I am a mathematics major and I constantly hear people (including my professors) saying that when you are not actively thinking about a given problem and playing tennis for instance your subconscious keeps thinking about it.

When I take a rest after hours of thinking and come back a couple of hours later to solve the problem I do not really notice major differences in my understanding. Here are some people that claim this is possible though:

The latter of which links to an article in a journal on dream research as scientific basis for the claims.

However, is this actually possible, can you confirm that this actually happens?

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    It happens to some people sometimes: for example, I'm walking home from work, enjoying the walk and the going home, and suddenly see a solution to the software programming problem which I'd been working on that day in the office. However, what exactly is your question: are you asking whether it ever happens? Sometimes happens? Reliably happens? Can you quote a specific allegation about this topic, to be researched? – ChrisW Jun 18 '13 at 19:57
  • Alright, edited. – Xena Jun 18 '13 at 20:03
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    In psychology, this is called incubation. Just FYI. – Ana Jun 18 '13 at 20:23
  • Do you have formal references to the claim? – Wertilq Jun 18 '13 at 21:13
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    Here's at least two links that could serve as claims - care2.com/greenliving/solve-problems-while-you-sleep.html and medium.com/better-humans/dfb12da75a3d The latter also links to the following article - archiv.ub.uni-heidelberg.de/ojs/index.php/IJoDR/article/view/… - which might serve as a stepping stone to an answer. – rjzii Jun 18 '13 at 21:15

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