Advantages and Disadvantages of learning mathematics and physics subjects through lecture videos

For postgraduate research, neither watching video lectures nor just reading a book are going to help you enough.

You're going to have to actively engage with the subject matter, by solving problems, and keeping up with current research literature in journals.

Following on from the OP's comment: I do understand that your question is "which is better - books or videos". And the answer to your question is neither. It's a false opposition.

Neither are necessary, and neither are sufficient. You have to learn the core content of maths and physics by solving problems. And to do postgraduate research, you have to keep up with the current research literature in journals (including preprint archives where appropriate).

The most important advantage/disadvange IMHO is personal preference.

• Advantages of video lectures:
  • a good video can teach the important ideas in a very fast way. It is not that a book couldn't do that, but it may be easier to start with a introductory video and then dig more in-depth into a book.
  • some things (experiments in natural sciences) can much better be shown by video (and even better in reality)
  • lectures by design come in "digestible" pieces
  • It may be easier to schedule time for video, as it is known how long it will take.
• Advantages of books:
  • you can better set the pace
  • you can better decide where to stop in between
  • easier flip back/forward to recall things.
  • things that take much thinking/working time of you fit better with the concept of books. E.g. calculation of examples/excercises. In depth study that derives the formulae. Few lecturers take the time to develop the exact formulae.
  • I find it easier to have a number of books open for quick reference (and papers).
  • The screen is not only needed for video, but possibly also for editor (sorting notes, computing examples, etc.), web pages etc.

Looks rather complementary than exclusive to me. Additional self-study (by book) is usually recommended also for (live) lectures. I think it even more important for video lectures, because you cannot ask questions. It will depend on what level of understanding you want to achieve, though.

I have studied through difficult math topics using basically three approaches:

• Videolectures
• Books
• Tutorial Papers

To get the basics of the topic you are studying and "leveling up" with the other people in the field, I think this three resources are very good. I do not see why would you single one out in favor of the other. I've basically seen like 4 Machine Learning Summer Schools, 3 Online Courses, 3 books, and that was only to be aware of what was happening around me.

After that I had to engage a lot on Online communities, conferences, papers, etc.

I find that a good practice is to set alerts for authors that you wish to follow and are prolific in the specific area you are doing your research on.