Here is my sad story. I am a former theoretical (very theoretical!) physicist from Russia. I am a MSc and after graduation I decided to specialize in pure mathematics. However my wish was not sufficient. Initially I started to apply to numerous PhD jobs in Europe, but received only rejections. One postdoc suggested I should try to apply to American graduate schools. It brought no result too, although the results of exams were reasonable. I applied to a variety of programs from MIT to Oklahoma State university, but no one accepted me. Then I lowered my ambitions and have been applying in some European master's programs. Even expensive programs reject me. They say I do not have enough credits to study at the masters level. But I disagree. My mathematical preparation was deep and some people from my department in the alma mater are now successful mathematicians.

I guess I have a decent academic record. Have two publications in a prestigious American physics journal. GPA is high enough to have some deals with Ivies. But nothing helps me. I still want to have a mathematics career. Any advise how to launch it?

Thank you for your reply.
Russia does not use the ECTS system, so I do not know the exact value. Even if it is 300, not all of them are in mathematics. The universities meant this kind credits, of course.
Surprisingly, the percentage of math professors that replied me is extremely high, approximately 40-50% and the total number of letters I sent is ~17. Unfortunately, they never said "I want you", but something like this: "you should apply and we'll see". "I have no money now" was the frequent answer, too.
I tried the following destinations for a PhD:
Sweden (Uppsala);
Norway (Bergen, Oslo);
Austria (Vienna);
Belgium (KU Leuven);
UK (Warwick);
Germany (TUM, Berlin math school).
I applied for US programs because there is a popular belief that PhDs from the United States are more successful in academia, which is my dream.
Now waiting for admission results from a Swedish master's program (Lund). Is Sweden a good place for my dreams?

I would suggest that you apply for an European agency which can assess your degree and transfer it into equivalent ECTS. Check this website for certificate of equivalence of your degree. It is a bit expensive but you can google for something cheaper.
https://www.kmk.org/zab/central-office-for-foreign-education.html
The answer is that you are good and we have no money is very popular in academia. So far I see that you have applied for top universities in Europe where the competition is still very high. The same as US. You might have to lower your ambition a bit and go for a middle rank university. Applying for tens of universities might not help if the competition is high.

What is a middle rank university? Provide a couple of examples. For instance, the university of Oslo is ranked 151-200 in the Shanghai mathematics ranking . Is it still high?
Do you want to say my dreams for academia are simply unrealistic?

The dream is realistic. Just google list of universities in Germany, Belgium, Netherlands, Austria and Finland. Target all not only the top 3-4 universities. Notice that PhD students in Norway in particular are very well paid (among top worldwide) and the environment in international This means the competition is very high. I would look more into Germany (not the top ones) , Austria (also not TU Wien, TU Graz).