Consider radically deemphasizing the importance of proofs in mathematics. If it is true most of the time, it is good enough. If it is true all the time, then that is just an extra bonus. Characterizing some of the exceptions of something that is true most of the time is nice. Characterizing all of the exceptions (if any) is just an extra bonus.

How far could we go with this approach? To a certain extent, it is already being done, for example, for the great many results that rely on the Riemann Hypothesis being true.

Avoids some of the aesthetic ugliness of proofs, which might impede education.

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