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Re:Elegant six-page proof reveals the emergence of random st... by gardnr on Monday April 25, 2022 @11:44PM (#31163713)
> 2 (of a scientific theory or solution to a problem) pleasingly ingenious and simple: the grand unified theory is compact and elegant in mathematical terms.

A 6 page proof described as "elegant" must be incredibly dense.

Re:Elegant six-page proof reveals the emergence of random st... by mjreacher on Tuesday April 26, 2022 @09:47AM (#31167409)
As the other poster noted, for a big math result this is comparatively rather short. For a concrete example[0], a recent important result related to the Arnold conjecture is 268 pages long, with another 100 pages in appendices.

[0]: https://arxiv.org/abs/2103.01507

Re:Elegant six-page proof reveals the emergence of random st... by alanbernstein on Tuesday April 26, 2022 @12:12AM (#31163867)
The proof section is 3.5 pages. That's really pretty short, as far as modern math results go. I get your point, though.
Re:Elegant six-page proof reveals the emergence of random st... by oaiey on Tuesday April 26, 2022 @01:06AM (#31164145)
The abstract is a one liner and the intro has in the first line a formula or two. No idea if this is the tone of math papers but I call this dense :)
Re:Elegant six-page proof reveals the emergence of random st... by jacoblambda on Tuesday April 26, 2022 @01:20AM (#31164215)
Compared to some of the papers I've read recently, this is extremely elegant and succinct and doesn't just jam all the math in line by line.

Comparatively one of the papers I looked at the other day was something like 100 pages long with a ~30 page proof section with very little free whitespace packed full of complex mathematics.

Re:Elegant six-page proof reveals the emergence of random st... by iciac on Tuesday April 26, 2022 @10:07AM (#31167651)
You might be interested in this 1 page paper by John Nash, which proves the existence of equilibria for finite N-player games (an extremely powerful result). In essence it uses a set theory result (Kakutani's fixed point theorem), and simply notes that his description of a N-player game meets the required conditions for that result to hold. http://www.sscnet.ucla.edu/polisci/faculty/chwe/austen/nash1...