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I was watching Numberphile's Parabolas and Archimedes featuring John Ball.

However, it is doubtful whether the Gauss quote quoted at the end of the video by Johnny Ball, "Oh the idiot! He discovered calculus and he let it go through his fingers," is really what Gauss said.

Did Gauss really call Archimedes an idiot?

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    $\begingroup$ Gauss was a German speaker. $\endgroup$
    – Mikhail Katz
    Commented Sep 23 at 11:33
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    $\begingroup$ And a Latin writer $\endgroup$
    – Alexandre Eremenko
    Commented Sep 23 at 12:03
  • $\begingroup$ Yukion the answer below seems to solve the issue. Could you validate it? $\endgroup$
    – Mauricio
    Commented Sep 24 at 11:42
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    $\begingroup$ Too short for me to edit, but he's always known as ‘Johnny’, not ‘John’.  (It's not a diminutive of his birth name, which is actually Graham.  In fact, the nickname refers to the footballer John Ball.) $\endgroup$
    – gidds
    Commented Sep 24 at 16:02

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In Dunnington, G. W., Gray, J., & Dohse, F. E. (2004). Carl Friedrich Gauss: Titan of Science. MAA. p. 218 one finds the following:

Archimedes was the man of antiquity whom Gauss esteemed most highly. He imagined him as a worthy old man of noble appearance. The only thing for which he could not pardon him was the fact that in his "sand calculating" he did not discover the arithmetic of position or decimal system of numbers. Gauss said, "How could he overlook that, and at what a pinnacle science would now be if Archimedes had made that discovery."

(emphasis is mine)

Johnny Ball's version is on some level a sensible paraphrasing of the above translation by Dunnington of 1955. Given that Dunnington is a widely read English text on Gauss it might well be that Ball has it from this passage.

Sadly, Dunnington does not provide a direct citation, so I'm still looking where he might have translated this from. I'll edit this once I find it. EDIT: Mauricio has discovered that the source of Dunnington's passage is likely Wolfgang Sartorius von Waltershausen (1856) Gauss zum Gedächtnis p. 84. This source is known to be hagiographic and contains apocryphal material. So it may well be that this is not an actual Gauss quote. So unless a primary passage can be found it is probably best to consider it unconfirmed.

I take it as virtually certain that the "idiot" part is just flair injected by Ball.

Also note the mathematical context of von Walthershausen, that Dunningworth mentioned and compare it to Ball's exposition. In von Waltershausen it's the "decadische Zahlensystem" (system of decadic numbers, my translation), in Dunnington it is "arithmetic of position or decimal system of numbers" while in Ball's exposition it is calculus. In this sense this type of story telling fits many criteria of the kind of historically false or problematic folklore discussed by many other examples.

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    $\begingroup$ Just noting here that Ball quote is about calculus, Dunnington seems to be about the decimal system. $\endgroup$
    – Mauricio
    Commented Sep 23 at 14:13
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    $\begingroup$ I found the same story in Gauss zum Gedächtnis a memorial written very soon after Gauss' death by Wolfgang Sartorius (1856), the same that wrote the 1+2+...+100 story. $\endgroup$
    – Mauricio
    Commented Sep 23 at 14:24
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    $\begingroup$ @Mauricio Thanks for pointing out Wolfgang Sartorius von Waltershausen. Dunnington paragraph appears to be a near verbatim translation of a passage of Gauss zum Gedächtnis p. 84. So much so that I think one must assume that this is the source of Dunnington's passage. It is certainly quite possible that this is not a real quote of Gauss. $\endgroup$
    – Georg Essl
    Commented Sep 23 at 15:16
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    $\begingroup$ @MikhailKatz I elaborated on that point. I think it's a bit tricky without knowing what Gauss actually said. There is a possibility that he did say something essentially of this sort and that in the actual context it does relate to calculus. Hand calculation, and numerical/number system strategies were a big part of practical calculus solutions, so there could be a connection. So the best I can do is warn of this being not a primarily sourced story (in the sense of provably coming from Gauss himself) at this point. $\endgroup$
    – Georg Essl
    Commented Sep 24 at 7:54
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    $\begingroup$ Whatever the actual quote, it seems like it would have been meant hyperbolically. Like when you make a silly mistake you think or say "Oh, I'm such an idiot!" $\endgroup$
    – Barmar
    Commented Sep 24 at 14:48

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