I've finally caught up on my backlog of entries for @esoterica. Phew!

There are not Exactly Five Objects
Article by Andreas Blass
In collection: Attention-grabbing titles
The purpose of this note is to present a solution to a problem posed informally by A. Wilkie at the 1977 ASL meeting in Wrocław: Formulate "the cardinality of the universe is not exactly five" as a Horn sentence. Although this solution is not new -- I found it and M. Morley found another solution during the same meeting -- continuing...
URL: jstor.org/stable/2274177?seq=1

New entry!
Article by Joshua Carlson and Alex Christensen and Pamela E. Harris and Zakiya Jones and Andrés Ramos Rodríguez
In collections: Attention-grabbing titles, Combinatorics, Easily explained, Puzzles, The act of doing maths
Warning. The reading of this paper will send you down many winding roads toward new and exciting research topics enumerating...
URL: arxiv.org/abs/2001.04817v3
PDF: arxiv.org/pdf/2001.04817v3

New entry!
Plane-filling curves on all uniform grids
Article by Jörg Arndt
In collections: Fun maths facts, Geometry, Things to make and do
We describe a search for plane-filling curves traversing all edges of a grid once. The curves are given by Lindenmayer systems with only one non-constant letter. All such curves for small orders on three grids have been found. For all uniform grids we show how...
URL: arxiv.org/abs/1607.02433v2
PDF: arxiv.org/pdf/1607.02433v2

New entry!
Paperfolding morphisms, planefilling curves, and fractal tiles
Article by Michel Dekking
In collections: Geometry, Things to make and do
An interesting class of automatic sequences emerges from iterated paperfolding. The sequences generate curves in the plane with an almost periodic structure. We generalize the results obtained by Davis and Knuth on the self-avoiding and planefilling...
URL: arxiv.org/abs/1011.5788v2
PDF: arxiv.org/pdf/1011.5788v2

New entry!
A Midsummer Knot's Dream
Article by Allison Henrich and Noël MacNaughton and Sneha Narayan and Oliver Pechenik and Robert Silversmith and Jennifer Townsend
In collections: Attention-grabbing titles, Easily explained, Games to play with friends, Protocols and strategies
In this paper, we introduce playing games on shadows of knots. We demonstrate two novel games, namely, To Knot or Not to...
URL: arxiv.org/abs/1003.4494v1
PDF: arxiv.org/pdf/1003.4494v1

Hmm. Newcastle University doesn't subscribe to the Journal of Symbolic Logic, so I'll never know why there are not exactly five objects. 🤷
cambridge.org/core/journals/jo

New entry!
Mangoes and Blueberries
Article by Bruce Reed
In collections: Attention-grabbing titles, Food
We prove the following conjecture of Erdős and Hajnal: For every integer $$k$$ there is an $$f(k)$$ such that if for a graph $$G$$, every subgraph $$H$$ of $$G$$ has a stable set containing vertices, then $$G$$ contains a set $$X$$ of at most $$f(k)$$ vertices such that $$G−X$$ is bipartite. This...

New entry!
You Could Have Invented Spectral Sequences
Article by Timothy Y. Chow
In collection: Attention-grabbing titles
The subject of spectral sequences has a reputation for being difficult for the beginner. Even G. W. Whitehead (quoted in John McCleary) once remarked, “The machinery of spectral sequences, stemming from the algebraic work of Lyndon and Koszul, seemed complicated and obscure to many topologists.”
URL: ams.org/notices/200601/fea-cho

New entry!
A minus sign that used to annoy me but now I know why it is there
Article by Peter Tingley
In collection: Attention-grabbing titles
We consider two well known constructions of link invariants. One uses skein theory: you resolve each crossing of the link as a linear combination of things that don't cross, until you eventually get a linear combination of links with no crossings, which you turn...
URL: arxiv.org/abs/1002.0555v2
PDF: arxiv.org/pdf/1002.0555v2

New entry!
The No-Flippancy Game
Article by Isha Agarwal and Matvey Borodin and Aidan Duncan and Kaylee Ji and Tanya Khovanova and Shane Lee and Boyan Litchev and Anshul Rastogi and Garima Rastogi and Andrew Zhao
In collections: Easily explained, Games to play with friends
We analyze a coin-based game with two players where, before starting the game, each player selects a string of length $$n$$ comprised...
URL: arxiv.org/abs/2006.09588v1
PDF: arxiv.org/pdf/2006.09588v1

New entry!
An Interesting Serendipitous Real Number
Article by John Ewing and Ciprian Foias
In collection: Fun maths facts
This is the story of a remarkable real number, the discovery of which was due to a misprint. Namely, in the mid-seventies, while Ciprian was at the University of Bucharest, one of his former students approached him with the following question: If $$x_1 \gt 0$$ and \(x_{n+1} = \left(1...

figuring out the third wiener took an additional 6 years

Is this a nephroid?

The baby's stomach seems to be able to measure three hours to the second.
Is it too late to apply for the longitude prize?

Our second L-P is finally out. Early reviews describe him as "sleepy" and "cuddly".

I can't imagine what prompted this integer sequence: "Least multiple of n in which the n-th digit from left is 3."
oeis.org/A113558

Me on The Aperiodical: the enormous difficulty of telling the truth about escalators with statistics aperiodical.com/2020/09/the-en

Interactive 3d knot table: prideout.net/knotgl/

One of many interesting visualizations on "the little grasshopper", prideout.net/, by Philip Rideout (author of the svg3d Python library that I linked earlier)