I am currently taking a meager Philosophy 101 class, so right now I know that I know nothing. But my professor knows a lot.
So, in introductory philosophy classes there comes a time when one learns to ask, "What makes me me?", i.e. personal identity, and my professor tells us there are five theories: the brain theory, the body theory, the soul theory, the memory theory, and, hushed and solemn, we are told of the no-identity theory. The former four postulate that one's identity lies in the theories' respective locations; you can choose the one that you would like to propagate.
However, the theory that you have no identity comes from Hume. He put forth that we make up this fantastical idea of "personal identity" and then go running after it hither and thither. According to him, there is no such thing; it is just an idea. This guy definitely made quite a fuss back in the 1700s (for this and a handful of other reasons).
THE DEATH OF A PHILOSOPHER
As my professor was delighting us with Hume, he shared some mythology about Hume's final moments. According to him, the tale is that Adam Smith, one of Hume's top students, visits Hume on his death bed. Smith shows Hume this fancy book he's just written and it's brimming with his teacher's ideas. Hume is pleased when he is handed the book, and happily skims through it. Then he closes it, kisses the cover, and dies.