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
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”.
Robert Hannigan, the Director of British intelligence agency GCHQ, gave a speech at MIT recently on the currently contentious issue of backdoors into encryption.
To accompany his speech, and maybe to reaffirm GCHQ’s credentials on the subject, he published two papers written by James Ellis in 1970 about what would become public key encryption: “The Possibility of Secure Non-Secret Digital Encryption” and “The Possibility of Secure Non-Secret Analogue Encryption”.
The story famously goes that two decades after Rivest, Shamir and Adleman announced the RSA algorithm for public key cryptography, GCHQ admitted that their employee Clifford Cocks had come up with essentially the same thing four years before, inspired by James Ellis’s papers on the possibility of cryptography without a secret key.
Rober Hannigan’s speech, Front doors and strong locks: encryption, privacy and intelligence gathering in the digital era.
Read the papers: “The Possibility of Secure Non-Secret Digital Encryption” and “The Possibility of Secure Non-Secret Analogue Encryption” by James Ellis.
It’s not only actors who get shiny awards around this time of year – mathematicians are in on it too!
There have been a few medals, gongs and otherwise prizes awarded to some terrifically clever people in the past month or so, so I thought I’d do a round-up of the ones I’m aware of.
Ohio State University mathematician Niles Johnson got in touch on Friday to tell us that our π Approximation Challenge last year had inspired him to hatch an audacious plan to measure a really big π.
The word ‘geometry’ is derived from the Greek for ‘measurement of land’, and Dr. Johnson took that quite literally: he wanted to measure the Great Circle Earthworks in Heath, Ohio; a part of the Newark Earthworks (not their original name) built over 2,000 years ago.