  As the debate concerning the Axiom of Choice rumbled on, it became apparent that the proofs of a number of significant mathematical theorems made essential use of it, thereby leading many mathematicians to treat it as an indispensable tool of their trade.  Hilbert, for example, came to regard AC as an essential principle of mathematics[5] and employed it in his defence of classical mathematical reasoning against the attacks of the intuitionists.  Indeed his ε-operators are essentially just choice functions (see the entry on the   epsilon calculus).