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A mathematician is always asking, “What assumptions are you making? And are they justified?” This can be annoying. But it can also be very productive.
To a mathematician, the structure underlying the bullet hole problem is a phenomenon called survivorship bias. It arises again and again, in all kinds of contexts. And once you’re familiar with it, as Wald was, you’re primed to notice it wherever it’s hiding.
MATHEMATICS IS THE EXTENSION OF COMMON SENSE BY OTHER MEANS
basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe doesn’t object.