“I’m proud that I’ve lived to see… so many of the things that I’ve worked on being so widely adopted that no one even thinks about where they came from.” Solomon Golomb (1932-2016)
Solomon Golomb, who died on Sunday May 1st, was a man who revelled in the key objects in a recreational mathematician’s toolbox: number sequences, shapes and words (in many languages). He also carved out a distinguished career by, broadly speaking, transferring his detailed knowledge of the mathematics behind integer sequences to engineering problems in the nascent field of digital communications, and his discoveries are very much still in use today.
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
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.