Some practices and advice that I gained from my time doing a PhD in mathematics: 1. Find a time of day to read and work on problems that works for you and make

Some practices and advice that I gained from my time doing a PhD in mathematics: 1. Find a time of day to read and work on problems that works for you and make it interruption-free. For me it was up at 6AM and working until 9 or 10AM with no phone or laptop. If you can do longer or fit in another session, go for it. 2. I found that I process new material in the background, so either going to the gym or taking a long walk gave my mind the break and mental space to process what it had just ingested. 3. In mathematics, it's common to present the most terse, stripped-down version of a result which can rob it of the background and context. I found it was often helpful to find the author's previous work, PhD thesis or talks in order to understand how they got to their result. 4. Don't be afraid to get a little side-tracked or obsessed with something that's not directly related to what you're currently working on. Part of training to be a mathematician is learning the ability to hold seemingly unrelated concepts in your head for long periods of time until the connection becomes apparent. Learn to love difficult things!