Is it research to just combine other people’s work? I am currently a second-year undergraduate double-majoring in math and computer science. I am currently doing a joint research paper with one of the faculty in my university.

My advisor gave me research problem A. I thought about the problem for one week and managed to break problem A to sub-problems A₁, A₂, ..., An. Next, I started researching on A₁. After reading several papers, I found that an author had already solved problem A₁. I repeated this for A₂, ..., An and they have all been solved previously. Now I take the solutions for all of them, with proper citations of course, and piece them into a solution to my original problem. I write a paper and get it published.

Now here is my problem: I feel like a fraud. I have not personally solved any of the Ai. Heck, the only work I’ve done is to break down the problem, searched for solutions to the subproblems, and to combine other people’s solutions. Is this really what research is about? I really feel disheartened and want to know other people’s opinions. I feel like anybody can really do what I did.
Research is not just about inventing things. Finding out the best options to solve the sub-problems is also part of research and is also a major part of why people publish &mdash; to have their work used for a purpose.

Research can simply be anything that makes a contribution to science/knowledge/understanding (see here) which can be any of the following.


Finding novel approaches to existing problems
Formulating new problems and solutions to them
Doing an in-depth study on an established field
Making meaningful connections between the unrelated
Extending on top of existing developments
Combining the best practices to solve subproblems of a bigger problem
...


The list can go on. The main point here is as long as you have cited the existing solutions A₁, A₂, ..., An and that such a combination has not been published before, then you have no need to feel guilty of the work you did. You have done real work to search for the best solutions to each subproblem and went through the trouble of combing them to get a meaningful result &mdash; you have achieved an advancement in research.

Summarizing the comments:


A subproblem Ai may as well be ensembles/extensions of previous work.
If no-one else has published the work before, then it is not as trivial as you think it is.
The imposter syndrome; it is common for many in their research career. Overcome it.
You shed light on how problem A can be solved which might be overlooked before.