How does one's phd(in pure math) prospect change after doing a masters compared to applying for phd directly after bachelors?
In many countries, it is sort of normal to do a masters after bachelors and do then go on to do a phd. But some people have told me that after masters, you are expected to be more specialized, thus your range of prospective advisors decrease compared to bachelors. This seems reasonable to me. But what other points should I be aware of if I plan to apply for a phd after doing a masters? Many people have a thesis component in their masters, but usually it is in the last semester, after the application process is over. So does the thesis even matter from a application point of view?