Is my supervisor making things clearer or confusing?

Question

I am struggling a lot these days while presenting in front of my supervisor. I make many mistakes, sometimes very stupid mistakes, and he is now saying, "You need to avoid these mistakes." I am not able to focus on theorems, lemmas, etc. but instead focus on things like how to avoid mistakes in front of him. Many times I feel nervous in front of him, sometimes sweating in front him due to nervousness. Although he tries to make me calm but also give strict feedback.

The one question that makes me worry is that he knows the things I am presenting in front of him, but he doesn't try to clarify things. To me it appears that he creates confusion in the proof that I try to present.

Question: Is my supervisor making things clearer or confusing?

On the comment of @Magicsowon I am going to add a detail here. When I discuss things with him he asks, "What is this?" Now the problem is there can be multiple definitions of the same term. Then I often assume the wrong one and do the proof. In the literature I follow, things are not defined in a good way so most of the time it happens that there is a confusion on concepts.

Answer 1

When and why would I, as a supervisor, ask students "What's this?" rather than just telling them (assuming that "this" is something I already know about)? The most likely situation is that I can't tell whether the student understands the relevant definition. If I already knew that the student didn't understand the definition, then I'd explain it, but if I'm unsure about the student's understanding, then I might ask questions intended to show me what the student knows or doesn't know. The student might view such questions the way you did, as "making things doubtful", but that wouldn't be my primary intent. (It might be a good side effect; if the student has a wrong idea, causing doubt about that idea might be a good preface to explaining the correct idea or to sending the student to study it.)

I'm worried by the last part of the material you edited in at the end of the question, the part about multiple definitions of the same term, assuming the wrong definition, things not defined in a good way, and a confusion of concepts. This sounds like a recipe for a disaster. I would recommend that, as soon as you see two genuinely different definitions of the same term, you try to determine whether they are equivalent. If they aren't, or if you can't decide whether they are, then ask your adviser to explain. Are there really two different concepts with the same name? If so, which interpretation of the name should you use? Getting the definition clear is necessary before any other work involving that concept; anything built on unclear definitions will be unclear (if not outright nonsense).

Answer 2

Since I struggled a lot with making presentations as a graduate student, I'll tell you what worked for me. There are two things to worry about. Content, in other words your theorems and lemmas, and presentation. Presentation is what you will have on your slides and what you will say and do to get your point across to the audience. Then there are your "mistakes". Maybe you don't understand clearly some textbook concepts, maybe you make some presentation mistakes like putting too much on slides, or looking at your shoes while you talk.

One important thing to understand is that you cannot worry about those things during your talk. You have to automate the process. That means train for your talks. If it takes you a week, or two, so be it. Just be organized about it. Before everything, make a check list with all the things you worry about -- what your adviser said, what you think should be included in the presentation, etc.

First, make sure you get right the scientific content. Your explanations of what you do, have to be clear and concise. It helps trying to explain what you do to your peers, if they want to listen. Then, make sure you understand the concepts that need to be understood to explain your results. If someone would ask you about a concept, a theorem directly related to your work, or a paper relevant to it, make sure you at least know what they are talking about. If there are other mistakes you make, let your adviser point them out. See if you have time to fix them, if not, stop worrying. Research is made of fixed mistakes anyway.

Second, make your slides in such way that they contain the minimum necessary to outline your work and its importance. If there are things you really don't understand yet, better not insist on them, or not include them at all.

Third, start training. Write down, if you have to, what you want to say. Practice in front of the mirror, or phone camera, until you can present without the slides. Then go back and try again to present in front of your adviser. It will definitely be better.

Edit: I won't erase the answer, though I think it doesn't help OP. Maybe it will help others.