Throughout my Ph.D., I have had difficulty in solving (maths in) research paper from other researchers. After the basic few steps, the researchers assume either one thing or the other thing, or have a complex integral or derivate (or any other) format and then come up with the solution that is entirely unknown to me. Sometimes after rigorous effort, I find the way authors solve. But mostly, I assume what they did is right and then carry on (which is not the right way).

How do other researchers (students) deal with this issue?

PS. I am from wireless telecommunication background

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    Learn more math...? There's no royal road. – Nate Eldredge Sep 26 '18 at 5:04
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    @NateEldredge in some branches of physics and engineering, authors often omit important mathematical steps and definitions or make serious mathematical errors in their papers, even in top physics/engineering journals. I work in mathematical physics, and I've found sometimes that even the top mathematicians in my field don't understand the math underlying physics papers in our area. I don't think this is an issue of OP not knowing enough math, it could just be that mathematical rigour is not a high priority in journal papers in that research area. – Darren Ong Sep 26 '18 at 7:18
  • @NateEldredge. Thanks for the comment. Yes, you are right one need to sharpen the math skills. But as DarrenOng pointed out, since we are engineers and not extensively trained for maths, it sometimes get a bit tough to merge Idea or design with math. This also leaves less time for us to practice more math due to time constraint. Example, the other day I was stuck with an equation in a paper where authors say that eq(x) can be solved to Hyper-geometric function. Now I have been looking for some time now and could not find how? Hence, I assumed what he said is correct. – Sjaffry Sep 28 '18 at 1:17

I would start with e-mailing the authors, or perhaps other experts in your area that you are close to and asking for help from them. I've found that a lot of researchers, even big names, are happy to discuss details about their work (or at least they seem to respond to questions of this nature more frequently than you would expect).

Keep in mind however, that in some fields of physics and engineering (I am not sure if this is true of yours) mathematical rigor isn't a high priority, and so it can be impossible to verify the mathematical reasoning in the paper, even for expert mathematicians working in your area. As a mathematician I find this frustrating, but my understanding is that researchers in physics/engineering are more concerned with the big-picture ideas than making sure all the mathematical details are correct, and perhaps you can take that attitude too.

As an example, my collaborators and I were trying to understand this physics paper (from a top physics journal, written by a distinguished physicist), and we found it impossible to understand the mathematics- there was a step in the calculation where they had an infinite sum that clearly diverged! We emailed the author, and he acknowledged that the sum diverged and the calculations in the paper were not correct, but the idea was still valid. This is a fairly typical point of view in physics and engineering from my experience. So it might be good to adjust your expectations on to what extent you can recreate the mathematics in a physics or engineering paper.

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    How was "the idea...still valid," despite "the calculations in the paper [being] not correct"? I appreciate that a result can be valid, even if the proof is wrong, but how can we know whether a result is valid if there's no correct proof? – user2768 Sep 26 '18 at 8:34
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    @user2768 typically when physicists say this their idea "intuitively" makes sense, and/or they have numerical/experimental evidence to back them up. Both were true in my anecdote, and in any case my collaborators and I were able to rigorously prove their claims eventually (after a lot of effort). This is just something one has to get used to in mathematical physics: mathematicians and physicists have very different standards of rigor. – Darren Ong Sep 26 '18 at 10:11
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    I suppose less mathematical rigor should be expected by anyone who hasn't been extensively trained in mathematics, yet relies on mathematics, which includes physicists and many other disciplines, e.g., computer science, economics, engineering, ... – user2768 Sep 26 '18 at 11:47

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