At the beginning of the 20th century, a lot of people were entranced by a new branch of math called Set Theory. Basically, a set is a collection of objects. The thinking of the time was that anything could be turned into a set: The set of all types of fruit and the set of all US Presidents were both completely valid. Additionally, and this is important, sets can contain other sets (like the set of all sets in the preceding sentence). In 1901 famous mathematician Bertrand Russell made quite a splash when he realized that this way of thinking had a fatal flaw: namely, not anything can be made into a set.
Russell decided to get meta about things and described a set that contained all those sets which do not contain themselves. The set of all fruit doesn’t contain itself, so it can be included in Russell’s set, along with many others. But what about Russell’s set itself? It doesn’t contain itself, so surely it should be included as well. But wait…now it DOES contain itself, so naturally we have to take it out. But we now we have to put it back…and so on. This logical paradox caused a complete reformation of Set Theory, one of the most important branches of math today.