You keep repeating to your self say on loop 5: Number 5 number 5 number 5, etc. on each loop. And try not to reminisce about earlier loops.
No way. I'd have to write it down on my sleeve.
One could also take splits on a watch...
Does not work very well if it is 5 F and you are wearing big gloves or mittens, and you are strapped into a very tight fitting pole strap - not much dexterity to do anything.
I had an old lady open up powergels for me to save me a minute of trying to fiddle around with removing poles, gloves... Luckily there were few competitors, and the many volunteers at the refreshment table were anxious to be helpful.
If it's important enough, you can find ways. A watch doesn't have to be worn on a wrist, and a button doesn't have to be pressed written a finger, at least not your own. Sounds like it's not necessary for a math professor who is good at counting, but for others...
I actually was able to keep an eye on the mileage on my Garmin even without my reading glasses - light was bright enough.