Considering departure from physics into mathematics for my PhD.
Hello, I'm a PhD student wrapping up my first year and have to find an advisor soon. Due to a lack of funding in the physics department at my university, I was pushed to look at wider areas. But, honestly, I like what I found. There is a mathematics professor in probabilistic number theory whom I have spoken to. He seems very supportive and like he'd be an amazing mentor. I don't completely understand his work but it seems very interesting, more interesting than almost anything I've found in physics honestly.
But, he seems like the type of person who has been surrounded by brilliance for so long that he may be underestimating what a normie such as myself is capable of. He's considered my shift very casually, and I'd basically be switching from only having known physics (most rigorous math course taken being Linear Algebra) directly into graduate-level real analysis. I was wondering if someone could let me know if it's really as doable as his laid back demeaner makes it seem. In my mind I could see myself working 50+hours a week this summer and all of next year to try to learn everything I need to. That'd be fine if it's enough. But, would this be enough? Is this truly doable? I mean it in an objective sense, not in philosophically "do I have it in me/am I worthy" kind of sense. I myself have not been the most brilliant among my peers and have not so much as touched a proof in a while. Actually, I had one proof-based question in my stat mech final, and that's the only time I've touched a proof in the last year. Any advice would be greatly appreciated and also any guesses as to the probabilities of the different outcomes (from flunking out to succeeding) are welcome.