Another strategy that goes about the problem from the side is what Tiago Forte of Building a Second Brain calls The Slow Burn approach (9 min audio explanation). It’s basically the approach of letting hard and motivating problems flow with you for a long period of time, collecting insights, ideas, resources, and different view points along the way.
Richard Feynman supposedly gave the advice of always keeping in mind 12 favorite questions, and see if anything new that comes up shines a light on any of them.
You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!”
In How to Take Smart Notes, the author discusses the Zettelkasten method. It is based on the method of a prolific social scientist (Niklas Luhmann) to research; Something like: Have a trusted system for storing and reviewing notes, and engage with whatever you find interesting (and keep everything in the system). Once in a while, some ideas will develop into something coherent which could be published.
[This book] describes how [Luhmann] implemented [the tools of note-taking] into his workflow so he could honestly say: “I never force myself to do anything Idon’t feel like. Whenever I am stuck, I do something else.” A good structure allows you to do that, to move seamlessly from one task to another – without threatening the whole arrangement or losing sight of the bigger picture.