failure

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In mathematical research even a failed attempt at solving a problem may increase your understanding. A better understanding of something that doesn't work may lead to something that will.

There are many other places where this "rule" applies.

Two of the best known promoters of this idea were
Thomas Edison: "I have not failed. I've just found 10,000 ways that won't work."
and
Henry Ford: Failure is only the opportunity to begin again more intelligently.

Oh yes, the YA chess coach says:
To improve your game, play stronger players and study your losses.
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