books when I was in highschool. However suddenly everything changed when I 16 when my father died so I had to take the responsibility to support my family. Nonetheless at the same time tried and tried to keep my dream of becoming a great physicist alongside of spending lots of time working to support my family (we don't get any money from the government in my country); and that extreme desire for becoming a ('the') great physicist when the circumstances were the worst caused me a severe mental break down and being hospitalized too (it was about 5 years ago)..

Afterwards I couldn't think about physics anymore because it was making me sick. It took me a few years my mind to be repaired (=being recovered) and I started studying mathematics instead but this time I had a much better financial circumstances and I could finished by self-learning all BSc and MSc books that I would need to know them in my studies in MSc. 

After finishing my MSc I want to continue my studies in top universities esp. in Canada. I have a strong belief that I will have a high GPA and good research results in my MSc; however my low GPA in BSc and a huge gap between BSc and MSc and also being my BSc in physics irrelevant to mathematics that I want to study in PhD makes things less hopeful when I want to apply for PhD especially if I desire to get an admission with scholarship. 

If I write about my strong enthusiasm for science then I have to say my period of mental breakdown too and if I don't say about my enthusiasm they should probably consider someone who has started and finished young with better and relevant BSc.. I am sure that some universities in Canada ask for BSc transcripts as well as MSc when applying for PhD. 

Please help me what should I do when there is much less hope even if I can show a dramatic results in MSc. Thanks!
You do what you can with what you have. You have a record with some pluses and some minuses. That won't change. What you need is an explanation for why your record is what it is but that also suggests that you will be successful in future studies as the obstacles are behind you. 

In many universities there is an opportunity to personalize the application through interviews and other communication. Contact with a specific professor with whom you wish to work is often possible - and even preferred in some places. Having an idea about what it is that you want to study/research in a doctoral program is helpful. 

But in general, the time between degrees isn't a big problem. The low GPA in early studies isn't a huge problem if it is overbalanced by better performance in recent work. Having goals and good work habits is a definite plus. Knowing enough about a field to begin research relatively soon is very positive. Do what you can with what you have. Focus on the positives, not the negatives.