TITLE: How do you not forget old math?
QUESTION [104 upvotes]: I am trying to not forget my old math. I finished my PhD in real algebraic geometry a few years ago and then switched to the industry for financial reasons. Now I get the feeling that I want to do a postdoc and I face the dilemma that I actually have forgotten a lot of my algebraic geometry classics. Sometimes they are minor things and if I browse a book I recall everything, and sometimes they are major (I don't really think I have a mental lapse though!). So I see myself reading a lot of books in order to recall some of my old math. 
It gets frustrating that I have to repeat reading 80% of the article that I once used to read and understand. Maybe the new math that I have been feeding myself should be blamed too (I tried learning more differential geometry and fractal theory after doing algebraic geometry and hardly looked back at algebraic geometry after that). I have never tried avoiding to forget old math, especially parts that I do not use in a daily basis (esp. now that I work in the industry). But this can and will be fatal if I do apply for a postdoc. So now I want to read again, yes, but I don't want to forget again. 
Is there a magic recipe for this? Usually I do find it helpful to always connect even the most abstract of mathematics with something that is tangible as an example, either in real life or in easier math (e.g. connect invertible sheaves and Picard group to line bundles, vector bundles to tangent bundles and tangent spaces .. etc.). This usually helps me not to forget things, but some of the math that I used to learn is too abstract to make such a connection, or maybe I just didn't learn correctly to apply such a connection. So my approach now, when I start reading something new or old, is to find a practical example ASAP, or ask myself why the originator of the theory first thought of developing this in the first place, before even getting any deeper into the subject. I must be honest though, sometimes this is very difficult to do (esp. if you read references for which such connection is not made).

REPLY [6 votes]: This is not an answer, rather information I think might be useful to you for better clarifying this question and for possibly changing your personal views on what you believe you have forgotten. To preface my response, your brain automatically stores most memories by cues for later retrieval, encountering these cues invokes said memory, for example the smell of chocolate cake could be a retrieval cue for a memory of your sixth birthday.
With that said, if a person describes something and you are unable to recall it, that doesn’t necessarily mean you forgot it, rather that their description was not one of the retrieval cues you used to store it. For example, people often wake up thinking they “forgot” a dream they had that night, but when they encounter some random object during the day it cues back the memory and the contents of their dream come flooding back to them. We all have stored memories that are unconscious to us - that is data our brain has recorded (sort of) but which can only be accessed by certain cues (cues we often don't know exist).
In your case you might believe you have forgotten say Bob's theorem in algebraic geometry simply because the enunciation of "Bob's theorem" does not trigger a recall of its contents. Thus it may be that despite having read a proof of Bob's theorem three years ago, your brain is no longer using the name of that theorem as a memory cue. However this does not rule out the possibility that other cues still exist for content related to Bob's theorem, for example it may be that some obsecure lemma used in the proof is actually a memory cue for the theorem and thus though you can't recall Bob's theorem now, if someone were to show you the lemma used in the proof, you would then be able to recall part of Bob's theorem.
For an overview, see: https://en.wikipedia.org/wiki/Cue-dependent_forgetting
Now lastly I want to comment that as we can see here, even common terms like "forget" are often not rigorous enough to describe what is happening cognitively to people in everyday situations, to make matters worse there are currently many psychological theories about memory that roughly say the same thing but which use different terminology or worse theories that in my opinion say and do nothing at all apart from create complex terminology to state elementary observations. Though like a lot of cognitive science I personally think this is because its almost always impossible to get useful biological measurements from within the brain (with our current knowledge/technology) as so far as they relate to what we see, thus instead we have to reverse engineer what exact processes are occurring within the brain based on the results of how test subjects perform on various tasks, like say someone trying to figure out server side code (this would be some cognitive process) by sending search queries (these would be the psychological tests) to an interface on a website (this would be the test subject) - its an incredibly difficult task as one can create many different scripts (biological processes in the brain) that all respond the same way to search queries (produce the same results in psychological tests) i.e. we have no way of knowing what script(s) (biological processes) are responsible for what. Like a doctor trying to diagnose a patient with only knowledge of their symptoms and not being allowed to administer any tests that involve physically interacting with them. However this is clearly an oversimplification (also I'm getting off-topic) and I should preface this last paragraph by saying that I am by all means a layperson at the will of only my own judgement and online research. The little I know is from reading articles/texts online as well as half a lay persons' book (which I undoubtedly am) by Matthew Walker during an unfortunate stint in a substance abuse program where apart from studying math without the internet that was all I found to do. I would not dare call myself a mathematician as I've not even completed my formal undergraduate education yet, though I can say for myself that worrying about my poor memory/mental-health with respect to my peers has brought me a fair amount of misery so (for whatever my advice is worth) I don't recommend dwelling on it, there are things I and I imagine everyone else has done/experienced be it simply aging or whatever that provide no net benefit no matter how you look at the situation, but I guess that's life.