I am currently studying mathematics and I am getting conflicting opinions on whether referencing a solution manual when working on problems is a good thing or a bad thing. For examples in many problem solving books for Olympiad or Putnam, the authors recommend you to study the solution even if can solve the problem on your own to perhaps emphasize a specific technique and on the other hand, some other people have told me that it is better not to have a solution manual. The concrete example was a post here for Spivak's Calculus on Manifolds
" @mruncleramos: I've come to realize over time that it is better not to have a solutions manual.
@Daverz: How did you come to that realization?
When you get totally stuck, it's better IMO to have a solution you can learn from than to just forget about it. Also, the solution might better than or just different from your own, and you can learn from that also.
@mathwonk: anyone at the level of spivaks book is harmed more than helped by a solutions manual. i.e. if you need a solutions manual, you aren't getting spivak.
so the most useful answer is to advise the asker to go back to work trying to grasp the subject and work the problems himself.
this was essentially mruncleamos's answer.
a beginning grad student should be able to read this book and do most of these problems."
So all this goes back to my question from your experiences whether a solution helps or harms/hinders in advanced mathematics.
The mathematics that I am currently studying are literally 'elementary' compared to many of the topics discussed on this site so I would like your insights to be able to develop good study habits early on.