How Gödel s Incompleteness Theorems Work | Quanta Magazine
In the 89 years since Gödel s discovery, mathematicians have stumbled upon just the kinds of unanswerable questions his theorems foretold. For example, Gödel himself helped establish that the continuum hypothesis, which concerns the sizes of infinity, is undecidable, as is the halting problem, which asks whether a computer program fed with a random input will run forever or eventually halt. Undecidable questions have even arisen in physics, suggesting that Gödelian incompleteness afflicts not just math, but in some ill-understood way reality.
Here s a simplified, informal rundown of how Gödel proved his theorems.
The coolest.