This might be more of a philosophical question, but why in mathematics is the tendency to only accept formal proof as a means of finding out what's true? In the physical sciences there's no such thing, and yet we feel we know a lot about the world around us through experimentation and "softer" inferences. For example, if we search exhaustively for counterexamples to some proposition, why is a failure to find them never considered good enough? Could one idea be that when it's at least possible to prove a statement, that a lack of proof is a kind of evidence that it's false?
2026-03-28 06:30:28.1774679428
"Probable" truth in mathematics
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