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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 the article Applications of lucid dreams: An online study 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, 2013 at 19:57
  • Alright, edited.
    – Xena
    Jun 18, 2013 at 20:03
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    In psychology, this is called incubation. Just FYI.
    – Ana
    Jun 18, 2013 at 20:23
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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, 2013 at 21:15
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    I think a lot of people are going to be able to say, anecdotally, 'yes that's happened to me and I remember it well' - in fact I think everyone reading this question has had this happen before - but it's an entirely different thing to actually prove it happened through a cited source. As much as we may want to confirm this through our own experiences, we should remember that good answers need citation, and that comments are not a substitute for answers.
    – Zibbobz
    Oct 31, 2022 at 13:27

2 Answers 2

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The paper Sleep onset is a creative sweet spot addresses this — except it's not about dreaming. It tested a wakeup technique that was allegedly used by a bunch of famous scientists and other big names.

To summarize, the paper found that the trick to solving a series of math problems clicked more often for the participants who entered the earliest stage of sleep but not deeper (so early that people may not realize they were asleep, also the phase in which hypnic jerks happen).

Here's the abstract:

The ability to think creatively is paramount to facing new challenges, but how creativity arises remains mysterious. Here, we show that the brain activity common to the twilight zone between sleep and wakefulness (nonrapid eye movement sleep stage 1 or N1) ignites creative sparks. Participants (N = 103) were exposed to mathematical problems without knowing that a hidden rule allowed solving them almost instantly. We found that spending at least 15 s in N1 during a resting period tripled the chance to discover the hidden rule (83% versus 30% when participants remained awake), and this effect vanished if subjects reached deeper sleep. Our findings suggest that there is a creative sweet spot within the sleep-onset period, and hitting it requires individuals balancing falling asleep easily against falling asleep too deeply.

Another part of the paper that stuck out was that it didn't immediately click for participants after they woke up:

This delayed Eureka occurred roughly 30 min after awakening and could thus correspond to the time for sleep inertia to vanish [typically less than 30 min].

I didn't look for research on activities like tennis as that's really a different question. What does "without active thinking" mean when you're awake? If you can carry out a conversation while playing tennis, what's stopping you from thinking about your problem instead?

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  • "What does "without active thinking" mean when you're awake?" — For me it's the difference in my internal monologue. When I'm most creative or productive my conscious thoughts tend to be observation and analysis of what I'm physically doing and subconsciously thinking, as opposed to controlling the situation or making decisions. — A trivial example is that most of this comment was produced by my fingers, not by my conscious mind. Until I saw it on the screen, I knew only what I was going to say but not what the actual words would be. I then consciously made a few edits to it.
    – Ray Butterworth
    Nov 2, 2022 at 13:57
  • To reverse the tennis situation, consider what the player is thinking versus what they are doing. Players use their conscious mind to observe the other player and anticipate what that player might do next. But it doesn't control the physical motions. The decision to rapidly shift to the left and use a backhand to return the ball in a specific way happens far too quickly to be done consciously. Imagine all the muscle movements and coordination that's required. Or, consider a concert pianist mapping thousands of black dots into finger motions far faster than anyone can consciously think.
    – Ray Butterworth
    Nov 2, 2022 at 14:06
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It probably is possible to solve problems without active thinking, because thinking itself and creating new ideas is a rather passive process.

Problem-solving is tightly coupled to learning, understanding, and creativity. This is probably represented in the brain with neurons and synapses.

While you sleep, you are probably growing new synapses. Your dreams are also an indicator of what's going on in your mind. And it's a very passive process, as well.

You mentioned something of your personal experience:

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.

The following is conjecture, but let's think about exercise science for a minute:

Here, an adaptive response happens only after a stimulus that's intense enough. You won't actually build more muscle after 1 light workout that barely caused fatigue, you have to exert yourself.

Principle of Supercompensation in exercise science

Same might be true for problem-solving, you have to really think hard in your waking hours to give those neurons and synapses a reason to grow while you sleep.

So, as with all things in science, you'd have to quantify your own experience with the subject.

How long did you study? How intensely did you study? How long did you rest before returning to the subject, and how are you measuring your progress from problem towards solution?

There may be some individual variation, but overall this is how you'd study the exact metrics of this particular topic.

References:

The synaptic plasticity and memory hypothesis: encoding, storage and persistence

REM sleep selectively prunes and maintains new synapses in development and learning

Sleep deprivation inhibits adult neurogenesis in the hippocampus by elevating glucocorticoids

Physical Stimulus-Performance-Adaptation : Understanding the physiological relationship

Here's an experiment that shows how particles self-assemble, when electricity is applied to them. Just conjecture, but in the brain similar things are probably also happening, as neurons become charged they might attract particles to form synapses:

Self-Assembling Wires by Standford Complexity Group

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    I believe most things you write here in isolation are true (besides maybe stretching the muscle/brain analogy a bit, and missing the importance of scaling down synapses during sleep, rather than building new ones), but it's not supported by anything (references/citations), and doesn't directly address the question asked.
    – Bryan Krause
    Oct 28, 2022 at 18:37
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    This sites does not like answers that are based on conjecture and require them to be backed up with evidence.
    – Joe W
    Oct 28, 2022 at 19:11
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    Yeah, but we have a collective case of imposter syndrome. We don't believe anything we say if we don't back it up with external research.
    – Cristobol Polychronopolis
    Oct 28, 2022 at 19:20
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    @oliver_siegel I wouldn't describe this site as professional, but rather as more structured than you're thinking if you have in mind sites like Reddit where discussion is on-topic. StackExchange in general has a Q&A model where answers are for answers only, and not for just talking about a topic. Skeptics.SE has a specific model of scientific skepticism which is based on supplying referenced evidence in support or contradiction to notable claims made in the media and other sources. See also skeptics.meta.stackexchange.com/questions/5/…
    – Bryan Krause
    Oct 28, 2022 at 19:32
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    @oliver_siegel There are 10,764 questions here; 1,377 don't currently have an answer that is either upvoted or accepted. So yes, not 100% of questions get answered in part because there's a higher barrier to answering than other sites. The intended benefit, which I think works well, though, is a much higher quality standard. Someone can post a question here when what they want is a well-researched answer, and won't get the types of answers they don't want.
    – Bryan Krause
    Oct 28, 2022 at 19:49

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