Questions and Answers

Two quotations:

“In re mathematica ars proponendi pluris facienda est quam solvendi.”
(In mathematics the art of asking [questions] is more valuable than solving [them].)
— Georg Cantor (1845–1918), Doctoral Thesis, 1867

and

“The uncreative mind can spot wrong answers, but it takes a very creative mind to spot wrong questions.”
— Antony Jay (1930–)

It’s a common but still dispiriting experience for me to see an excellent tool being applied to the wrong problem. Conclusions are only as sound as (a) the logical reasoning used and, crucially, (b) the validity of the premises, which includes the applicability of the method itself. Both “the right answer to the wrong question” and “the wrong answer to the right question” are wrong, but the former is more devastating because it carries an aura of (false) respectability that can lead one into making bad decisions with great confidence.

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