Timeline for What is the oldest open math problem outside of number theory?
Current License: CC BY-SA 4.0
14 events
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| Sep 16 at 17:25 | comment | added | paul garrett | Wow! Thanks for the info, Loren S. and NM :) | |
| Sep 16 at 0:33 | comment | added | N M | There is actually a bizarre story surrounding the "Charles Euler" paper. Apparently Euler entered a Paris Academy prize competition in his son's name (Carl/Carolus/Charles). Jacobi speculates that this was because he had been teased for winning these competitions so many times. For proof of the true author Jacobi cites the inscription: "The father decided that all the stars in heaven should move." | |
| Sep 15 at 23:37 | comment | added | LSpice | Motivated by @paulgarrett's question, I tried to check the original. As far as I could tell, "the quoted Suzuki" was not named in the post, but I assume it's the same as in the comment, and so edited it in. (It is indeed "Charles Euler" in the original. 🤷) Also, for some strange reason, the quotation marks in the quote from Laplace seemed to be backwards (opening quotation marks). I turned them around, which is hopefully what was intended. | |
| Sep 15 at 23:34 | history | edited | LSpice | CC BY-SA 4.0 |
Title of "quoted Suzuki"; backwards apostrophes
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| Sep 15 at 23:05 | comment | added | paul garrett | A quibble, and a question: was the quote really "Charles Euler", or was it possibly "Chasles, Euler..." ? | |
| Sep 15 at 0:24 | comment | added | Francois Ziegler | However much you narrow or expand the problem, I think it will include boundedness of the elements (semimajor axes etc.), which Laplace (1787, 1795) thought he had proved; whereby (per Suzuki, p. 251): “so far as Laplace is concerned, the stability of this solar system has been assured, and the general problem of a system of planets operating under the inverse square law is of no concern”. (In fact, Laplace only solved what we would call that problem’s linearization.) | |
| Sep 14 at 17:57 | history | edited | Francois Ziegler | CC BY-SA 4.0 |
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| Sep 14 at 15:37 | comment | added | Timothy Chow | I see you have edited the question to clarify, but the number of planets is not the only critical parameter; the mass-ratio is also important. See for example this abstract. | |
| Sep 14 at 13:30 | comment | added | Timothy Chow | Right, but precisely how many masses are we including in our mathematical idealization of the solar system? Just the eight planets? Or do we include dwarf planets? How close do the masses, positions, and velocities in our mathematical idealization have to be to the masses of the actual physical objects they're modeling? Arnold's result concerns "solar systems" with parameter values that are many orders of magnitude different from those in our actual solar system. At what point are we asking questions about the space of all possible solar systems rather than "the" solar system? | |
| Sep 14 at 13:22 | history | edited | Francois Ziegler | CC BY-SA 4.0 |
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| Sep 14 at 12:47 | comment | added | Francois Ziegler | Suzuki (1996, §1.5 “The Stability Question Raised”) discusses the two versions: “non-gravitational causes”, versus analysis of the purely gravitational problem (p. 24). The latter is the mathematical problem I have in mind, discussed by Laskar. | |
| Sep 14 at 12:41 | comment | added | Timothy Chow | That question, or some version of it, is still open, but it isn't the question Newton asked. This article by Scott Tremaine gives some more information about what the early discussions of the problem looked like. | |
| Sep 14 at 12:36 | comment | added | Timothy Chow | I was about to suggest this one, but it's a little murky. First, is it a physics question about the actual solar system, or a math question about the equations of Newtonian mechanics? If the latter, what is the question exactly? E.g., Arnold's work on the KAM theorem tells us that there are some solar-system-like systems that are stable. So maybe the question is determining which systems are stable and which aren't. In addition to the article you linked to, this Quanta article is also interesting. | |
| Sep 14 at 12:27 | history | answered | Francois Ziegler | CC BY-SA 4.0 |