Peel the potatoes and cut them into slices about 1/2 inch thick.

Bring water with salt to a boil. When it starts boiling, add the potatoes and cook until tender (the water should cover them). Once cooked, turn off the heat and set aside.

Put the mayonnaise in a bowl and gradually add some of the hot potato cooking water, mixing well until smooth. Slowly add this mixture back to the potatoes, stirring gently.