Timeline for Has anything (other than what is in the obituary written by M. Noether) survived of Paul Gordan's defense of infinitesimals?
Current License: CC BY-SA 4.0
16 events
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| S Dec 19, 2021 at 10:55 | history | edited | Glorfindel | CC BY-SA 4.0 |
typos corrected
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| S Dec 19, 2021 at 10:55 | history | suggested | CommunityBot | CC BY-SA 4.0 |
Changed 'witten' to 'written' in the title.
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| Dec 19, 2021 at 1:30 | review | Suggested edits | |||
| S Dec 19, 2021 at 10:55 | |||||
| Mar 28, 2018 at 16:19 | vote | accept | Peter Heinig | ||
| Sep 18, 2017 at 15:31 | comment | added | Mikhail Katz | Hi Peter, in his fine answer Carlo seems rather pessimistic about finding any trace of this but it may still be worth contacting the experts you mentioned in case other universities had other practices. As far as Cauchy is concerned I would prefer communication by private mail if you are interested. | |
| Sep 18, 2017 at 5:41 | comment | added | Peter Heinig | @MikhailKatz: if one takes the conclusions of [Gordon M. Fisher: Cauchy and the infinitely small. Historia Mathematica 5 (1978), 313-331] at face value, then Gerald Edgar is right with "in 1861 infinitesimals and limits were equally bad in terms of rigor". Roughly, Fisher demonstrates that Cauchy was not committed to the contemporary notion of 'limit'. E.g., op. cit. p. 330: "In his textbooks, Cauchy sometimes argued as if he were dealing with actual infinitesimals. The variables with limit zero that he often used were not fully analyzed, but they had "values" [...]" I recommend op.cit. | |
| Sep 17, 2017 at 12:58 | comment | added | Mikhail Katz | @GeraldEdgar, I thought Cauchy was the one who rigorized analysis in your view. Cauchy died in 1857. Thus Cauchy had been dead for 4 years in 1861. Barring any posthumous contributions by Cauchy (that I am not aware of), analysis would have been rigorized at least 4 years before 1861 then. Why do you say then that "limits were bad in terms of rigor" in 1861? | |
| Sep 16, 2017 at 3:04 | review | Close votes | |||
| Sep 16, 2017 at 8:44 | |||||
| Sep 15, 2017 at 20:47 | history | edited | Peter Heinig | CC BY-SA 3.0 |
Additions.
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| Sep 15, 2017 at 16:45 | history | edited | Peter Heinig | CC BY-SA 3.0 |
Deleted anachronistic, pessimistic and speculative paragraph.
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| Sep 15, 2017 at 13:28 | comment | added | Gerald Edgar | Perhaps we should note that this (1861) is before Dedekind, Weierstrass, Cantor et. al. made limits more rigorous. So in fact we could argue that in 1861 infinitesimals and limits were equally bad in terms of rigor. By around 1900, limits had reached a modern sort of rigor. And by around 1960 (Robinson), so did infinitesimals. | |
| Sep 15, 2017 at 13:11 | answer | added | Carlo Beenakker | timeline score: 12 | |
| Sep 15, 2017 at 7:38 | comment | added | Mikhail Katz | The last paragraph of your answer can probably be deleted. First, the kind of argument you propose involves a distinction between theory and model that was simply not available at the time, so Gordan could not have formulated even a remote approximation of such an argument (perhaps Frege conceivably could, but Gordan was no Frege). Second, we have no way of knowing whether the archives for the disputatio exist and/or have possibly been preserved, so there is no reason to be overly pessimistic about it. | |
| Sep 15, 2017 at 5:54 | history | edited | Peter Heinig | CC BY-SA 3.0 |
Added an explicit remark that the philosophical content of this question is rather boring and expected; the hope is for at least of mathematics of the matter to have survived.
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| Sep 15, 2017 at 5:40 | history | edited | Peter Heinig | CC BY-SA 3.0 |
Stylistic improvements.
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| Sep 14, 2017 at 15:00 | history | asked | Peter Heinig | CC BY-SA 3.0 |