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I am a Ph.D. student in management science and I am interested in Dynamic Pricing. I need to define some problems and work on them as my thesis

Most papers in this field are full of complicated proofs covering different topics. If I read each paper in detail to fully understand all proofs, it will take much time. However, if I just read the main ideas and results, I am worried whether I will be able to prove any result in my own research.

I would be thankful if someone can explain what strategy is better to read these papers, some of which have as many as 30 pages. In some cases, I do not completely understand proofs and miss the point.

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    $\begingroup$ Talk to your adviser... They should be helping you along these lines $\endgroup$
    – AirSquid
    Aug 10 '20 at 18:46
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I think a two-pass approach might be useful, based on the Pareto principle (20% of the papers in any area give you 80% of the overall benefit). Read each paper closely enough to follow what they are saying ("Lagrangian relaxation solves left-handed, red-haired problems faster than ordinary branch and cut in months with 31 days") and to get a sense of the reasoning (and limits of generality), but don't sweat the proofs. If this is one of the 80% of papers that go in your reference file (to be used later to pad lit reviews, but not otherwise), you're not going to remember the proofs anyway.

If the paper seems useful to you, go through it again more thoroughly, checking the validity of the proofs as much as possible (which may also help you understand why the problem being red-haired made a difference, or what goes horribly wrong in February). You might want to take notes on places where you got stuck, so that if you have to revisit the paper at a later date you don't get stuck in the same place. In addition to helping you understand the content, checking the proofs may occasionally result in you catching the authors dealing off the bottom of the deck, which then spares you relying on results that might not be correct.

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Exploring literature is a numbers game. We have to accept that we'll never know everything, so the priority is to maximise the probability of becoming familiar with the most important stuff, and accept that we'll miss out on some things, and that's ok. As a new researcher, you will forget the proofs in a week, but intuition is what sticks and makes you understand the field, so that's, to me, the goal to maximise.

I start by reading the abstract. If that looks relevant, I read the conclusions. If those look legit, I then read the introduction. If that also looks relevant, I will then skip all the filler material and go straight to the "new" contributions, which is typically a couple of pages. I will only revert back to the filler material if I'm missing information to understand the new contribution.

Honestly, if a paper is not written in a good, understandable way, and is unnecessarily packed with math, I'll pass. I only have so much time, so I find it optimal to spend time on papers that are relevant and well-written.

That's not a golden rule though. Sometimes I do spend time understanding badly written papers (btw to me a paper full of proofs and no intuition building or graphs is a badly written paper), if they're highly cited by other prominent authors. This is an indicator that there's good stuff there.

One cheat I use when there's an important but badly written paper, is to track down papers that cite it, and see if one of the newer authors explains the original paper in a better way, which is almost always the case for prominent papers. I've found papers that explain a 30-page paper in half a page. I might spend 3 hours tracking that paper down, but it beats spending a month on the original paper.

Remember, as living persons, time is our most valuable resource. Sure, the way I do things I surely miss out on some very good stuff, but at least my time is efficiently spent.

Finally, don't be too worried about not understanding proofs. Some proofs take years of building intuition to properly understand.

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    $\begingroup$ In that vein: start with literature reviews not original papers. They are there to give you an overview. $\endgroup$
    – PSLP
    Aug 13 '20 at 11:46

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