Question

One is supposed to be devoted to pure mathematics. Is it beneficial for one to pursue a master degree before applying a math PhD in the United States?

Backgrounds

The question is due to the harsh situation of undergrad students who are outside the U.S. and want to apply for a pure math PhD in the U.S. After an application process, one received no offer or no satisfactory offers. I wonder whether it's beneficial to apply for a master degree first, as a springboard towards a PhD position?

I googled online and found some similar posts. However, I found nothing exactly matches what I want to ask, such as:

1. One can determine whether he/she really wants to do math via a master life. while I suppose that one is devoted to pure mathematics.
2. To attend some required courses (for PhD applicants) which aren't available in his/her university. They don't require a lot, and in the situation I'm interested in, there is not shortcoming from this kind of restriction.

I want to know the pure pragmatic effect of a master degree. Does the fame or honor of the graduate school increase the chance of admission for students? Do (good) scores in the graduate school de facto prove the strength and ability of students? Are these more convincing than scores/works in the undergraduate school?

Thanks for information.