Why add salt to potato water?

To add flavor. Add some butter and cream afterwards when mashing- delicious

Salt also lowers the boiling temp of the water, so you can use less energy to cook.

If you reduce the amount of water you use and increase the amount of salt, the result will be salt crusted potatoes, with added flavor and sweetness.

Actually folks, heavily salting the water allows it to boil to a hotter temperature. This in turn cooks the potato's starch more thoroughly, resulting in a more creamy texture. Google 'Syracuse salt potatoes' for more information.

First, as a physicist I would argue that:

-salt RISES the boiling point of water. Every student knows that.

-by osmosis, being the water salty results in a lower content of water in the potato. That is, the potato absorbs LESS water while cooking (there are some videos in YouTube showing this fact.) With less content of water, potatoes become crispier after roasting.

i thought potatoes were more dry after i boiled with salted water vs unsalted - was making mashed potatoes i added salted while mashing potatoes while I boiled them unsalted and they were juicer salt draws the water out can boil potatoes faster is cut to smaller pieces anyways no salt necessary

Pasta absorbs boiling water as it cooks, so the salted water actually seasons it. But whole unskinned potatoes absorb little if any water when they cook/boil, so they do not get seasoned. Although I have no data, I suspect that neither the small increase in boiling temperature nor the tiny bit of osmosis resulting from salting the water would be of much consequence. However, cut and/or peeled potatoes might indeed be seasoned somewhat, depending on how much cooking water they absorb.