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In the Handbook of Mathematical Logic, the Paris-Harrington variant ofRamsey's theorem is celebrated as the first result of a long 'search' for apurely mathematical incompleteness result in first-order arithmetic. This paperquestions the existence of any such search and the status of theParis-Harrington result as the first mathematical incompleteness result. Infact, I argue that Gentzen gave the first such result, and that it was restatedby Goodstein in a number-theoretic form.

Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History