One of the most fun things about mathematics is the surprising appearance from time to time of truths that are counter-intuitive. The existence of different orders of infinity, for example, or the impossibility of a set that contains all sets. Perhaps it is examples like these that make me wary that my own thinking may be ruling out viable possibilities. And thus, I sometimes generate new thoughts by considering a favorite truth and prodding myself to "Consider the opposite." As a result, I may discover one of my thoughts to be wrong--or, what is more exciting, a pair of opposite truths.
I like these lines from Robert Frost:
"We dance around the ring and suppose,
but the Secret sits in the middle and knows."
Holiday Party
The chemistry of creativity in the flesh
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