How should I proceed when a (famous) professor says I'm not good enough for research?

I'd say this is psychological assault. When someone attacks your fundamentals in such a way it tends to be part of a manipulative scheme, whether to dissuade you from doing something or to goad you into doing something. This kind of unprovoked cruelty usually aims to overwhelm your defenses so to speak. You should ask yourself what might the other person actually want or what you can give them they see.

I do not think him calling you not cut out for research has anything to do with the impression you give at all, besides just being a student. You are a graduate student and put that professor on a pedestal based on his reputation, which is probably something he is used to or even something he came to expect at this point in his career. He probably knows a line like "You are not cut out for this, think about what else you can do" would work on most students, if coming from him.

It could be something said during a heated conversation about you pestering him so much, but since you are still interacting with him, that does not seem to be the case. So what else do you have? Time to put in for a pet project of his? Being an unwitting part of some mind game for his amusement? Or something more personal? If you decide to keep working with him after such disrespectful treatment, you should pay attention to what he might try to goad you towards in between lines. Does he occasionally go off tangent about some other work, like industry or part of some community, or try to invite you for a dinner with family? I would not be surprised if something like that pops up, except of course if it is just psychopathic amusement.

Initially, Heisenberg wanted to study maths but the professor in Munich asked him about the books he already read and based on that, he told him, that he won't be able to succceed and he will not allow him to enter there (however that process went in detail, I read it in a book from Heisenberg "Physics and beyond").

And Einstein? His marks were so worse that he couldn't find a job for a while. And later, even when he worked as a patent specialist and set up special theory in his free-time, his boss couldn't believe, once he published it, that Einstein did that.

Sure, these are very special cases but it seems that even cracks are not seen as what they are. Finally, I wouldn't worry about that jerk, even if he is a world class researcher. And even if you won't be, that doesn't matter. You don't need his opinions to continue what you wanna' do.

There may be various reasons for what he says and what you hear. There is no particular order in the points below.

The professor

He may be an asshole

Some people have a huge ego and they feel like the masters of the world. They do not care about others and thrive on making them miserable. The extreme case is a psychopath.

→ my advice: find someone else

He may be neuro-atypical (I am not sure how this is correctly called today - feel free to correct with the right word)

He wants to say: "In my opinion you may not be fully suited for research because it seems that you do not know how to count and this is going to be a problem in the long term"

He says "you suck at research"

→ my advice: find someone else, except if you want to account for his behaviour

He may be from a different culture

My friend from the Netherlands tells me things straight away and it took me some time to understand that this is how it works in his country. It is a country close to mine (France) and the difference will be even bigger across the globe.

→ my advice: if you want to continue with him you need to get used to that

From your description it seems that this is case nr 1 and I would just find someone else and spend these years in a more mentally suitable environment

You

Make a 360° review (well, a 180° in your case) - requesting genuine feedback:

• ask some other teachers what they think of you
• ask your peers
• have a look at yourself and say loud three good and three bad things about you

Based on that you need to decide if you are suited for academia.

You may be good enough - not everyone will be the next Einstein. You can flourish in something else than pure research (such as teaching)

You many not be good enough, but there is no measurement for that. I saw brilliant people who barely made it to visibility, and complete idiots who were everywhere and, let me check your question, ah yes - were perceived as world experts in their field.

I like @Xavier's observation that the professor's notion of inherent ability in individuals badly reflects back to him as a teacher.

That said, probably all of us know people who we felt were not good at what they were learning and should rather try something else. I'm drawing from my surely limited experience as a computer science tutor in the college lab. There were a few students who showed talent but also a few I believed would never be good IT professionals, at least not technically good. And don't think that I was naively impressed with nerdy males and their previous knowledge: What I see as an indicator for a perspective in the field is an attitude, the general excitement about and the ability to solve problems and puzzles.

It is probably an — unpleasant — service to give the "untalented" students feedback and encourage them to try something different. I suppose that's what your professor is thinking. (I'm glad that was not my role then; I simply supported everybody with what they needed.)

It hurts to see somebody pursue something they are struggling with and which does not bring them joy.

And that would be my litmus test: Does what you are doing bring you joy? If you love Mathematics, by all means stay in it. Passion and joy arise from meaningful interaction with the subject matter and the people. Passion and joy are indicators, however subjective, for understanding, succeeding, achieving. They are, in a feedback loop, also very strong motivators which usually produce results. The cases where people are really irrecoverably bad at something and still enjoy doing it full-time are rare.

people are born with the ability to know if their proofs are correct

What people are really born with is the desire to learn. And this goes for all people. What is research really if not the process of learning on a subject? We do this every day with every aspect of our life. Granted, academic research has evolved to have some very strong guidelines, but the truth is that a new revelation can come to anyone by chance (penicillin), rigorous experimentation (The light bulb) or any other way.

