Peel potatoes. Cut potatoes into chunks. Place in a medium saucepan and cover with water. Boil potatoes until done. Drain water. Cover pan and set aside.
While the potatoes are boiling, peel and finely chop garlic. Sauté the garlic in the olive oil in a small frying pan. Just when garlic is turning golden, add the paprika, and remove from heat.
Pour garlic-paprika and oil into the pan of potatoes and mash, mixing well. Add a few tablespoons of oil to make a smooth mixture, then salt to taste and serve.