Hi,some tips needed.

I quit my masters in automotive engineering from a very reputed university in Germany.I had finished all my course-work in 2 years,had 1 year of thesis and internship left.But,I couldn't take the emperical dominated engineering stuff.So,I decided to pursue my long-lost dream of taking-up mathematics,although I took a lot of applied math electives during engineering.The main reason for mechanical engineering was because of family tradition.I still love mech.engineering but I love math more.So,right now I am giving the integrated phd. entrance exams for applied and pure math programs in India.Unfortunately,I failed in the first attempt.

Would you advice me to continue down this path?I am now 24 and most proff. I meet suggest I first gain work-experience and secure my future.This is what is bothering me a lot.

Q. If I score well in the GRE subject test,would it help boost my phd application for a university abroad?

My main interests in mathematics are:

Abstract algebra,multivariable calculus,topology,financial calculus,complex analysis and I love fractals and non-linearity models.

As a hobby,I design and analyse physical models using FEM and other tools.

Thank you.Your advice is greatly appreciated.