[HN Gopher] Mathematicians Prove 30-Year-Old Andre-Oort Conjecture
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Mathematicians Prove 30-Year-Old Andre-Oort Conjecture
Author : theafh
Score : 79 points
Date : 2022-02-03 14:59 UTC (8 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| marto1 wrote:
| > To prove the Andre-Oort conjecture, Pila needed to show that a
| non-Shimura variety living inside a Shimura variety doesn't have
| a lot of special points.
|
| This looks just so advanced to me. Is that how people sound when
| they talk about programming ?
| xigoi wrote:
| Yes.
|
| >Build, test, and deploy with CI/CD that works with any
| language, platform, and cloud. Connect to GitHub or any other
| Git provider and deploy continuously.
|
| (from https://azure.microsoft.com/en-us/services/devops/)
|
| >Kubernetes, also known as K8s, is an open-source system for
| automating deployment, scaling, and management of containerized
| applications.
|
| (from https://kubernetes.io/)
| bluquark wrote:
| The paragraphs you quoted are at least partially self-
| explanatory, mostly using common English words like
| "platform" in a metaphorical sense. Whereas the paragraph the
| grandparent quoted has several concepts that are opaquely
| named after mathematicians, providing not even a hint of what
| they might mean.
| xigoi wrote:
| "Git" is literally a random word. "Kubernetes" also doesn't
| tell you anything.
| ljhsiung wrote:
| Just a lot of standardization and years of intuiting what these
| mean.
|
| In this case, you definitely need some intuition of elliptic
| curves and "special points" that is hard to explain, but Quanta
| does it decently.
|
| Here's an example from the ARM Architecture Reference Manual
| (B.2.3.6) that often throws people for a loop--
|
| > For a read or a write RW1 from an Observer that is Ordered-
| before a read or a write RW2 from a different Observer, the
| External visibility requirement requires that RW2 is not
| Observed-by RW1. This means that an Architecturally well-formed
| execution must not exhibit a cycle in the Ordered-before
| relation.
| _0ffh wrote:
| I'm not sure I understand the ARM manual example. It seems
| obvious that an operation should not be able to see what is
| supposed to happen "after" it executes, and that a time-like
| construct should not contain loops (outside of SF
| literature). I'm sure I'm missing a lot of detail here, but I
| really can't say that I feel confused by it.
|
| Ed. Oh wait, so maybe I'm just sufficiently similar to the
| intended audience. But wouldn't everyone who reads such a
| manual be?
| bluquark wrote:
| No, only functional programmers sound like this!
| gavagai691 wrote:
| Probably nothing is quite so abstruse as abstract mathematics,
| and few subjects in math are as abstruse as arithmetic geometry
| (the subject of this paper).
| seemaze wrote:
| I am consistently impressed by the publication quality at Quanta
| Magazine. Their articles are a joy to read for an audience of any
| background. I also enjoy Aeon[0] and Psyche[1]. Can anyone
| recommend publishers of similar quality in other domains?
|
| [0] https://aeon.co
|
| [1] https://psyche.co/
| gavagai691 wrote:
| Unfortunately, I don't think anything matches Quanta for what
| they do (covering cutting-edge advances in science in an
| accurate and accessible manner).
|
| One of the things that really helps Quanta is that if there is
| an article about math, typically it is written by a
| mathematician (and likewise for other areas). For "softer"
| subjects, e.g. politics, history or law, the Atlantic is often
| similar in this regard, and I enjoy their articles.
| gavagai691 wrote:
| Another huge advance in number theory--alongside the subconvexity
| result posted last month--in a vastly different area of the
| subject. 2021 was a great year for number theory. (This of course
| assumes both results are correct!)
| RcouF1uZ4gsC wrote:
| > 2021 was a great year for number theory.
|
| Maybe it was because for the last two years everyone was stuck
| at home because of Covid.
|
| There are only so many Netflix movies/shows you can watch
| before you start playing around with number theory out of sheer
| boredom.
| gavagai691 wrote:
| The people who write these kinds of papers, believe it or
| not, prefer to spend most of their time playing with numbers
| compared to watching Netflix. (This is not to say that they
| don't enjoy spending any time on the latter.)
| ximeng wrote:
| https://news.ycombinator.com/item?id=29929935 Think this is the
| subconvexity one?
|
| https://news.ycombinator.com/item?id=29790830 This one is also
| related to primes.
| alex_suzuki wrote:
| I wonder how the authors perceive the world around them. Because
| after opening and skimming the PDF I certainly felt transported
| to a strange, alien place... with no resemblance of my own
| surroundings.
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