Balancing (Re)building Foundations and Research

Question

I'm a third year postdoc in mathematics.

I have been reasonably productive; however, I'm starting to feel some of my foundations in my subject slipping (especially since I specialized in my field fairly early into my PhD). The techniques I use in my research relate to a certain type of object, so the general knowledge in my field has slowly becoming lost. My work mixes a lot of fields, so I also have the enjoyment of knowing many fields shallowly instead of one specialization extremely deeply. I am now realizing that it would be useful to go back and learn some of the foundations in my field much more deeply as well as the foundations in related fields.

This realization is daunting, considering how much time I spent before in graduate school to get some understanding. I want to keep my research at about the same pace and then also do this.

Have others had this experience?

If so, what kind of plan led them to have a firmer understanding of their field?

Answer 1

This feeling is pretty normal at that stage. (I also guess that the feeling that one should know foundations better does never really vanish for many people.) To keep up your pace, but still broaden your foundations I suggest that you

• choose some books you'd like to go through and reserve some time every week to work on it,
• embrace the fact, that you will be able to pick up new stuff in your field more quickly than during graduate studies,
• be aware that you'll pick up more and more foundations "on the fly" while doing research.