Value of Solving Unsolved / Edge-case Mathematical Problems

Question

I just came across Unsolved Problems in Group Theory, of which there are 100's of very specific, detailed problems, such as these:

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15.68. Does there exist an infinite finitely generated 2-group (of finite exponent) all of whose proper subgroups are locally finite?

16.78. Do there exist linear non-abelian simple groups without involutions?

17.9. Is there a group containing a left Engel element whose inverse is not a left Engel element?

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In learning about the basics of group theory, it is an interesting subject. It has applications in many fields. But the applications as far as I can tell rely on the common body of knowledge in group theory (or in a mathematical field). Basically stuff you can find in textbooks or Wikipedia.

So I was wondering if one could explain the value in answering these 100's of questions. I can see answering some questions like a very relevant theorem perhaps, but the detail of these questions is very deep and there are so many. It seems like many more questions could be proposed as well, lots of edge-cases etc.. I know I am missing a lot of context so I hope this comes across okay. I am hoping to find it interesting, right now it feels overwhelming :)

Answer 1

Each of these problems comes with the name of the person who sent it. If one of them strikes you, it could be worthwhile to have a look at the kind of research this person does, either via their published papers or their personal webpage, to see what kind of mathematics they are doing and specifically what problems they are trying to solve from a broader perspective.

This can help give some context to a specific problem, but of course becomes horrifyingly time-consuming if you don't focus one one or two problems.

I think that this kind of list is made for researchers who need a break in their own work, to seek new ideas or see whether there is a question there that they happen to have the right tools to solve.