O homem que provou que a matemática é incompleta Kurt Gödel

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Os Teoremas da Incompletude de Gödel • No vídeo de hoje, o professor Felipe Guisoli irá nos contar a história do impasse entre dois dos maiores matemáticos da história: David Hilbert e Kurt Gödel. • Hilbert e Gödel eram contemporâneos e ambos eram importantes figuras na matemática do início do século XX. Hilbert acreditava que a matemática era uma ciência completa e que, eventualmente, todas as questões matemáticas poderiam ser resolvidas com base em um conjunto de axiomas. Ele queria encontrar um conjunto de axiomas completo que pudesse provar todas as verdades matemáticas. • No entanto, Gödel demonstrou que isso não era possível. Ele mostrou que, em qualquer sistema axiomático, haveria sempre verdades matemáticas que não poderiam ser provadas a partir desses axiomas. Isso ficou conhecido como o Teorema da Incompletude de Gödel . • Este impasse teve um grande impacto na matemática e na filosofia da ciência. Isso levantou a questão de se a matemática era realmente uma ciência completa e, se não fosse, como poderíamos ter certeza de que as coisas que consideramos verdades matemáticas eram realmente verdadeiras. • Neste vídeo, o professor Felipe Guisoli nos conta a história completa deste impasse e como ele mudou a forma como pensamos sobre a matemática e a ciência em geral. 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