First of all , I appreciate your reply and I learnt a lot from you. Indeed , pure mathematics is something theoretical. Personally , I wish I can study in a cheapest way and get a job as a lecturer in Malaysia. I am very interested to pursue knowledge and hoping that I can make something new that's why I am here for PHD. Yet , I do need some financial assistance so that I can study without any concerns. I managed to make a mini thesis when I was in year 4 and my lecturer said I am quite suitable for a jump to PHD. I did find a supervisor which is pretty good in local university.

THE MAIN REASON I want to study overseas because I might learn new things from those modern countries. But , do you think it is actually almost the same if I studied in local U since nowadays we can access a lot of knowledge from internet , plus pure mathematics do not require any experiment apparatus ( maximally a PC with good processing power ) . For me ,

Local U - fast(don't have to wait for admissions , visas,those might take a year etc) , cheap (I got a fellowship which the salary is near to a fresh graduate) and less problematic (my parents will be comfortable with me)

Overseas - can learn from grand-masters in mathematical field . I did see a lot of scientist from Malaysia succeed in their field if they did research overseas , but we don't see a lot locally . I don't know what is the reasons though . Was it because the knowledge difference between modern countries and Malaysia?

I don't really mind studying environment though . For me , Malaysian has a good environment , what worries me was the knowledge , I am just scared I can't learn something new forever if I studied locally. As job prospects , I am not sure whether local PHD have less employability than overseas PHDs?

I truly need some suggestions on whether to take it Local U or Oversea . Anyway , thanks for your patience if you did read through my post . Regards.

I can only speak from my perspective as a semi molecular biologist/bioinformatician.

A lot depends on what kind of opportunities that your future supervisor can open up for you. Does he/she have a good network of connections and encourages collaboration, like a few months of training and research in other labs?

It's also not just a matter of having access to information and data, it's also a learning/mentoring process of what kind of data you need, how to parse them, what to do with the output and what's the next step of action when it doesn't work. ify you get into a good place overseas, at least there's a lot of chance of discussing with other people in similar or related fields and you can try out different approaches. This kind of environment does foster creativity and hone your research skills.

I would suggest to ask your potential supervisor what are the chances for training and collaborations, though I'm not sure how common it is to do so in maths.

Thanks for your suggestions ! I think I get what you meant , it's the supervisor that matters compared to university. By the way , which country have you been pursuing phd ?

Lastly , I have a simple question , by right i am going to apply for phd next year , while waiting for approval , and if I get  , then visa applications(if overseas ) and other sort of stuffs , these procedures take a few months to do . During these few months , what should i do ? Part time job ? Or brush up my knowledge for the research ?

As for finding a part time job, it depends. Some supervisors will ask you to start working in the lab as RA while prepping your proposal and if they didn't you might need to find a part time job because it will take some time for you to write your proposal and getting it approved by your supervisor.

Germany.

For what you want to do while waiting, I agree with this:
Just find a supervisor first, then only you can plan your next step.