Read: Lehman, Leighton, and Meyer: 1, 2, 3. Chapter 2 was only marginally treated, and will come back in the second week of the course.

In the lecture I mentioned that mathematics as we know it today actually may be "inconsistent", which means that one day someone actually may prove "false" and thereby invalidate all mathematical results as we know them.

A great short story by the Science Fiction writer Ted Chiang about this can be found here: Division by Zero.