Kurt Gödel - The Incompleteness Theorem

Kurt Gödel é quase um anônimo comparado ao seu amigo Einstein. Interessante que os dois gênios modificaram nossa maneira de entender a Física e a Matemática. Einstein nos levando além da Física Clássica e Gödel estabelecendo "a priori" que a Matemática não é a língua da natureza pois seus "sistemas" nunca são completos. Dito de outra forma, que é impossível computar tudo. A vida continua e agora matematicamos sem as pretensões de outros séculos.

Source: http://en.wikipedia.org/wiki/Kurt_Gödel#The_Incompleteness_Theorem

In 1931 and while still in Vienna, Gödel published his famous incompleteness theorems in "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme" (called in English "On formally undecidable propositions of Principia Mathematica and related systems"). In that article, he proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g. the Peano axioms or ZFC), that:

1. If the system is consistent, it cannot be complete.
2. The consistency of the axioms cannot be proven within the system.

Albert Einstein was also living at Princeton during this time. Gödel and Einstein subsequently developed a strong friendship, and were known to take long walks together to and from the Institute for Advanced Study. The nature of their conversations was a mystery to the other Institute members. Economist Oskar Morgenstern recounts that toward the end of his life Einstein confided that his "own work no longer meant much, that he came to the Institute merely…to have the privilege of walking home with Gödel".^[10]