Failed at all meetings
First of all, OP, take a deep breath.
There are two well-used tropes on SE, one is 'get mental health support' and 'impostor syndrome'. Both have their place. And if you really feel it is a mental health issue, go for it.
However: I do not think your case is either. You have an objective (I do not say real, you will soon see why) reason to feel down. You have been just shoved to the side by an insensitive PI.
Of course your question is, were you just lucky in your PhD?
Yes, you may have been lucky that you had a good PhD topic. You may have been lucky that you just needed to scratch its surface and results would gush out. Yes. That's luck. That's researcher's luck, it's the luck of the one who can harvest it; the expert in the field. It may be luck or not, but it's still yours and deservedly so.
Others, say, equally talented to you, may have spent their whole PhD on some miserly results to be scraped together in some work paper, who knows? They were less lucky. Was it their fault? Not necessarily. They were good researchers, just picked the wrong topic.
Almost unavoidably, you will run into bad luck periods, but, on the long run, good research comes from honing your instinct on where good luck can be more regularly found to loiter around.
Let's move to the second one. Collaboration. Comes this guy spewing stuff at you and you are lost. You do not get them. Note: &quot;them&quot;, not the &quot;math&quot;. They confuse these two. They think you don't get the math, but that's not what happened - they simply didn't explain it properly.
Sometimes, you find people, where conversation flows naturally, as if you always had worked together. There is a natural intersection of ideas, even where you do not understand them, you fill it with insights and interpolations from your own experience, quite naturally. It is exhilarating to work in such conditions, and rare. But it happens. And it's the most fun science can be.
You got the opposite. You got some - perhaps famous - guy as mentor that you simply couldn't tango with. It's not your fault.
Or perhaps it is? Your PhD supervisor does not listen to you - well, perhaps your choice of mentors is what needs to be improved?
So, your mentor found a counterexample to your conjecture and left the room. What does he want to prove? That's simple to see one? That if you have not such superior vision into the field, you are not worth to discuss with? How did you get to this guy? Ask yourself this question.
Whether the counterexample may have been obvious, it may be not, I cannot judge. A famous chess master made once a complete beginner's blunder in the opening moves of a game. It happens. It's not nice, but it's not an excuse for a put-down.
If he is that dismissive of your work, cut your losses, and get a different mentor. Find colleagues, mentors etc. who you have a common language of mathematics, where you understand what they say when they say it (I do not say that you need to understand their math fully, only you understand what they communicate). Find a place where you intertwine into the scientific discussion. You do not have to be a Gauss, Galois or Grothendieck to be a good mathematician. Having luck is fair game if you put in your part of the effort (note: I say effort not talent - if you can do a PhD in math, that's a given).
TL;DR

You feel down for an objective reason, not for some mental health problem. You have been treated badly.

You are entitled to luck in the choice of your research topics. You were lucky in your PhD thesis. Expect also some bad luck in your career, but develop the scent for the good places.

Collaboration requires effort from both sides, not dropping packages and expecting someone to pick them up, which is what your mentor did. Perhaps that's the way to test you, but it's not a way to treat people. Get a different mentor.

As with luck, the right collaboration partner can make results come out easy. It will feel effortless and not because the partner does everything. Like luck, find where these people loiter around.

So, perhaps the one thing where you are really not yet good at is finding the right people to work with. Your supervisor, as well as your mentor are both not exactly the most ideal of colleagues. Maybe, however, you are just in a difficult location. Clearly that's something you should work on changing.


It's not your fault. You are entitled to researcher's luck. You are entitled to a proper explanation of fresh concepts, or else direction where to read them up before &quot;wasting&quot; the precious mentor's time. First and Foremost, you are entitled to be treated as a human.
Get out of there and either a mentor or position or even just visit to a group who are interested in your stuff and who you can communicate with.
Good luck. If it comes, it's yours.