If you really like to think about pointless stuff you should take the History of Math course here at Platteville. The last 2-3 weeks is dedicated to proving that we actually know nothing about mathematics. Here is what I remember:

If the system we have come up with known as mathematics is real you should be able to break it down to its simplest term and then it would logically progress from there. But what is that simplest term? It you try to logically break the mathematic system down this is how it goes(according to mathematicians in the 19-very early 20th centeries). Advanced Mathematics is based on calculus which is based on algebra and geometry which are both based on arithmetic which is based on numbers which are parts of sets(the set of integers, the set of real numbers, the set of complex numbers, etc). So by this break down the smallest system with in mathmatics is sets. So many people started to work on set theory and they were fine when they were working with finite sets. They could calculate intersections and unions and find the cardinality. Then someone came along and developed the idea of the Super set. The Super set is a set with larger cardinality then its subset. For example {1,2,3,4} is a super set to {1,2,3}. This man then said that every set imaginable has a super set. Then someone said "Well what about the integers, there not a finite set" so they started to work on infinite sets and this is where the problem came. The set of all numbers up to infinity is what an infinite set is. But since all sets have a super set then what is bigger than infinity.

Set theroy was supposed to be the foundation that all of mathematical thought was supposed to be built up from. But it now had a large crack in it and thanks to the work of a few other men it started to crumble and fall apart. This is where mathematics starts to break down and there are more examples and theroms that prove that we really don't know any of the mathematics that we claim to know. I just don't remember enough of the examples to state them here. With out a firm foundation how can we build the rest of mathematics, in other words how can we be sure of anything if were not sure of the basics.

This also begs the question: Was mathematics invented or discovered? This was actually the topic of the final paper we had to write in this history class.