To me, the fact that you are pondering if you are good enough for research given his remark is, in itself, research of yourself. So apparently you are a natural. Congrats!

I really appreciate him and his opinion, so I took it really bad.

This guy may be a very good expert in the subject matter. But being good in a certain research area does not make you a good person, a good advisor, a good leader, or a good person. It sounds to me as if he is either trying to make you feel bad in order to push you forward, or he generally does not believe in you. The first one is pointing low self-esteem for him and in my opinion, is a very bad way to push your subtenant. The second one is ok. Not everyone gets along with everyone and it is a clear indication for you both to carry on without the other. If the second one is true there is no reason for criticism or insults and you should ignore him and carry on.

You should take this situation to improve yourself. You will, no doubt, meet some more poor bosses, advisors, managers, and other unpleasant people. Use this opportunity to teach yourself how to cope with these people and come up as a better person.

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Research can be very frustrating. You read all the works around you and talk with your colleagues about what they are doing. These works are well-rehearsed and organized showing only the good side and "selling" the work and these colleagues are the sellers and are experts at describing their work as good. While you can only see your failures and bad directions it seems as though everyone else is doing much better than you. It is like the Instagram effect for the academia. It shows only the good side in others emphasizing your failures. You must remember: A research is bound to fail a couple of times before it succeeds. You are definitely not the problem. I went through a similar feeling myself on my M.Sc. eventually I found a cool and elegant solution to a problem and was proud of my work but not before much frustration.

From other answers here which probably comes from other researches, it sounds like the research world does not want to lose you. So please don't despair and stay as one of us. I wish you luck!

If people are born with the ability to be leaders and educators, this professor is out of place. Sorry for the lack of further elaboration [*], but I really think that the argument can be so easily reverted that I feel sorry for him. Taking your story at face value, and assuming it is not just an episode, I would start to think that this person cannot be solely well known for his/her publications.

In my view this is an attempt to make you feel guilty about anything, something, and give you the burden to find out the best guilt you have. Any random guilt you pick would do to justify his stand. Any guilt goes.

Stand tall, take a step back, look at it as something really weird, and keep on reasoning.

[*] See other excellent answers.

"people are born with the ability to know if their proofs are correct"

Aside from this statement being utter and complete poppycock, even if it is correct the conclusion your professor draws from it that you cannot be a successful research mathematician is a non sequitur. I know many successful mathematicians who are, to put it mildly, not good at writing correct proofs or at spotting the weaknesses of their own written arguments. And I know famous papers solving important open problems that do a poor job of communicating the ideas in the proof, to the extent that someone trying to read and understand the proof has to do substantial independent work to verify the arguments and fill in many of the logical and conceptual gaps.

In other words, even if your professor’s statement is literally true (and of course it isn’t), many and perhaps even most mathematicians in academia do not belong to that group of innately-endowed proof-wizards. And yet they somehow manage to make up for it with hard work, creativity, and various other talents and abilities that are complementary to (and, I should think, ultimately more important) than proof writing.

How can I know if he is right?

This is the question every grad program admissions committee would love to have the magic answer to. But there is no magic answer. The only answer is: keep working on your research and you’ll eventually find out if you’re good enough. The rest of us certainly can’t predict your eventual level of success, including Professor Know-It-All here.

A final thought: academia famously has the structure of a pyramid that gets narrower as one advances up the career hierarchy. That means your professor likely teaches at a less prestigious graduate school than the one he himself went to. Aside from his sounding like a generally toxic and unkind person, it seems possible that when he says you’re not good enough, in his mind he’s comparing you to his super-brilliant peers from the famous school he attended, some of whom probably ended up even more successful than him, causing him to be envious and somewhat bitter. It may be that you are not quite at their level of brilliance, or even at his level - statistically that would be the case for most graduate students in a comparison with their advisor/mentor - but again, to assume that this means you cannot have a successful and rewarding research career because you’re not one of the absolute best people one can find out there is illogical, cruel, and probably wrong.

Hope this helps, and good luck!

There are two aspects to this, the claim that you are producing proofs with gross errors, and the claim that the problem is unfixable short of being born with different genes.

