Swiss cheese holes in my education. Do I go back and fill them? In this recent blog post the author lists several interesting concepts he has discovered pertaining to learning. One thing he mentions is the following:


  Mastery is more important than passing grades. You will reach limits
  in learning when you have a "Swiss cheese" foundation full of
  misconception holes. Master each concept before building on top.
  ~Salman Khan


(This is actually from Salman's TED talk which you can view here.) My questions is as follows: I graduated about a year ago with a Master's in Applied Physics from a reputable university. I've been a B student throughout my academic career and I feel like I started building on un-mastered concepts somewhere towards the end of high school. Despite obtaining a relatively tough engineering degree, I cut corners whenever possible. If I could pass an exam by being able to do all the exercises, I would get to that level and stop there. I would rarely - if ever - go for complete mastery. As a result I feel like I have Swiss cheese holes in my understanding that date back to high school. 

If Albert Einstein's quote is anything to go by: 


  If you can't explain it simply, you don't understand it well enough.


I'm afraid I can't simply explain a whole lot. For instance I would not be able to explain simply:


What is the proof of Euler's identity? 
Why can you express a wave as an imaginary exponential? 
How does a photon have momentum, but not mass?
What is the intuitive understanding of eigenfunctions, eigenvalues and their physical manifestations?


With the wealth of knowledge available today on the internet, I could look up any one of my knowledge gaps, and with some effort I feel confident I would be able to fill them. My question is, would that be worth it?
First, for context, I'd disagree strongly with a too strict notion that "mastery" is required before "moving forward", for several reasons. It is easier to understand the purpose of something after one sees how it is used. It is all too easy to acquire a fake mastery that is not functional, but only refers to some artificial tasks created for a textbook, and, all the worse, may be wastes of time. And, finally, the kind of "mastery" we are often led to think we should attain is basically unattainable... That is, unless one keeps ones list of things-to-master really short, very elementary, and uncomplicated, this "mastery" is just unreachable on the terms a novice or even journeyman conceives.

So... don't over-interpret "mastery".

On the other hand, _of_course_ it is good to go back and fill in. And one will find oneself doing this many times, as one discovers, upon "stressing" one's knowledge, that what one thought one knew "well enough" was not quite good enough. 

For that matter, even with an excellent memory, things slip out of a person's head.

My bottom line recommendation is to maintain (at least) two "threads", one to review and backfill, the other to move forward.

The latter is surprisingly useful at helping review make more sense! :)