Have all math problems been solved? What is mathematical research?

In this video, we look at some commonly asked questions concerning what mathematicians do. The following questions are addressed in the video, with relevant timestamps:

0:00 Introduction
0:28 What is mathematical research?
0:53 How do you find a problem to work on?
4:46 How do you start working on a problem?
7:10 What do you do when you're totally stuck?
9:49 Do you revise old (or undergraduate) material?

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These videos are separate from my research and teaching roles at the Australian National University, University of Sydney, and Beijing University.

These videos are made using the open-source library -- Manim -- created by 3blue1brown: https://github.com/3b1b/manim