Timeline for Unrigorous British mathematics prior to G.H. Hardy
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2022 at 14:10 | comment | added | Tom Copeland | Despite the exhortations against divergent series / formal power series by Abel, since at least Laplace, such series have found important applications in physics. See, e.g., "Divergent series: past, present, future . . . " by Christiane Rousseau (arxiv.org/pdf/1312.5712.pdf). | |
| Sep 27, 2022 at 20:42 | comment | added | Tom Copeland | (cont.) One of Ramanujan's favorite heuristics, called Ramanujan's Master Formula/Theorem, and Hardy's explication of this in his book Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work exemplifies this interplay. | |
| Sep 27, 2022 at 20:36 | comment | added | Tom Copeland | @TimothyChow, when I was investigating divergent series and harmonic analysis years ago, I came across an early paper by H in which he explicitly presents the interchange of two operations, such as integration and summation, as a heuristic for assigning meaning to divergent series. I believe this was well before he met R or wrote his treatise on divergent series, so he was predisposed to assign meaning to the calcs in R's letter, rejected by others. This interplay between heuristics and rigor marks H's style, who must have studied Cauchy, and is enhanced in the relationship between H and R. | |
| May 12, 2022 at 22:11 | comment | added | Leo Moos | Minor quibble: Lagrange was not French, but Italian. (His nationality put him in a precarious position during the French Revolution, when all foreign nationals were expelled from the country. However, the expulsion decree granted him a personal exemption. He later acquired the French citizenship in 1802.) | |
| May 12, 2022 at 22:01 | comment | added | Timothy Chow | @HAHelfgott He wasn't the only critic of infinitesimals. Perhaps the most famous critic, Berkeley, was Irish. See Florian Cajori's article Discussion of Fluxions: From Berkeley to Woodhouse for more historical information. | |
| May 12, 2022 at 19:59 | comment | added | H A Helfgott | Well, but Babbage was swimming against the current, wasn't he? | |
| May 12, 2022 at 17:22 | comment | added | Dave L Renfro | (+1) for the distinction between abstraction and rigor (in the sense of precision and logical correctness) as probably being especially relevant in the difference between mathematics in Britain and "the continent" during the 1800s. British mathematics during this time also seems to me a lot more focused on issues arising out of formal manipulations and topics more directly relevant for mathematical physics (of that time). | |
| May 12, 2022 at 15:42 | review | Suggested edits | |||
| May 12, 2022 at 18:33 | |||||
| May 12, 2022 at 15:14 | comment | added | Trunk | The association with Ramanujan is incidental - it only relates to how I made my own casual discovery that mathematics in UK at the earlier period of GH Hardy's career ~ 1900 was not as strict on proofs that were thorough and general. Academic mathematicians like respondents here of course already knew this. My surprise at this was largely based on my having never reflected on how the Age of Reason was really a long transition within mathematics as well as within sciences in general. Hardy's predecessors would have demanded less proof of R's theorems - had R been British... | |
| May 12, 2022 at 13:28 | comment | added | Timothy Chow | It occurs to me that even today, people sometimes talk about "formal" manipulations (e.g., of infinite series or products) that are heuristic and not "rigorous." Given that the OP mentioned Ramanujan, perhaps this is the real question: Did Hardy complain about the lack of rigor in Ramanujan's arguments in a way that Hardy's predecessors might not have? And if so, was that because Hardy was influenced by Continental mathematicians? | |
| May 12, 2022 at 12:57 | history | answered | Timothy Chow | CC BY-SA 4.0 |