I noticed on myself that running long distances is also willpower training.

Being able to force myself to stick to something hard/painful causes me to also expand my ability to stick to other things.

And when I can't run (for example due to injury) it also affects my ability to stick to a lot of other things that should not be affected by my knee.

Another reason why I think running is so beneficial is because when you start it you see obvious, epic improvements in your performance.

I literally was doing runs I did not think possible just a month earlier.

It changes your perspective on what is and what is not possible.

And if this happens to you it may cause you to start investigating and making a lot of other health-related changes.

Steve Magness has a great book on the topic called Do Hard Things. It’s a great read, but makes extra sense for folks who run of engage in hard endurance exercise.

There's definitely a lot of psychological interplay with running and willpower/self discipline. I think I read somewhere that there are disproportionate number of professionals/PhDs/otherwise successful people who are into ultra running, in part because they have the resources and flexibility needed for the training, but also because the ability to delay gratification and work towards a long term goal is required in both venues.

On a more micro level, a good run can make the rest of life's challenges much less daunting...as I say to my wife: busy days seem a lot less overwhelming if you start them by dragging yourself out of a warm bed to run 8 miles in freezing rain.

Alan Turing was a serious marathon runner and came close to qualifying for the 1948 olympics. https://mathshistory.st-andrews.ac.uk/Extras/Turing_running/