[HN Gopher] In a moment, mathematicians merge probability and nu...
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In a moment, mathematicians merge probability and number theory
Author : rbanffy
Score : 46 points
Date : 2023-01-15 18:54 UTC (4 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| eastWestMath wrote:
| Coming from category theory, and having followed the work
| studying probability theory categorically (e.g. Fritz, Perrone,
| Lucyshyn-Wright's stuff, Leinster's notion of the magnitude of a
| category), is this actually interesting? The actual category
| theory seems pretty rudimentary, and I'm not sure if they've
| invented anything new on that side (they don't reference any of
| the authors I've mentioned, so it doesn't seem like there was
| much scholarship on that end).
|
| It feels like Quanta just takes press releases from a few big
| departments and asks a writer to get a few quotes to flesh out an
| article.
| hackandthink wrote:
| The title of the post promises to much.
|
| "In a Moment, Mathematicians Merge Probability and Number
| Theory" - I really expected some deep connections between
| Probability and Number Theory.
|
| I do not like the quanta magazine title as well. "Probability
| and Number Theory Collide -- in a Moment"
|
| Guess it should be funny, I would call it "bemuht" (german).
| joe_the_user wrote:
| As far as I can tell, the article says nothing about category
| theory and doesn't claim to. It's a popularization of recent
| probabilistic investigations in number theory, popularization
| of math is what Quanta does.
|
| When it says "Mathematicians are taking ideas developed to
| study random numbers and applying them to a broad range of
| categories" I'm pretty sure it means category in the non-
| technical sense, category as in classifying into categories.
| The term doesn't appear again in the article.
| eastWestMath wrote:
| Oh, I'm talking about the paper they're hyping up. I'm just
| not terribly impressed, and I think if was written by people
| at UCSD instead of Harvard nobody would have even noticed it.
| rst123 wrote:
| I don't know if this work is particularly ground breaking, but
| this looks to be more concerned with applications towards
| number theory (specifically cohen-lenstra heuristics) rather
| than adding to the category theory literature.
| eastWestMath wrote:
| My issue is that I can't see a cursory literature review into
| the established category literature on these methods - how do
| they even know they have something new/novel if they haven't
| checked?
|
| This is a bit like the recent news about the "ML discovered a
| new fast matrix multiplication" press push out of Google,
| where researchers in the field just sort of rolled their
| eyes.
| ur-whale wrote:
| So, category theory is the new gospel, I guess, that from
| which all mathematics is derived?
| eastWestMath wrote:
| "I've discovered a new thing about Y in X's! Oh, no I
| haven't actually looked at the X literature about Y."
| This is hardly specific to category theory.
| karmakaze wrote:
| > In work published in the Annals of Mathematics in 2016,
| Ellenberg, along with Akshay Venkatesh and Craig
| Westerland, used moments to study the statistics of class
| groups in a slightly different setting than Cohen and
| Lenstra had considered. This idea was reused several times.
| But each time researchers used the moments, they would lean
| on the quirks of their particular problem to prove that the
| infinite set of equations had a solution. That meant their
| techniques were not transferable. The next mathematician
| who needed to use moments would have to solve the moment
| problem all over again.
|
| Are you suggesting that this need to solve the moment
| problem all over again could have been avoided by searching
| Category Theory developments?
| impendia wrote:
| As I said in another comment, this research isn't about
| category theory. [Edit: Well, not about the foundations
| anyway.]
|
| The use of moments as a method for understanding
| probability distributions isn't particularly new. What is
| new, is the introduction and adaptation of this framework
| for trying to understand the Cohen-Lenstra heuristics -- a
| smaller-scope problem in number theory that has seen a lot
| of attention recently.
|
| The people quoted are among the world's leading experts in
| this topic, and I would say that Melanie Wood is _the_
| foremost expert. This is definitely novel.
| impendia wrote:
| > this looks to be more concerned with applications towards
| number theory (specifically cohen-lenstra heuristics) rather
| than adding to the category theory literature.
|
| (I'm a specialist in this area of number theory)
|
| This is correct. The word "category" is being used in its
| colloquial English sense; this is not work on category
| theory.
|
| [Edit: I'm mistaken in the above point; see comment below]
| eastWestMath wrote:
| The paper is absolutely a construction on categories.
| impendia wrote:
| Okay, looking at the paper more carefully (I'd just
| looked at the article before, and was arguing from my
| knowledge of the field more generally), I take it back --
| there is definitely some formal category theory here.
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