Bring a large pot of water to boil for pasta. Meanwhile, melt butter over low heat in a small saucepan. Add Gorgonzola and cook, stirring frequently, until cheese melts. Keep warm while you cook the pasta.
Tear arugula into bits, or use a scissors to cut it. Pieces should not be too small. Cook pasta until it is tender but not mushy. Remove and reserve a little cooking water, then drain pasta and toss it with arugula and cheese mixture, adding a bit of water if mixture seems dry.
Taste and add seasoning. Dish should take plenty of black pepper. Serve.