To paraphrase Clausewitz: Mathematics is the extension of common sense by other means. Without the rigorous structure that math provides, common sense can lead you astray. That’s what happened to the officers who wanted to armor the parts of the planes that were already strong enough. But formal mathematics without common sense—without the constant interplay between abstract reasoning and our intuitions about quantity, time, space, motion, behavior, and uncertainty—would just be a sterile exercise in rule-following and bookkeeping. In other words, math would actually be what the peevish
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