Which mathematician developed the incompleteness theorems, showing that any consistent formal system capable of expressing basic arithmetic contains statements that cannot be proved or disproved within that system?
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Kurt Gödel
Published in 1931, Gödel's incompleteness theorems fundamentally changed mathematics by proving that no formal system can be both complete and consistent. A close friend of Albert Einstein, Gödel demonstrated that there will always be true mathematical statements that cannot be proven using a fixed set of rules.