Other forms: madmen
Madman is an old fashioned, derogatory term for a severely mentally ill person. These days, calling someone with a serious psychiatric illness a madman would be offensive.
You're most likely to hear dangerous criminals described as madmen, although it's also common to use this word for someone who acts recklessly: "Look how fast that madman is driving!" Another way to use madman is to emphasize the intensity of something: "She worked on that paper like a madman, writing the entire thing in just a few hours."