Is there a specific terminology in mathematics community for "flow" at math studying?

Question

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 in 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!

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

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

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

Answer 1

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.

Answer 2

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.

Answer 3

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.