Kurt Gödel
Gödel’s Incompleteness Theorems: History, Proofs, Implications
Suman Ganguli
In 1931, a 25-year-old Kurt Gödel published a paper in mathematical logic titled “On Formally Undecidable Propositions of Principia Mathematica and Related Systems.” This paper contained the proofs of two remarkable “incompleteness theorems,” which state:
For any consistent axiomatic formal system that can express facts about basic arithmetic,
1. there are true statements that are unprovable within the system
2. the system’s consistency cannot be proven within the system
https://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf
https://en.wikipedia.org/wiki/On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems