What did Gödel show with his first incompleteness theorem?

By Philippos Papayannopoulos It's very common to read and hear people talking about Kurt Gödel's famous (first) incompleteness theorem, in popular media, books, discussions, etc. Which is a very good thing I think, given how wonderful and ingenious the ideas and the reasoning behind this theorem are. But even though it's more than almost 85 [...]