fill a large saucepan two-thirds full of water. add the salt.
using a vegetable peeler, peel the potatoes. put a peeled potato on the cutting board. cut the potato in half lengthwise. holding a potato half cut side down, slice it lengthwise into 1-inch slices. now hold the slices and cut them in the opposite direction to make 1-inch pieces. be sure to keep your fingers clear of the knife blade. add the potato to the pan. repeat with the remaining potatoes.
put the pan on the stove and switch on the heat to high. bring the water to a boil and boil the potatoes, uncovered, until tender, about 10 minuites.( you can check by scooping out a potato cube with a slotted spoon, and poking the cube with a fork. it should go in easily) turn off the heat.
put a colander into the sink. remove the pan from the stove and pour the water and potatoes into the colander. be very careful; the steam from the boiling water can burn you.
return the potatoes to the pan. mash them with a potato masher. add the milk and butter. continue to mash until the butter and milk are mixed inches potatoes can be smooth or lumpy as you like. season with salt and pepper.