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Arne Beurling worked extensively in harmonic analysis, complex analysis and potential theory.
In 1940 he single-handedly deciphered and reverse-engineereded the Geheimfernschreiber (or "Fish cyphers") used by Nazi Germany, and created a decryption device that enabled Sweden to decrypt German teleprinter traffic passing through Sweden from Norway. In this way, Swedish authorities knew about Operation Barbarossa before it occurred.