Surely one of the uses of a private library is to preserve what one once knew and can't retain.
I am no mathematician, but was curious about Goedel's proof, and so read a few years back a book taking the non-mathematician through an outline of the ideas and the course of the proof. I remember having a great deal of difficulty, but also, toward the end, grasping, to some limited extent, the idea. But I haven't retained that momentary sense of understanding, and the book still sits on the shelf as a reminder of what I once knew.
Mathematics is perhaps the field in which this happens most obviously. When my son was taking high school calculus I pulled out my old high school calculus textbook, and found folded inside it a piece of paper, with my name on it, and in my old handwriting, covered with symbols I didn't understand. I struck me as very strange that here I was looking at my own work--even something as simple as a randomly preserved set of math exercises--and I did not understand it.
Don Novello's Father Guido Sarducci does a little routine (it's easy enough to find on You Tube) called the five-minute university, based on the idea that, in five minutes, you can teach, not everything you learned in four years of college, but everything you will remember from college five years after graduating. Two years of college Spanish? "Como esta Usted?" "Muy bien." That's it.
It's funny, but there's some truth behind it. And it's not just facts, but insights and intuitions and perceived connections that will fade with time, leaving some faint but inexplicable sense that something may well be the case without the confidence that I can explain or even know exactly why.
The medieval philosophers, if I remember correctly, identified the three faculties of the soul as memory, intelligence, and will. Is memory inevitably so mutable? Is some sort of re-charge or repetition necessary? And is that why I keep that silly book about Goedel's proof on the shelf?