Does mathematics contain contradictions? That is, might there be a result that could be proved true by one mathematician and could be proved false by another? If so, mathematics would be in deep trouble! Hoping to show this situation was impossible, Hilbert asked (in the early 20-th century) whether there is a formal system strong enough to encompass all of mathematics and which could be proved to contain no contradictions. Around 1930, Goedel showed Hilbert's goal could not be realized. We will discuss Goedel's "Incompleteness" theorems and explain how they relate to Hilbert's program.