[HN Gopher] New math revives geometry's oldest problems
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New math revives geometry's oldest problems
Author : pykello
Score : 140 points
Date : 2025-09-26 22:57 UTC (1 days ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| OgsyedIE wrote:
| It's been a while since I left math for industry but I once heard
| that the shape and contents of "the space of all problem sets and
| solution sets for enumerative geometry on arbitrary n-manifolds"
| is something that is amenable to investigation through something
| called Gromov-Witten theory. I did a quick number of searches on
| GW theory just now and cannot decipher the results so I still
| don't know if that claim had any merit to it but a sanity check
| suggests there's no obvious computational reason that it couldn't
| be true for n=2 or 3.
| hn-ifs wrote:
| I enjoyed reading that, but understood absolutely none of it.
| dmbche wrote:
| Same - I get the gist, but "how many lines lie on a cubic face"
| doesn't make sense as a question to me, what is a "line" in
| this context? I struggle to understand the issue as my only
| understanding is that the face is divided by line width which
| determines how many lines, but that's nonsensical and non
| interesting.
|
| As an aside (again, as a layperson) I've had this feeling with
| most Quanta articles, it's interesting and I feel like I get
| the gist but that's all. Kinda like it's both too simplified
| and touching on too deep concepts to tie together the article.
|
| Sorry for the rambling.
|
| Edit0: how many _straight_ lines _going through the whole
| length of the face it is on_ on a cubic surface. Honestly, I
| just hadn 't really pictured a cubic surface to start with -
| that was the main part. Had that picture been higher up I think
| I would have liked the article right away! Thank you peeps
| OgsyedIE wrote:
| Google is actually still fairly decent for this kind of
| query. Just type:
|
| 27 lines on a cubic surface
|
| Into the search bar and go to the image results. It will
| 'click' mentally in practically no time at all.
| ecesena wrote:
| There's a picture at the bottom. I think the text there is a
| bit more clear (maybe?): you have a cubic surface and want to
| see if there's any "straight line" that lives/lies on the
| surface. It turns out there's 27 lol.
| gsf_emergency_2 wrote:
| YouTube and wikipedia are better than quantmag for this
|
| (Clebsch or Klein surfaces)
|
| https://en.wikipedia.org/wiki/Cubic_surface#/media/File:Cleb.
| ..
|
| https://youtu.be/lLBOiiFs87Q
|
| https://en.wikipedia.org/wiki/Clebsch_surface
|
| https://nathanfieldsteel.github.io/2019/10/15/27-Lines.html
| jandrewrogers wrote:
| For the articles from Quanta where I have a lot of prior
| knowledge, which is decidedly a small fraction of them, I think
| they mostly do a good job of accurately conveying the gist. It
| gives me more confidence in the articles that are outside my
| wheelhouse.
|
| Quanta is one of the few examples in popular media I can think
| of where the Gell-Mann Amnesia effect does not seem to be
| operative. Or at least, if they are shoveling slop then they
| have a preternatural ability to hide it.
| nenenejej wrote:
| A circle can be in or out, so two states. 2 ^ 3 = 8.
|
| Not a proof but just something visual I noticed.
| xandrius wrote:
| That would imply that given the number of points (in this case
| 3) there would always be an answer.
|
| For, example would it hold if we put the restriction to 4, 5 or
| 10 points?
| ufocia wrote:
| "Slide whichever circle is smaller entirely inside the bigger
| one, and now the answer is zero: You can't draw any lines that
| touch each circle only once."
|
| This sounds false. If the smaller circle is at the edge of the
| larger one, it is still entirely inside the larger one while a
| tangent line could touch both of them at the edge.
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