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Eugine_Nier comments on Rationality Quotes March 2012 - Less Wrong
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Not true. The "old limit definition" was non-existent beyond the intuitive notion of limit, and people were fully aware that this was not a satisfactory situation.
We need to clarify what time period we're talking about. I'm not aware of anyone in the generation of Newton/Leibniz and the second generation (e.g., Daniel Bernoulli and Euler) who felt that way, but it's not as if I've read everything these people ever wrote.
The earliest criticism I'm aware of is Berkeley in 1734, but he wasn't a mathematician. As for mathematicians, the earliest I'm aware of is Lagrange in 1797.
I'm also curious about this history.