Effective use of extra time during a PhD I am a PhD student in mathematics starting my third year with the goal of a tenure track position at an R1 university. I believe I have enough research completed that I could graduate this year if I chose to, however my funding situation allows me to stay in my program for up to 6 years fully funded and with little teaching obligation (I do have the opportunity to teach a full course over the summer and plan to do so). I am currently planning to stay for all 6 years, unless I receive a very good offer in my 5th year. I have somewhat different taste in problems from my advisor, so I am currently working on becoming a more independent researcher.

My question is on how to best take advantage of the remaining years of my degree. Is there anything more subtle than "do more research"? What can I do to prepare myself for a postdoc or otherwise get ahead? Are there things that can be done as a graduate student in this situation that cannot easily be done as a postdoc or that are much better to start earlier?
Very interesting question, the answer of course depends on you and your preference. A few pieces from a Y3 postdoc...


Advice 1: Think of a skill that you feel as your biggest weakness. If possible, try working on improving it. This can be a management workshop, a presentation class, whatever. As a postdoc, having a well-rounded skillset is going to be useful.
Advice 2: Think of an area adjacent to yours which you considered to learn about, and then try to take an online course or something like that for it. Having broader overview helps a bunch.
Advice 3: Present your work to others. Write a bunch of profs of interest that you'd like to visit their lab and give a lecture about your PhD topic. But also, consider giving public-oriented "outreach" lectures, so that interested general public knows what's happening in your field. One feels this to be  important, given we're usully paid from their taxes.
Start writing that book that you always wanted ;)