Axiom of Choice

“For another indication of the controversy that initially surrounded the Axiom of Choice, consider this anecdote (recounted by Jan Mycielski in Notices of the AMS vol. 53 no. 2 page 209). Tarski, one of the early great researchers in set theory and logic, proved that AC is equivalent to the statement that any infinite set X has the same cardinality as the Cartesian product X x X. He submitted his article to Comptes Rendus Acad. Sci. Paris, where it was refereed by two very famous mathematicians, Fréchet and Lebesgue. Both wrote letters rejecting the article. Fréchet wrote that an implication between two well known truths is not a new result. And Lebesgue wrote that an implication between two false statements is of no interest. Tarski said that he never again submitted a paper to the Comptes Rendus.”

Source: Axiom of Choice