Overview
Goedel's Incompleteness Theorems, published by [[kurt-goedel|Kurt Goedel]] in 1931, are two theorems that have had a profound impact on the foundations of mathematics. The first theorem states that any formal system powerful enough to describe basic arithmetic is either incomplete or inconsistent. This theorem is often linked to the work of [[bertrand-russell|Bertrand Russell]] and his [[principia-mathematica|Principia Mathematica]]. The second theorem shows that if a formal system is consistent, it cannot prove its own consistency, a concept that has been explored in the context of [[computer-science|computer science]] and [[artificial-intelligence|artificial intelligence]].