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.
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.
> 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?
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.
What is your definition of 'these methods' and what is the established literature on them that you'd want to see cited? I'd be surprised if the specific construction and results that they need have been published.
The two authors are no slouches... I certainly wouldn't roll my eyes at them.
“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.
> 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]
It's weird. It definitely reads like the Quanta author either didn't know what a mathematical category is, or didn't think it merited explanation, despite explaining simpler things in excruciating detail in the article.
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.
