Math PhD after graduating with average grades I am currently an MSc student in math in Europe (I'm doing mainly analysis and applied math). During my Bachelor's I've had mainly average grades (I'm not sure what the exact GPA equivalent is, but it would be around 2.5, I guess). Now, in Master's, I've been getting only good grades and I am looking forward to finishing with distinction/honors. 

My first PhD option would be at the university I have been studying in the last few years, which is good and well-known, but below the ones in the US or the top unis in the UK. Some of the programs are funded, depending on the advisor. How important are my Bachelor's grades? Am I overestimating myself if I go and talk to a possible PhD advisor and, moreover, ask him if I can enroll on a paid PhD program?
This is the sort of thing you won't know until you apply and someone with authority to decide evaluates your background. However, in general, your most recent work will weigh more heavily in a decision for most people who think about it for more than a minute. 

However, you are in competition with others who don't have your "disadvantage" so you need to have some way to explain it. If your recent work overwhelms the past then you are more likely to be successful. 

A doctoral advisor will be more interested in your potential for the future than in your past and will be looking for both deep knowledge and enthusiasm. Most likely the issue of getting funding or not depends on how much confidence he/she has in you rather then your past. But there will be competition, even there. 

But if you don't ask, you don't get an answer.