Timeline for Meaning of Kronecker's comment to Lindemann
Current License: CC BY-SA 4.0
8 events
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| Mar 25, 2023 at 15:53 | history | edited | Franz Lemmermeyer | CC BY-SA 4.0 |
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| Aug 6, 2010 at 4:54 | comment | added | T.. | Gerry, Kronecker's quotation that you cited is in effect saying that (1) "general" irrational numbers don't exist [i.e., are not meaningful mathematically], but (2) specific constructs like $\pi$ and $exp(\sqrt{163}$ are not problematic, insofar as they are a shorthand for explicit controlled sequences of finite calculations, and (3) it is harmless but optional to construe those "specific" irrationals as numbers that genuinely exist. | |
| Aug 5, 2010 at 5:08 | comment | added | Gerry Myerson | (continued) irrational numbers do not exist?” Edwards continues, We can only guess what Kronecker said to Lindemann that Lindemann remembered in this way, but I am confident that he would not have said that irrational numbers did not exist. | |
| Aug 5, 2010 at 5:06 | comment | added | Gerry Myerson | Edwards comes back to the Lindemann story in math.nyu.edu/faculty/edwardsd/athens.pdf which may be the same as his essay of the same title published in Math. Intell. in 2009. He writes, In 1904, after Kronecker had been dead for more than a dozen years, Ferdinand Lindemann published a reminiscence about Kronecker that has become a part of the Kronecker legend and that is surely wrong. According to Lindemann, Kronecker asked him, apparently in a jocular way, “What is the use of your beautiful researches about the number pi? Why think about such problems when (to be continued...) | |
| Aug 4, 2010 at 22:36 | comment | added | T.. | +$n$; thanks for the debunking. However, there remains the same question for Kronecker's non-apocryphal comment quoted by Gerry, in which he expresses reservations about "irrationals" and "the concept of infinite series". | |
| Aug 4, 2010 at 6:11 | comment | added | Franz Lemmermeyer | Just "God made the integers" - the Jahresberichte are online; see mathematik.uni-bielefeld.de/~rehmann/DML/dml_links.html | |
| Aug 4, 2010 at 5:47 | comment | added | Gerry Myerson | Wow. I always thought Dauben was a careful writer. What about the other Weber reference that I gave in my comment on the question, the one in the Jahresbericht? | |
| Aug 4, 2010 at 5:36 | history | answered | Franz Lemmermeyer | CC BY-SA 2.5 |