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Comment by gardnr | Hacker News Reader

> 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.

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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

The proof section is 3.5 pages. That's really pretty short, as far as modern math results go. I get your point, though.

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 :)

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.

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...

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