What is the point of a thesis defense presentation?

An important part of research is communicating the results of your work. (At least where I work) this is why we insist on candidates making an oral presentation.

It does serve a verification purpose, in the sense that you are expected to have mastered the topic to a level where you can explaining by yourself to an audience of appropriate background.

The point of the thesis presentation is so the examiners can see if you actually did the work in the thesis or not.

It's quite easy to paraphrase content from e.g. publications, to ask one's supervisor for assistance tackling technical aspects of the work. So, by seeing you present the work and asking you some questions about the content, the examiners can assess whether you actually understand what you're talking/writing about.

Think of it as a presentation followed by an oral examination on the content. Some tips (I am not a mathematician but hopefully these are generally applicable):

• Be clear about what problem your work is addressing.
• Be clear about why that problem is actually worth addressing.
• Make sure you give due credit to the relevant literature (e.g. with citations).
• Don't spend more than 1/3 of the presentation on the points above.
• Focus on what your contributions were to solving the problem described above.

Hope this helps.

Probably not all, but a good part of it, for a public presentation, is just giving you a chance to be the center of attention for an hour and to energize students who might be able to attend it. In part it is a "brag" on the part of the faculty about what great students they produce.

There are places, I'm sure, where it is a bit of an ordeal, and it is often scary, but it is also a welcoming you to the core of the profession (for doctoral presentations anyway). Yes, you are good, and we are happy to sit and listen to you for a while as you demonstrate it.

And if it isn't like that for a public presentation, then something is probably broken.

Non-public presentations are more in the line of an exam requirement and you will probably be judged on the quality of your organization and presentation. At the MS level, I would hope that people would realize that you don't yet have a lot of experience doing these things and so expect the student to be a bit halting in delivery, if not organization.

What you need to do is to present the core ideas of the thesis, focusing on insights, and not details. If details are required they will probably come in the question/answer part. Don't be tedious or overly pedantic in your talk.