and if he cant explain it he doesnt know it as the einesteinean quote goes

who should we believe?

I’d say neither

Sorry for yet another critical remark, people are probably already tired of them. But I am really worried about the dangerous trend of using numerical software without clear (or even any) understanding of how it works, or mathematical principles behind it.

]]>“Real” Analysis is a Degenerate Case of Discrete Analysis. Also the question of numerical stability become important. We simply should not expect this or that procedure for differentiating functions defined by computer programs to be universally meaningful and applicable. ]]>

If applied appropriately, I’m all for it, but caution should be exercised.

As for the synthetic differential geometry (as well as the “dual numbers” in AD), it’s just a sleek way to work with the jets of functions and maps.

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