My thesis could be described as a collection of six chapters that all explored different niches in my field of maths. I have a couple of appendices that contain summaries of results and listings of computer code. It’s all self-contained and linked and good.
And still, nine years later, I have a folder with bits and pieces of at least three other chapters. Projects that didn’t end up getting finished. Ideas that fizzled out or didn’t come together. Every now and then I think, “What if…?” It would have been nice to adapt some of the techniques that I used to get one more result. It would have been cool to just push that bit further and classify one more type of mathematical object.
Except: there’s only so long to do a PhD. There’s only so much space in a thesis. There has to be some sense that Result A is worth more than Result B, that Potential Chapter X is a more powerful contribution than Potential Chapter Y. Your thesis is finite. You have to stop somewhere.
What doesn’t make the cut in your thesis?
Make a list of the half-projects and the maybes that didn’t quite make it. Make a list of the reasons why. Make a list of what you would need to do to take them further. Your examiners might not pick this thread up in the viva, but you’ll build up a good summary for yourself.
Leave it in a good enough state that one day you could pick it up and keep playing with it. If you’ve got plans to do this already, in your post-doc, in your spare time, that’s good. But if passing your PhD is your exit from academia, leave some notes just in case you want to explore later on.
You never know when inspiration will strike.