Solvitur ambulando: What math problems have you solved by simply walking?

[TMM]

Solvitur ambulando is a Latin phrase that means, "it is solved by walking."

Historically, after an arduous struggle to understand a problem, mathematicians resorted to taking an excursion. Such experiences of subconscious allusions also came subtly by mundane activities, such as boarding a bus, going on a hike, or crossing a street. For example, Henri Poincaré's idea on Fuchsian Groups and Leo Szilard's idea of neutron chain reactions.

For me, it was while I was on a fishing trip taking a break from a week's attempt on a fluid mechanics problem when the idea came: that the method by which Piotr Szymański's unsteady Poiseuille pipe flow equation is derived is similar to that of the confined Lamb-Oseen vortex.

What similar experience did you have in your mathematical career or personal development?

[aleksey]

There's this semi-famous quote by N. N. Taleb where he gives the advice: "to become a philosopher, start by walking very slowly" [1][2]. Though I do have a few instances that come to mind (my memory is really fuzzy, so I don't remember all the details):

1. When I am working on a maths problem, sometimes I get frustrated, and need to take a break. I do so by walking outside. In fact, sometimes I do maths in the park while sitting on their "picnic tables," the fresh air makes it easier to work with a pencil and paper.
2. I remember whilst walking, I got the not-so-original idea to apply concepts in graph theory to the analysis of social networks and reverse code engineering (RCE) problems.
   1. On that reverse engineering note, I remember being suck in an airport and thinking of using systems dynamics modelling [3] to solve RCE problems with them.
3. Another instance of "solvitur ambulando" that I can recall is not really a mathematics problem, but a fix to a software bug for a software project that I can work on - I think that it was like a function that is to print text output onto a screen, and I had the not-so-brilliant idea of just instructing the print() function to only print out strings that match the criterion, as opposed to coming up with a complicated evaluation boolean or integer function to determine if the string meets the criteria needed.
4. This last one is a more concrete example, and it connects to my "walking to the park" approach to doing maths: I wrote a four-part series where I proved (or falsified) algebraic equalities with just a graphing calculator, some pens, and a huge stack of papers. If you want to read them here:
   • Part 1: https://medium.com/math-simplified/alge ... 416e8ad972
   • Part 2: https://medium.com/math-simplified/alge ... 7c3311598e
   • Part 3: https://levelup.gitconnected.com/algebr ... a5b6e03cad
   • Part 4: https://levelup.gitconnected.com/algebr ... 1c847654bd

I do apologize in advance for the self-promotion in that last part :p

1. https://www.azquotes.com/quote/684225
2. I think from his book The Bed of Procrustes: https://en.wikipedia.org/wiki/The_Bed_of_Procrustes
3. https://en.wikipedia.org/wiki/System_dynamics