In mathematical logic, Godel's incomplete theorem is two theorems that Godel proved and published in 1930. In short, the first theorem points out that in any compatible mathematical formal theory, as long as it is strong enough to include piano's arithmetic axiom, a proposition that can neither be proved nor proved in the system can be constructed in it.
This theorem is one of the most famous theorems outside mathematics, and it is also one of the most easily misunderstood theorems. There is a theorem in formal logic that can easily be misstated. Many propositions sound like Godel's incomplete theorem, but they are actually wrong. Later, we can see some misunderstandings about Godel's theorem.
Godel
Godel (65438+April 28th, 0906-1978 65438+10/4), born in Brno, Czech Republic, is a mathematician, logician and philosopher. Godel went from 1938 to the Institute for Advanced Studies in Princeton, USA, and became a professor there from 1953, which developed the work of von Neumann and bernays.
His main contribution is to prove the "incompleteness theorem" of the system of formal number theory (that is, arithmetic logic) in terms of logic and mathematical basis. His papers "Principles of Mathematics" were published in 193 1 (referring to the books written by Whitehead and Russell) and "Undeterminable Propositions of Forms in Related Systems", which are one of the most important documents based on logic and mathematics in the 20th century.