Keep active the whole time. For example, if you are trying to think about a hard problem and you are feeling stuck, ask lots of questions and try to analyze why you are stuck. Think even whether you should switch to a different problem, but not too fast because if you keep doing that you will never do anything. One of the most important things is to keep asking more and more questions and eventually you will find some that you can answer and are interesting, or will help you answer other questions. Some of my best results have been a result of trying to solve unsuccessfully one problem but developing ideas that enabled me to solve others. Another piece of advice is to keep mathematically curious to the extent that you would be interested in proving things even if you know they are known results. Don’t be too hasty to look at the literature to find out whether something is known because if you manage to prove it by yourself you will really understand it. So keep on thinking and if you keep on thinking and having ideas and generating and learning for yourself, eventually the results will start coming.
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