Kurt Godel's equation

In the early twentieth century, it was generally accepted that everything real could be substantiated by mathematics, and that everything proved by mathematics was true. However, in 1931, the brilliant mathematician Kurt Godel created an elegant though rather nasty-looking formula to challenge that belief. Here’s a tiny segment of his equation

With this equation, Godel demonstrated that any mathematical or symbolic system of logic will always be incomplete and contain assumptions that cannot be proved. This means that nearly every scientific notion we hold will contain suppositions that may be false. Truth cannot be entirely known, for no matter how much evidence you collect, your knowledge will always be incomplete.

Douglas Hofstadter, a professor of cognitive and computer science at Indiana University, believes that Godel’s incompleteness theorem directly applies to our belief about who we are:

“Just as we cannot see our faces with our own eyes, is it not inconceivable to expect that we cannot mirror our complete mental structures in the symbols which carry them out? All the limitative theorems of mathematics and the theory of computation suggests that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: is guarantees that you can never represent yourself totally.”

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