From Mark C. Wilson of the University of Auckland, a little public service announcement for anyone who’s ever been involved with a mathematical journal.
There is much dissatisfaction with the current state of research
publication, but little information on community attitudes and priorities.
I have started a survey which I hope you will fill in (I estimate 10-15
minutes, and it is completely anonymous). The results will be made publicly
available later this year. I hope that it will help to focus our efforts as
a community by allowing us to work toward broadly agreed goals. I want to
get as representative and as large a sample of the world mathematical
community as possible. Please forward to your local colleagues.
Please answer this survey if and only if you have been involved with a
mathematical journal as editor, reviewer/referee, author or reader in the
last 3 years. By “mathematical” we also mean to include theoretical
computer science and mathematical statistics journals, and disciplinary
journals used by applied mathematicians. Essentially, any journal covered
by Mathematical Reviews qualifies.
Answer the survey
Here’s something fun you might want to spend some money on: a poster of the Mandelbrot set, in the style of an old-fashioned navigation chart.
The Kickstarter has already racked up many multiples of the original funding goal with three weeks still to go, so it’s at the “effectively a pre-order” stage. The posters start at \$26.
Kickstarter: Mandelmap poster by Bill Tavis.
Conjecture Every planar graph without 4-cycles and 5-cycles is 3-colourable.
In a paper just uploaded to the arXiv, Vincent Cohen-Addad, Michael Hebdige, Daniel Kral, Zhentao Li and Esteban Salgado show the construction of a graph with no cycles of length 4 or 5 which isn’t 3-colourable: it isn’t possible to assign colours to its vertices so that no pair of adjacent vertices have the same colour, using only three different colours. This is a counterexample to a conjecture of Richard Steinberg from 1976.
The problem was listed in the Open Problem Garden as of “outstanding” importance.
Read the paper: Steinberg’s conjecture is false
via Parcly Taxel on Twitter
Warning: you could make a very strong argument I’ve thought far too much about something inconsequential. If that makes your stomach turn, look away now.
This morning in the shower, I had an idle thought about my towel. It was, as always, folded neatly on the toilet seat. A problem that’s been bugging me for a few days is how to pick up the towel by a section of the long edge, so when it unfolds it’s the right way round.
The problem is that the short edge and the long edge look the same, and once I’ve folded the towel over a couple of times and had a shower only a madman* would remember which is which. But my towel isn’t square, so it occurred to me that either the longer or the shorter edge, after folding, could be the edge I want. Since I never make a diagonal fold, the long edge is only ever folded on top of the long edge, and likewise for the short edge. I fold the towel until it fits comfortably on top of the toilet seat, and by the time I’ve finished my shower I can’t be relied upon to remember which sequence of folds I did.
Which got me thinking about the ratio between the width and height of my towel: if I know this ratio then, by looking at the towel and counting the number of folds, I can work out which folds I’ve done, and hence which of the sides will unfold to be the long edge.
Here’s another one of my favourite maths objects: the Correntator. It’s a simple mechanical tool to add up amounts of money. I bought it for about a tenner (new money) at a market.
This video is extremely shonky. Blame my phone, which can’t bring itself to record for more than 250 seconds at a time.
More information about the Correntator.
Previously unseen footage has been unearthed by The Aperiodical’s crack team of investigative journalists of Kevin Bacon and Paul Erdős writing a paper together, and a still from this is shown above. This has massive consequences for the important topics of Erdős numbers, Bacon numbers and Erdős-Bacon numbers.
There’s been a lot of maths news this month, but we’ve all been too busy to keep up with it. So, in case you missed anything, here’s a summary of the biggest stories this month. We’ve got two new facts about primes, the best way of packing spheres in lots of dimensions, and the ongoing debate about the place of maths in society, as well as the place of society in maths.
A surprisingly simple pattern in the primes
Kannan Soundararajan and Robert Lemke Oliver have noticed that the last digits of adjacent prime numbers aren’t uniformly distributed – if one prime ends in a 1, for example, the next prime number is less likely to end in a 1 than another odd digit. Top maths journos Evelyn Lamb and Erica Klarreich have both written very accessible pieces about this, in the Nature blog and Quanta magazine, respectively.
Oliver and Soundararajan’s paper on the discovery is titled “Unexpected biases in the distribution of consecutive primes”.