True. It’s also interesting to note that a lot of Newton and Leibniz’s original reasoning about infinitesimals itself went through the same sort of three step process: first it was accepted because it was all there was, then rigour became fashionable and it was thrown out. Finally, only last century, it was shown that such ideas can be made perfectly rigorous in the right setting [see: nonstandard analysis].
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Math existed for thousands of years before modern rigor.
True. It’s also interesting to note that a lot of Newton and Leibniz’s original reasoning about infinitesimals itself went through the same sort of three step process: first it was accepted because it was all there was, then rigour became fashionable and it was thrown out. Finally, only last century, it was shown that such ideas can be made perfectly rigorous in the right setting [see: nonstandard analysis].