“Hypochondriasis” was first diagnosed as we understand it today in the 19th century.
This debilitating condition is the result of an inaccurate perception of the condition of body or mind despite the absence of an actual medical condition. An individual suffering from hypochondriasis is known as a hypochondriac.
Hypochondriacs become unduly alarmed about any physical or psychological symptoms they detect, no matter how minor the symptom may be, and are convinced that they have, or are about to be diagnosed with, a serious illness. (thx, Wikipedia)
These people cannot be convinced that they are just fine no matter how many tests you run which demonstrate they are just like everyone else. Science cannot dissuade them. About 3% of all patients visiting their primary care physician have this problem.
The treatment, I am told, is the effort to help each patient find a better way to overcome the way his/her medically unexplained symptoms and illness concerns rule her/his life. Current research makes clear that this excessive worry can be helped by either appropriate medicine (targeting the anxiety) or targeted psychotherapy.
Source: Pyromaniacs: Something Dreadful