The second claim reveals a weakness in the professor, not you. Some people are "naturals" at some activity such as singing or drawing. Some naturals have so little understanding of the process of learning their skill that they are useless as teachers of that skill. Take his advice on the topics on which he is expert, but ignore anything he says about the process of learning to write proofs.

You do need to consider whether you are producing too many errors in your proofs. If so, you should study writing and evaluating proofs. To some extent, practice helps, but you may need a mentor to look over your proofs and discuss where you went wrong. That mentor has to be someone who, unlike well-known professor, knows people can learn, and is able and willing to teach. Maybe your primary advisor can either be that mentor or recommend someone.

Some of my research problems drifted from my advisor's area of expertise, so I reached out to a researcher [this Professor] from my department.

It sounds as though you are still formally "signed up" with your original advisor, who should have some responsibility for your wellbeing. Maybe you could have an informal chat with your advisor about the nature and the manner of the professor's comments, and ask them to be present in any future meetings?

In my opinion the quoted comments are unprofessional and deserve a reprimand, but the way forward will depend on your institution and its internal politics. Maybe having someone else present will be enough to make him behave like a grown-up.

There are two key points which need to be addressed here, although the other answers cover things.

1.) You do not need to be a 'genius' to contribute to any subject. The notion of 'genius' is not necessarily a useful one and it would actually probably be detrimental to a subject if everyone who went into that subject was a 'genius'. Certainly in the long run, there are some people you might perceive as being 'geniuses' who actually did harm to their subject. Please read the blog post by Terry Tao on this matter.

2.) Life is too short to be dealing with toxic supervisors. There are other people who you can work with. For example, ironically I have been in a different situation to you where the supervisor was saying that I was not fit to contribute anything to any subject because I was not good at writing up computer codes and doing smooth, pretty presentations (even though he knew I had been teaching graduate level pure mathematics modules). This is clearly absurd.

My advice is, the supervisor is not going to change their personality, biases or opinion about you. The easiest solution is to change supervisor. Now, when you speak to whoever you need to about changing supervisor, you can say that you do not get on particularly well with the current supervisor, that your skills are different and that you have different ideas about things and different abilities. But also as part of the pitch, try to make it clear that your way of working and the research you would like to do is much better aligned to the new supervisor who you are proposing to change to.

Also, this is off the record, but in my experience the supervisors who often use bullying or undermining behaviour like this are often relying on other people to do a lot of the work for them, so they have a kind of kneejerk reaction when they perceive any weakness from a student. Check their papers from the last seven years and see if they have written any papers by themselves, likely they have not.

Complementarily to @Dmitry Savostyanov's excellent answer I'd like to point out that you need to be very careful about impostor syndrom.

Some people might be toxic for bad reasons (lack of empathy, need to denigrate people to shine, narcissism, ...). This should not make you think that you are unfit for research. If you feel like an impostor, your thesis will likely be very hard mentally. It will also be harder for you to work correctly.

It can be hard but try to take a step back. If you have been admitted in PhD, it probably means that you were among grad school's top student. Hence, if you work correctly there is no reason you cannot do a decent thesis. I don't know how long you have been in thesis but once you'll have published one or two paper, it will be easier to feel legitimate. Don't feel low if your paper is not accepted at the first time though, as conference typically accept 15-30% of submitted paper, having a paper refused doesn't mean that there is a problem. On the other end, having a paper accepted generally means you are on the right way.

I am sorry that it happened to you. This is not a pleasant experience, and frankly it's a shame that toxic professors and supervisors are still common in academia.

Academic research is broad and multi-dimensional. Some people excel in writing proofs, others design and set up wonderful experiments, collect useful data and find beautiful dependencies within. Some people propose fantastic theorems, which take hundred years to prove, others prove or disprove them after hundred years. As a community, we do research in a variety of exciting ways, which mutually support each other.

No single researcher is equally excellent in doing all these things. We have our strong areas and our blind spots. But saying that someone is not fit for research based on a couple of shortcomings in their proof is completely unfair, unjustified, ridiculous and unkind. This is opposite what a University professor should do, in my opinion. A good supervisor would encourage a student to try different things to identify where their strength and passion are. A toxic person would identify a single error and draw far-reaching conclusions from it to undermine student's confidence and make them feel bad about themselves. This is an extremely short-sighted and unprofessional behaviour.

Please try to disregard this person's opinion. Find someone else to collaborate with. Academia is large and although toxic and self-important people are still common, there is also a plenty of kind and supportive and truly generous colleagues around. Don't hesitate to share your experience with others to prevent someone else from having the same negative experience as you just had.