I have read over 50 articles on a topic I am writing about but do not see any research gaps. I have spent a lot of time reading the introductions of papers, since it is there that I found the most interesting overview of the field and current state of study on the topic being researched. How can I find a gap in my topic within the academic area of study?
On the one hand, this is really something an advisor should be helping you with, and one of the reasons why there is typically an advisor-advisee relationship at early stages of a young researcher's career. In the light of your earlier question Finding an advisor outside of my Grad School, it seems like this is not an option for you. (I do hope you take Buffy's advice there to heart.)
On the other hand, a more promising place to start is not the introduction but the conclusion sections of papers. This is where people will very often put "future research directions" and similar. Now, I would not suggest you directly take one of these directions and pursue it, because chances are that the paper's author is already working on precisely that topic and has a year or more head start on it. However, it might give you an inspiration on a somewhat different possible way forward, especially if you have already read a lot in your subfield and might see ways of combining directions suggested by different papers.
Plus, if you find one such suggestion that resonates with you, you could always contact the author and politely ask their opinion of it. Yes, academics get lots of emails, and many of your emails will never be answered... but if you keep it short and to the point, people may be more helpful that one might anticipate.
Reading is not equal reading. Put on different lenses while reading.
"What are the goals of the paper?" → What could be different goal?
"How do the methods/proofs/… work in this paper?" → Can I show/achieve the same things differently?
"Why do they approach their problems like this?" → Could I approach this problem differently?
Also: Why do you want to find gaps? New research does not necessarily closes gaps. It may also develop new approach or open up topics…
Finally: Do not only read the introductions. To really get to the points you need to dig deeper and understand all the basics.
By doing a literature review, you have got off to a good start in your search for a project idea. I have some recommendations, some of which you may already have done:
- Read the discussion sections, where authors discuss what went well/badly.
- Appraise the research design and reporting methods according to the appropriate best practices standards (e.g. the EQUATOR network guidelines https://www.equator-network.org/). This will help to identify opportunities for improved design.
- Consider trying a replication study, where you aim to follow the methodologies of some of the best studies on the topic (according to your appraisal). You can compare results achieved by various methods. It is important that study results are externally reproducible, and this doesn't often get tested.
Consider the assumptions made in the design of the research that a paper describes. What simplifications constrain the generality of its results? You can then set about reducing or eliminating those simplifications. A way to go about that is to ponder, “Hmm, that result about x is cool. What are some (more general) properties about a whole class X for which their result is just a special case?” Or, similarly, “How far would one have to shift their question to cause their results to change in some significant way?”
Another avenue from which to attack your problem of finding new questions is to ponder how the paper’s conclusions could be wrong. A good way to approach that is to assume (for this purpose) that an omniscient god has just assured you that though their data is valid, their conclusion(s) from the data is (are) wrong. Then all you have to do is figure out some ways that they may have made the mistake that (for the sake of your purpose) they did make. That exercise should produce the makings of a good new research question.
And a complement to that approach is to assume that it’s their data that is invalid. Then what may have caused them to measure the thing wrong or to measure the wrong thing?