When I was first starting to read research papers in mathematics, I got some great advice from one of my professors. He said, "Always have paper and pencil with you when you read a paper. Read a little bit and then try to write the next part yourself. Look at what is written in the paper as a sequence of hints. That's all you are going to get. You need to fill in the details yourself and if you can't do that, you have not understood the paper." Over the years, I have realized that while research mathematics is kind of an extreme case, the same actually applies to any challenging text. So here is "the method":
- Read a sentence or paragraph or however much you need to get an idea.
- Write or say to yourself what you think is going to come next.
- Start from the beginning and read through the next chunk. Compare your continuation to what actually came next.
- Go to 2
You end up re-reading the whole piece many times this way. For long things, use major breaks like chapters or whatever to limit the look back.
If you are trying to really learn the material, you can do the whole process repeatedly. In that case, the checking in step 3 should start to show less and less divergence, mostly just style or sequencing. You need to be careful though not to devolve into memorization. You want to actually come up with the ideas that come next, not the words.
I do this kind of thing when I read hard material of any kind - not rigidly and sometimes changing chunks around. If I go slowly enough, unless the material is really over my head or I am lacking needed background or something, I always end up feeling like I have had the ideas that the author was trying to convey. That usually means that I can start to apply the ideas myself.
