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There'a a story that when someone wrote up a famous mathematician's work (Euler?), he found many errors, some quite serious. But all the theorems were true anyway.

Sounds like Tao's third stage, of informed intuition.

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Back in Euler's time there as a lot of informality. The rigor of the second half of the 19th century was still some time in the future.

It's still incredibly painful as a learner though when things don't quite pan out. You start gaslighting yourself and then handwaved/convince yourself away that this must be true given how consistent all the "downstream" work is, and that you just don't fully understand it.

So, I agree with the author that this is super helpful, even if we know the proofs are "true" in the end

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