About as useful as Feynman's algorithm for solving problems:
1. Write down the problem. 2. Think very hard. 3. Write down the solution.
1. Write down the problem. 2. Think very hard. 3. Write down the solution.
If your maths problem is actually a specific instance of a known broader problem then just stating that will point the way forward. In fact a proof that your problem is an instance of a broader problem can generally be a worthy paper in its own right.
I'm in CS research (with most of my work being applied to biological problems), so I'm a few steps removed from pure math, but I can completely related to this. It's why I find writing grants so difficult -- because they generally require you to identify and describe the problem and propose some potential solutions. But that's like 90% of the work for the whole thing!
One effect is like how Latin used to be the language of professionals, so you'd better learn Latin if you want to access the knowledge base.
* Forget about glory and peer recognition. One day you'll die and as time passes you'll be forgotten, including anything you made. Don't waste energy fighting it, just embrace it and carry on. Do it for that 1 mn moment of bliss when you found something nice.
* Accept repeated failure. It's ok.
* Spend time to learn why attempt N failed before going to attempt N+1,
* Before attempt N+1, go out for a walk, cook something nice, do something with your kids, have a beer, watch a movie