My Deliberate Quest to Read Proofs FasterJune 16th, 2014 · 64 comments
As a self-observant theoretician, I’ve learned that my research success depends on two intertwined factors: (1) my ability to digest and understand diverse results in my field; and (2) my ability to persistently attack good problems once identified.
Through practice over the past few years, I’ve become adept at the second factor. My deep work hours per week are quite high and have recently led to a correspondingly high rate of producing publishable results.
A nagging concern of mine, however, is that I’m not as good with the first factor. Indeed, I’m often frustrated with how long it takes me to digest interesting new results (and how often I end up aborting the process).
This concerns me because in my field voracious reading is required to keep the pipeline of good problems full.
What’s going wrong?
I’ve identified three issues that slow me down when reading existing work:
- The results I read tend to be heavily mathematical but also appear in venues with space constraints. As a result, many details are missing. In a standard theory paper in my field it’s common to encounter a lot of (semi) complex inequalities that are just plopped down in the paper with minimal derivation or explanation, and then combined to achieve the proof. This style of mathematics by fiat makes it difficult to understand the argument and tends to overwhelm me.
- Results are often expressed as a combination of text and math that can lead to ambiguity. (This morning, for example, I spent 90 minutes trying to understand the explanatory text that accompanied a frustratingly simple modular equivalence.) Often these ambiguities can be resolved in the larger context of the paper, but I have a tendency to remain where I get stuck, obsessing over the ambiguity until I get too tired to make any more progress.
- I tend to lose my concentration faster when reading than when thinking. This occurs because understanding someone else’s result requires that you keep organized and accessible in your mind an ever growing collection of definitions and intermediate claims — many of which can seem arbitrary at first. This is tiring and I often flag too quickly to make productive headway.
To be clear, I’m not terrible at reading papers. As a professor, of course, I already do this activity at a high level as measured by most objective scales. But given my interest in continuing to push my abilities, I know that I could be even better.
Here’s my project: I want to overcome these issues and push my ability to quickly digest relevant academic papers to an extreme. This experiment is useful to me for obvious professional reasons, but I hope that it might also provide a nice case study in how such deliberate improvement proceeds in a knowledge work setting.
To get started on this project, however, I need some help. Please share in the comments if you have specific strategies you think I should consider…