The earliest PROOF of the polygon triangulation theorem that I'm aware of is an unpublished 1899 manuscript of Dehn! See https://www.maths.ed.ac.uk/~v1ranick/papers/guggenheim.pdf

...Following a rabbit hole inspired by the Numberphile's recent video on Dehn invariants: https://www.youtube.com/watch?v=eYfpSAxGakI

A triangulated polygon, from Les Amusemens Mathématiques by André-Joseph Mancoucke, 1749. This is the earliest appearance I know of the theorem (stated without proof) that every simple polygon can be triangulated by diagonals. In particular, Mancoucke predates both Meister's (1770) and Poinsot's (1809) seminal treatises on polygons.

Depressingly hilarious.

No, you're not allowed to say "Well, at least we don't have these problems in MY department!"

https://thelastpsychiatrist.com/2011/08/grade_inflation.html

Lovely series of videos:

https://www.youtube.com/channel/UCotwjyJnb-4KW7bmsOoLfkg

Impostor Syndrome Exhibit 10 (and technically 11):

Buy my free book!

https://3dpancakes.typepad.com/ernie/2019/06/buy-my-free-book.html

This is not entirely my idea, the original paper includes a subdivision of an annular region. The provided code is all Mathematica though, which I don't have a copy of, so I coded up a quick&dirty version in OpenFl and threw it on Neocities

it is very dirty: double click to split a cell, scroll your mouse to cycle through cells

Survey on fusible numbers: https://arxiv.org/abs/1202.5614

Fusible numbers are what you get from 0 by operations \(f(x,y)=(x+y+1)/2\) restricted to \(|x-y|<1\). They model a puzzle of measuring time intervals using 1-minute fuses whose ends you can light when another fuse burns out, and are well-ordered with unknown order type. @jeffgerickson calls his (wrong) conjecture "one of my bugs that really should be better known" and points out the lack of progress since 2012: https://mathstodon.xyz/@jeffgerickson/101043945178816599

http://euro-math-soc.eu/news/18/11/16/ems-protest-against-detention-bet%C3%BCl-tanbay

Turkey has arrested Betül Tanbay (the former president of the Turkish Mathematical Society), accusing her of implausible crimes, as they have already done with so many others, especially other academics. The EMS asks the "research community to raise its voice against this shameful mistreatment of our colleague, so frighteningly reminiscent of our continent's darkest times". So count me as one of the voice-raisers.

Two new arXiv preprints:

https://arxiv.org/abs/1811.03432

https://arxiv.org/abs/1811.03427

The first shows that if a graph \(G\) has a non-crossing straight-line drawing (a.k.a. Fáry drawing) in which some set \(S\) of vertices is drawn on a single line then, for any point set \(X\) of size \(|S|\), \(G\) has a Fáry drawing in which the vertices in \(S\) are drawn on the points in \(X\).

The second shows that, in bounded degree planar graphs, one can always find such a set \(S\) of size \(\Omega(n^{0.8})\).

Survey on fusible numbers

Article by Xu, Junyan

In collection: Easily explained

We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we succeed in establishing some basic properties...

URL: http://arxiv.org/abs/1202.5614

PDF: http://arxiv.org/pdf/1202.5614v1

Entry: http://read.somethingorotherwhatever.com/entry/Xu2012

CS professor at Illinois

Joined May 2017