In German there is phrase concerning the complexity of finding the integral of a given function in contrast to the simplicity of finding its derivative. It has various slightly different formulations but can be stated as the following

Das Differenzieren ist ein Handwerk, das Integrieren eine Kunst.

which can be roughly translated to

While differentiation is a craft, integration is an art.

Nevertheless this would be my own translation as a native German speaker. Hence it is kind of an idiom in Germany it is hard to find its origins but I would be especially interested in these.

Therefore I am asking for two things: $(1)$ First of all is there an, I would call it "official", English equivalent which you have encountered somewhere before (e.g. within your mathematical education, in media, etc.)? $(2)$ Are you aware of the origins of this phrase either in German or in English? For example do you know a rather prominent person who has stated something similiar?

I am not sure whether my question is suitable here or if it would be better placed on a different site of the Stackexchange community (for example one MSE, or at the specific pages for the English and the German language). I guess especially the historical context - which I am interested in - in connection with the close relation to mathematics makes it fit in here perfectly. Howsoever let me know if it is the case that I should post this question on another site or when the question has been asked and answered before somewhere.

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    $\begingroup$ A minute or 2 of googling shows "differentiation is a science, integration is an art" is somewhat common. $\endgroup$ – kimchi lover Oct 27 '18 at 22:37
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    $\begingroup$ p550 of books.google.com/books?id=z5POAAAAMAAJ expresses this thought, in 1905. $\endgroup$ – kimchi lover Oct 27 '18 at 22:44
  • $\begingroup$ Asking for the first instance of this phrase (in any or all languages would seem to be ontopic here. As to idiomatic equivalences, that would go over to maybe EnglishUsage.SE $\endgroup$ – Carl Witthoft Oct 29 '18 at 12:39
  • $\begingroup$ @kimchilover This should be an answer! $\endgroup$ – Francois Ziegler Nov 6 '18 at 13:41
  • $\begingroup$ @kimchilover Still! It’s an answer that deserves visibility — and if/when a better one comes along it can still be accepted over yours. $\endgroup$ – Francois Ziegler Nov 6 '18 at 13:52

The 1905 textbook Lehrbuch der Mathematik: für Studierende der Naturwissenschaften und der Technik, Einführung in die Differential-und Integralrechnung und die Analytische Geometrie by Georg Scheffers has this zinger on p.550:

Schon hieraus erhellt, daß das Integrieren einen ganz anderen Charakter als das Differenzieren hat. Dies letztere ließe sich als eine Art Handwerk bezeichnen, das Integreieren demgegenüber als eine Kunst...

(Which means something like: From this it is clear that integration is unlike diffentiation in kind. The latter can be considered a kind of craft, but in contrast integration is an art...)

Scheffer's book looks like all calculus books, and it is hard to believe he originated the trope.


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