The difference when you do know (when, for example, we are looking for a new proof) is enormous. Like a Bridge problem 'if the thing is possible it must be necessary to lead the Ace and trump with the Ace in Dummy.'

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Quote text and notes from Wikiquote: John Edensor Littlewood (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.