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Timothy Chow
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I can think of two distinct reasons why a particular paper or book might seem daunting. The first is the sheer size. The second is that I don't understand what's going on.

If the only issue is sheer size, then I think the "just do it" advice that others have given is sound.

If the problem is that I don't understand what's going on, then my advice is perhaps contrarian:

Do everything in your power to not read the paper.

By this I don't mean that you should procrastinate. I mean that you should first ask yourself whether you really need to understand the paper. Is the knowledge you want available from some other, more accessible source? Does it suffice to extract a small piece from the paper that you really need while ignoring the rest? If the paper seems incomprehensible, then there's a decent chance that it's not optimally written, and that your difficulties are at least partially the author's fault. Before forcing yourself through something that is not well written, you had better be darn sure that the task is unavoidable.

Suppose after all that, you still find that your research goals are forcing you to understand this paper, because it contains essential material that is available nowhere else. If the paper is really that important, then chances are there are other people who have studied it carefully and have said useful things about it. So start by reading as much commentary as you can get your hands on (and talking to experts, if they are willing to give you their time). This should help you get some sense of the overall structure of the argument. Perhaps some parts are simply computational and there's not much for you to do other than verify that the argument is formally correct. But there may be parts which are driven by some key ideas that aren't articulated explicitly in the paper itself, but that have been pointed out by commentators. In these cases, it's important to know what the guiding ideas are when you're struggling through the argument.

As a concrete example, I remember really wanting to understand Razborov and Rudich's paper, Natural proofs. On my first read, I found the paper baffling, because the main result clearly had major conceptual content, but when I looked at the proof, the bulk of it seemed to be some kind of technical argument which I could follow line by line, but left me no wiser as to how such a powerful conceptual conclusion could be drawn. It was only when I read "around" the proof that I came to realize that the conceptual content could be captured in a very simple (albeit hand-waving) argument: if you had a property $\mathscr{P}$ that supposedly an $\mathsf{NP}$-hard function has but no polytime function has, and $\mathscr{P}$ is efficiently computable and is true of a random function with non-negligible probability, then you would have on your hands a powerful cryptanalytic weapon that could distinguish cryptographic functions from truly random functions. This was the conceptual core, and the technical argument that had baffled me was simply a careful verification that this hand-waving argument can be made precise.

The Razborov–Rudich paper is perhaps not the world's best example of a "daunting" paper, because it's well written and even the technically hardest parts are not that complicated, but I think it illustrates the sort of thing that can make a paper seem daunting, namely an argument that seems baffling, and that does not seem to reward repeated careful reading. In such cases, a patient "just do it" approach is not likely to get you very far. It's important to get some high-level understanding of what is going on.

In the absence of external commentary, you may have to generate your own commentary. The way I typically tackle this is to start by formulating a relatively weak, but still nontrivial, result $X$ that the paper implies. Without the results of the paper, I can't see how to prove $X$ with the tools I know. So how does the paper surmount the difficulties? What do I get stuck on when I try to prove $X$ myself, and where in the paper is that sticking point addressed or bypassed? Asking yourself such questions and trying to answer them helps you read with a sense of purpose, which is always better than simply slogging through an argument line by line.

Timothy Chow
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