There is an apocryphal story about a graduate mathematics student at the University of Virginia studying the properties of certain mathematical objects. In his fifth year some killjoy bastard elsewhere published a paper proving that there are no such mathematical objects. He dropped out of the program, and I never did hear where he is today. He's probably making my cappuccino right now.
If you feel like you have an achy breaky heart, you may not be imagining things. "Broken hearts" are indeed real, although in the medical community they go by the much less lyrical name of stress (tako-tsubo) cardiomyopathy.

A recent article in the Journal of the American College of Cardiology described stress (tako-tsubo) cardiomyopathy as "a rapidly reversible form of acute heart failure reported to be triggered by stressful events and associated with a distinctive left ventricular (LV) contraction pattern." Oooh, romantic. Shakespeare couldn't have written it better.