I have a question about an interesting terminology "flow".

Definition. In psychology, flow is the mental state of operation in which a person performing an activity is fully immersed in a feeling of energized focus, full involvement, and enjoyment in the process of the activity. In essence, flow is characterized by complete absorption in what one does, and a resulting loss in one's sense of space and time here.

So, in sum:

flow = a psychological state/feeling of having a highly energized focus at the work without sensing the time and space.

Moreover, it is noted that for some different fields there are specific terms including:

  1. "developers of computer software reference getting into a flow state as "wired in", or sometimes as The Zone, hack mode."
  2. "Stock market operators often use the term "in the pipe" to describe the psychological state of flow when trading during high volume days and market corrections."
  3. "Professional poker players use the term "playing the A-game" when referring to the state of highest concentration and strategical awareness, while pool players often call the state being in "dead stroke"."

My question is that:

I am curious to know is there any specific slang/terminology in mathematics community regarding the experiencing flow at math studying?

You can imagine after doing math for some hours, even very challenging topic, you just take a look at the clock and see it is too much passed, like in the twinkling of an eye!

Just for the sake of completeness and regarding a very good comment by @WillJagy:

I think for doing math it needs to have a kind of enthusiasm in math together with patience. I remember a great quote by Fields Medal winner, Maryam Mirzakhani:

"The beauty of mathematics only shows itself to more patient followers."

So, I think it needs to be passionately and patiently curious in doing math and then one can experience flow at doing math.


closed as off-topic by Will Jagy, Xander Henderson, Aloizio Macedo, user21820, Hans Lundmark May 5 '18 at 9:10

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is not about mathematics, within the scope defined in the help center." – Will Jagy, Xander Henderson, Aloizio Macedo, user21820, Hans Lundmark
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ The books we have by our best do not follow this model well. The common factor is a time of hard work, some kind of rest or interruption, then the key to the problem appearng in the mind, perhaps during sleep. The 3 types of effort you describe involve problems that do not take years to solve. $\endgroup$ – Will Jagy May 4 '18 at 23:51
  • $\begingroup$ @WillJagy: you mentioned a nice experience: sleep! Great! I also added some points inspired by your nice cooment. $\endgroup$ – Amin May 5 '18 at 0:08
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    $\begingroup$ Interesting question. My short answer - I don't think there's a word commonly used for this particular immersion in mathematics. Do read Poincare: vigeland.caltech.edu/ist4/lectures/Poincare%20Reflections.pdf $\endgroup$ – Ethan Bolker May 5 '18 at 0:15
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    $\begingroup$ Damn, clicked on this thinking it was going to be about vector flows $\endgroup$ – Shalop May 5 '18 at 0:19
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    $\begingroup$ I think any of the people who deal in computers that I know would laugh if I asked them if they ever described some kind of flow as "hack mode" $\endgroup$ – leibnewtz May 5 '18 at 0:28

Like you said, this notion is essentially from psychology. So there is no such word in mathematical terminology, to the best of my knowledge.

Now with the birth of Mathematics Education, there is a growing number of people interested in the psychological side of mathematics, so a partial answer to your question could potentially be found in books like Mathematical Mindsets by Jo Boaler, or The Mathematical Experience by Philip J. Davis and Reuben Hersh.

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    $\begingroup$ I think you're misinterpreting the question. Or, if not, your "so" as if it being a psychological notion implied that there isn't any mathematical slang to refer to this, is wrong. The OP gave examples that are not at all related to psychology. $\endgroup$ – Git Gud May 4 '18 at 23:54
  • $\begingroup$ I would be inclined to just say "focused". $\endgroup$ – user247327 May 4 '18 at 23:59
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    $\begingroup$ @GitGud Maybe that "so" was unfortunately chosen. But I am really not aware of a word mathematicians would use to refer to that state of mind. $\endgroup$ – Arnaud Mortier May 5 '18 at 0:01

I do not hear any of my colleagues refer to any such state, but I imagine that this is due to both an introverted reticence to talk about mental states, and possibly a denial that anything other than prolonged hard work is necessary and/or virtuous.

The description I myself use to describe a "transporting" lecture on something serious, or an epiphany achieved while brainstorming with someone, is "being in the zone".

When I have used this phrase, mostly I've met incomprehension. I do not know whether this is due to attitudes and vocabulary, or whether other people genuinely never work this way, or it's denial of that (scary? unreliable?) quirky aspect of the business.

And, yes, of course, it does seem that "years of conscientious preparation" is the necessary prep for various moments of epiphany... I guess my own conclusion is that I have no idea what's really happening inside my head. My grad students do also speak of something abruptly becoming completely obvious, after years of their "being dumb", etc. Yes, a discontinuous manifestation of (probably) continuous internal phenomena.

  • $\begingroup$ Nice explanation @paulgarrett. $\endgroup$ – Amin May 5 '18 at 0:34
  • $\begingroup$ Nice, just note that epiphany is different from flow. flow might include epiphany or not. However, they've lots of self-state similarity. $\endgroup$ – SdidS May 5 '18 at 4:03
  • $\begingroup$ People may also be scared that you "jinx" it away by mentioning it, as it is something that you absolutely cannot control. $\endgroup$ – Arnaud Mortier May 5 '18 at 8:40

I do remember I once read some psychological research that yielded results along the line:

"People are more capable on focussing on logical problems if they are bad-tempered."

For example the thought of having to do their tax return will cause people to become bad-tempered and thus enable them to actually better focus on the computations involved.

If I try to translate that to a mathematics setting I would conclude that too much relaxation ("flow"??) would be good for intuition (there are studies on how relaxation improves intuition as well) but it would rather hinder them when it comes to technical proofs.

If you really want the relevant papers, leave me a comment. I cannot promise you I will find them though and it will likely take some time.

  • $\begingroup$ Thanks @mol3574710n0fN074710n, but I don't it refers to what you say " too much relaxation". This is a kind of forgetting the time and space; like after doing math, you just take a look at clock and see it is too much passed but you didn't experience passing the time! $\endgroup$ – Amin May 5 '18 at 0:25
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    $\begingroup$ Yes, I think I can understand the difference. I also believe if the mathematician is relaxed but not sloppy and instead appreciates every detail of the problem as through a lense, this will not come as a trade-off but be beneficial. There is a state of mind called "hyperfocus" with ADHD people that probably fits that description. They will however not be able to "guide" their flow of thoughts in that state and will get caught in details - which might be very productive, depending on the problem. It is just a mindset where the ultimate "goal" loses its importance... $\endgroup$ – mol3574710n0fN074710n May 5 '18 at 0:35

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