Incompleteness theorems

Incompleteness Theorems are ideas about mathematics that tell us that there are things that you can never prove. This means that some questions might be hard and tricky to figure out, no matter how hard you try. So even if there's a lot of smart people working on the problem, they might not ever be able to figure it out!

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Chaitin's incompleteness theorem, Gödel's completeness theorem, Gödel's speed-up theorem, Gödel, Escher, Bach, Gödel machine, Löb's Theorem, Minds, Machines and Gödel, Non-standard model of arithmetic, Proof theory, Provability logic, Quining, Tarski's undefinability theorem