Part 5/11:
Gödel’s theorem illustrated that within any logical system capable of expressing arithmetic, some truths could not be proven by that system itself. This revelation drew comparisons to the Liar Paradox, where a statement refers to its truth and leads to contradictory conclusions. Mathematicians quickly recognized the significance of Gödel’s work; John von Neumann noted it would be “a landmark which will remain visible far in space and time.”