The Purpose of Master Thesis

Question

I am posting this question in the aftermath of the earlier posting in this link. Here are what I would like to know more about master and PhD thesis:

(1) I understand that schools' math departments have different policies and guidelines, but what is the generally accepted purpose of a master thesis?

(2) Now switching to PhD level: I often heard the term "original research" done by PhD candidates. What exactly does it mean? Does it mean solving an open question? Discovering new theorems?

(3) And I am curious to know this: If Ivy League PhD candidates are expected to break new ground in their thesis, what are generally expected of candidates at the bottom-of-the-ranking schools like these schools? In particular, am curious about this: Are the same yardsticks applied to both?

Thank you for your time and effort.

POST SCRIPT: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I am surprised that this posting was voted for getting closed. I believe that it is suited to be posted here since Academia SE is for wide variety of disciplines, and therefore only a few of them are math-related. Also, I have sharpened the focus of question (3). Thank you.

Answer 1

I can't comment on other countries, but in the USA the purpose of a master's thesis is to get you a master's degree. It need not be original, but of course there are quality standards.

Anything that you have discovered by yourself that you have not seen anywhere else could be considered original research. What academics generally mean when they say "original research" is something that you have discovered yourself that has never been published before. This could involve solving an open problem, but it also could be that you create something new that no one has considered before, and it could also be a tiny bit of progress on an obscure open problem.

It is not only ivy league PhD students who are expected to break new ground. This is a requirement for getting a PhD. Even Harvard's mathematics department's website, however, cautions their students that their PhD thesis may be their first paper and it may be virtually insignificant (or at least it did when I was applying to graduate school).

At the PhD student level things begin to equalize a bit, though of course there will always be outliers. No matter how poorly the school is regarded by others, people who have decided to take this career path tend to be far, far beyond the norm when it comes to mathematical talent, and if that's not the case then they likely will never finish. Even a low-ranking school won't tolerate PhD theses that don't meet the minimum standard of original research, and if they do they will turn from a low-ranking school into a school whose graduates no one will ever trust.