Timeline for Unrigorous British mathematics prior to G.H. Hardy
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 27, 2022 at 19:32 | comment | added | Tom Copeland | One should be careful in distinguishing the difference in meaning between British and English. | |
| May 17, 2022 at 22:08 | vote | accept | CommunityBot | moved from User.Id=216345 by developer User.Id=481663 | |
| May 16, 2022 at 10:53 | comment | added | Trunk | Prof Richards' paper suggest that with calculus things like issues with teachability and general credibility ("epistemological universality") of base concepts like limits played a role in how a formal and rigorous approach was slow to evolve. She also mentions the tussle between the exemplary and conceptual approaches in mathematics throughout Europe at the time. So we can conclude that Britain (including Cambridge) was no different to other places of that time in its lack of rigor in mathematics. Separate from Richards' paper, I see that induction proving is really only from the mid-1800s. | |
| May 13, 2022 at 15:45 | comment | added | BrockenDuck | This kind of reminds me of the Frensh rationalism vs British empiricism contrast | |
| May 12, 2022 at 14:52 | comment | added | Trunk | No need to become a Cambridge Fellow after all - found the Beenhakker reference from another (free) source. | |
| May 12, 2022 at 13:46 | comment | added | Todd Trimble | Very interesting. Some of it reminds me of what Rota said [in Indiscrete Thoughts] about Alfred Young (of Young tableaux fame): "Alfred Young's style of mathematical writing has unfortunately gone out of fashion: it is based on the assumption that the reader is to be treated as a gentleman with a sound mathematical education, and gentlemen need not be told the lowly details of proofs. As a consequence, we have to figure out certain inferences for which Young omits any explanation out of respect for his readers." [Of course, those papers are notorious nowadays for their apparent opacity.] | |
| May 12, 2022 at 12:49 | comment | added | Carlo Beenakker | @TimothyChow --- one example of "unrigorous English mathematics" which is discussed in this article is the law of the permanence of equivalent forms. I guess I can email the pdf of the article upon request (that should be "fair use"). | |
| May 12, 2022 at 10:49 | comment | added | Trunk | For once, I wish I was a Cambridge employee: then I'd have ready access to this article rather than paying £23 for a download. | |
| May 12, 2022 at 7:58 | comment | added | Padraig Ó Catháin | @TimothyChow I think the second proposal is closer to the truth. In the examples I've given Sylvester and Cayley are aware that they've proved the smallest interesting case of a general phenomenon. They consider it clear that the pattern they observed will generalise, and make this claim. I presume they would have tested further cases before writing. But, in my reading, they know that their proof is not complete. | |
| May 11, 2022 at 23:25 | comment | added | Timothy Chow | Carlo Beenakker, are there examples in this paper of unrigorous English mathematics? Based on your quote, I see at least two possible interpretations. 1. English mathematicians would give what we would consider to be incomplete proofs, but not regard them as being incomplete, and would make statements that we would consider to be imprecise but would regard them as being precise. 2. English mathematicians had the same understanding as we do of what constitutes a precise statement and a complete proof, but did not think it was always necessary to make precise statements and give complete proofs. | |
| May 11, 2022 at 14:25 | comment | added | Trunk | Some points on this: 1) Even in the 1800s, many diverse applications could be found for a single math concept. To me, this would more indicate a primacy of a math concept over any physical phenomena manifesting that same concept than vice-versa. 2) Validation of a theorem via vindication of its predications in areas of application would surely demand a thorough proof, lest exceptions make predication/design (e.g. engineering) based on it open to failure. 3) The pace of math 'discovery' in the physical world is slower than the pace of application discovery after its math concept development. | |
| May 11, 2022 at 11:29 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |