I have checked ArXiv, and it has about half-a-dozen papers with Dr. Piccirillo as author or co-author. None of them seem much easier than the others, nor am I clear on why Brad expects them to be. One only publishes results that are new and interesting, and one's early work is likely to retrace the steps of one's forebears. It's clear that when she started publishing mathematics, she was already swimming in the deep end. There is certainly some intrinsic drama in the discovery that the Conway knot is not slice, since it is the last of the knots with less than 13 crossings to be so classified, and was a loose end left by a lately-departed master. I can see why they chose to write it up: the field can at least be sketched comprehensibly -- at least, the Quanta article didn't completely lose this amateur -- and it boasts some fairly pretty pictures of complicated knots. If I really wanted to understand the described work, I think I would start with an old reference of Piccirillo's, the encouragingly-titled "A quick trip through knot theory", by Ralph H. Fox, in "Topology of 3-manifolds and related topics", 1962. But I'm not sure I would succeed: there seems to be algebraic topology involved, which has been my bête noire. On Sun, May 24, 2020 at 12:12 AM Brad Klee <bradklee@gmail.com> wrote:
Sorry, Dan, I am dense. Here’s another way to phrase my complaint:
Since Piccirillo has been rated a creative mathematician, it’s probably true that she has lots of interesting results that are part of her incremental progress toward ground breaking research.
Some of these results would probably be easier for the public to read and actually understand, even if not so original.
So why do we only hear about the end results, which are the most difficult to understand? What good does that do for readers of journals like Quanta?
—Brad
On May 23, 2020, at 9:59 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I thought what I wrote could hardly be clearer.
I'm agreeing that trying to read a math research paper is difficult or impossible without the appropriate background.
I'm disagreeing that anyone is intentionally encouraged to do that; rather the inscrutability of math research is built into the definition of research mathematics, which by nature abstruse.
—Dan
----- I’m confused, because you seem to be giving supporting evidence. Is your opinion that people should be left behind? Or that “research mathematicians” have no other choice? Or? —Brad
On May 23, 2020, at 9:02 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I strongly disagree with this statement to the extent it refers to pure math, and I think I've been around research mathematics long enough to have some idea what I'm talking about.
As we all know, math is hard for many people and, to make matters worse, it's not always taught well, particularly in grade school through high school. And it's a huge subject so that many major areas are not even well understood by established researchers in other parts of math. And finally, the expected audience of math research papers such as a Ph.D. dissertation is other researchers. It's hard enough doing the research in the first place no less trying to address a wide audience who will probably never be interested in one's research.
I don't know about other subjects, but I don't think this is true in pure math. Or applied math, for that matter.
—Dan
----- This is pretty typical of the academic system, which actively encourages researchers to leave most people behind.
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