Since math students will be stuck on some math at some point, what strategies or tips can help
(to assuage this recurrent reality of maths)?
Certainly, this wonderful website helps; here: one can ask questions, interact with different people, be referred to other information. Still, to what else can be one resort?
I thought to start with some quotes from the following two articles:
[Source:] As research mathematicians, Littlewood and Poincaré knew the value of letting a problem go. They both structured into their lives time for allowing the attention to disengage from the level of actively thinking about a problem. Littlewood went for walks in the country. Poincaré went on a geology excursion. And occasionally, with good luck, the sudden flash of deep inspiration occurred.
[Source:] ■ The first theme has to do with sleep and the role it plays in doing mathematics and AHA! experiences. Many of the participants commented at one time or another about the phenomenon of waking up to a solution, either in part or even fully formed.
■…he discusses how "a bridge gets built between two apparently unrelated fields".
■ Certain gaps in knowledge needed to be filled and my main role was to feel that these gaps could be filled. – Dick Askey
Best Answer
This, probably, is a more appropriate answer to: "Strategies - What to do when stuck on some math problem", but I thought it was still worth mentioning.
I've always thought that section 2.1 of this book is a rather nice and concise list of concrete advice regarding how to solve problems in analysis, particularly useful--I think-- for students who might not have a large experience in tackling proofs. If I'm stuck on a problem, having a read through it, sometimes, gives me an idea of what else I can try.