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Sep 25 at 17:49 comment added Kphysics Some sort of misunderstanding on Gauss' part, obviously. Babylonians used a positional sexagesimal numeral system starting around 2000BC, and apparently it was known to the greeks. Re "Greek Astronomy and Its Debt to the Babylonians" Leonard W. Clarke The British Journal for the History of Science Vol. 1, No. 1 (Jun., 1962), pp. 65-77 (13 pages)
Sep 24 at 19:22 comment added Barmar "How could he overlook that" is essentially the same thing. When I say "I'm such an idiot" it's exactly what I mean about myself.
Sep 24 at 17:46 comment added Georg Essl @Barmar and zeynel. Please read my answer carefully. It is unclear that Gauss said anything of this sort at all. But if we do take the given source seriously (von Waltershaus) it is clear that he didn't call Achimedes an idiot or fool. So these kinds of baseless speculations only serve to confuse the careless reader and are unhelpful at best.
Sep 24 at 17:31 comment added zeynel @Barmar I agree with this. I don't know German but he probably said something like "What a fool..."
Sep 24 at 14:48 comment added Barmar 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!"
Sep 24 at 7:54 comment added Georg Essl @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.
Sep 24 at 7:48 history edited Georg Essl CC BY-SA 4.0
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Sep 24 at 7:18 comment added Mikhail Katz Even according to the possibly apocryphal source, the issue is not infinitesimal calculus but rather the positional system for numbers. Ball's account is completely off. This should be emphasized.
Sep 24 at 7:15 history edited Georg Essl CC BY-SA 4.0
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Sep 23 at 15:21 history edited Georg Essl CC BY-SA 4.0
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Sep 23 at 15:16 comment added Georg Essl @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.
Sep 23 at 14:24 comment added Mauricio 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.
Sep 23 at 14:13 comment added Mauricio Just noting here that Ball quote is about calculus, Dunnington seems to be about the decimal system.
Sep 23 at 14:11 history edited Mauricio CC BY-SA 4.0
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Sep 23 at 13:04 history answered Georg Essl CC BY-SA 4.0