Axiom of Choice - Quotes

Quotes

"The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" — Jerry Bona

This is a joke: although the three are all mathematically equivalent, many mathematicians find the axiom of choice to be intuitive, the well-ordering principle to be counterintuitive, and Zorn's lemma to be too complex for any intuition.

"The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes." — Bertrand Russell

The observation here is that one can define a function to select from an infinite number of pairs of shoes by stating for example, to choose the left shoe. Without the axiom of choice, one cannot assert that such a function exists for pairs of socks, because left and right socks are (presumably) indistinguishable from each other.

"Tarski tried to publish his theorem in Comptes Rendus, but Fréchet and Lebesgue refused to present it. Fréchet wrote that an implication between two well known propositions is not a new result, and Lebesgue wrote that an implication between two false propositions is of no interest".

Polish-American mathematician Jan Mycielski relates this anecdote in a 2006 article in the Notices of the AMS.

"The axiom gets its name not because mathematicians prefer it to other axioms." — A. K. Dewdney

This quote comes from the famous April Fools' Day article in the computer recreations column of the Scientific American, April 1989.