I wrote a master thesis which went quite bad, due to communication problems with advisor, and my advisor said he is not willing to continue guiding me for PhD studies.
Specifically, I was asked to prove that the elementary theory of finite field is decidable, and I had no background on model theory. I had difficulty understanding, for example, the proofs of Riemann hypothesis for curves and Chebotarev's theorem. As such, I made mistakes when I wrote the thesis. It felt like the subject is too large for one thesis so I was unable to fill some details in some proofs. When I asked for guidance for some of the proofs, he did provide assistance, but only after six months time.
However, I have studied math on my own and I know that I am able to understand math by working on my own. Is there any hope for my math career if my thesis advisor said so? I have done couple of small new proofs for some old results, but they are so small that I guess I won't get a publication to any journal.