On Memorizing Research-Level Math
May 4, 2017
This Math Overflow post answer about how to not forget old math by Timothy Chow is so relevant I’m posting it here on my blog.
Forgetting lots of stuff is inevitable. But there are ways you can mitigate the damage of this information loss. I find that a useful technique is to try to organize your knowledge hierarchically.
Start by coming up with a big picture, and make sure you understand and remember that picture thoroughly. Then drill down to the next level of detail, and work on remembering that. For example, if I were trying to remember everything in a particular book, I might start by memorizing the table of contents, and then I’d work on remembering the theorem statements, and then finally the proofs. (Don’t take this illustration too literally; it’s better to come up with your own conceptual hierarchy than to slavishly follow the formal hierarchy of a published text. But I do think that a hierarchical approach is valuable.)
Organizing your knowledge like this helps you prioritize. You can then consciously decide that certain large swaths of knowledge are not worth your time at the moment, and just keep a “stub” in memory to remind you that that body of knowledge exists, should you ever need to dive into it. In areas of higher priority, you can plunge more deeply. By making sure you thoroughly internalize the top levels of the hierarchy, you reduce the risk of losing sight of entire areas of important knowledge. Generally it’s less catastrophic to forget the details than to forget about a whole region of the big picture, because you can often revisit the details as long as you know what details you need to dig up. (This is fortunate since the details are the most memory-intensive).
Having a hierarchy also helps you accrue new knowledge. Often when you encounter something new, you can relate it to something you already know, and file it in the same branch of your mental tree.