I live in an Asian country and completed my master's in Math in June 2020. I want to do a PhD in Europe, but I have had some difficulties in finding a suitable position. I do not believe doing a PhD in my country is a good option due to racism and corruption and related issues.
I have been thinking of writing to professors in Europe whose interests align with mine to discuss the possibility of an internship. This would help me get my foot in the door, and hopefully strengthen my PhD application. However, I don't have funding.
My thought was to send an e-mail that explained my situation (including past hardships, issues in my country, etc.) and providing my CV and master's thesis.
Is this the best way to approach professors in Europe about the possibility of an internship? Is this likely to work out (assuming I am qualified, etc.)?