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Subscript: We’re trying out a new shorter post format

We don’t have lots of time to write in-depth posts about maths news any more, what with having jobs and families to attend to, so we’ve set up this new Subscripts format for when we’ve seen a thing and want to share it but don’t have time to do any more than that.

That’s all!

Algebraic Combinatorics ditches Springer

The editorial board of the Journal of Algebraic Combinatorics have announced they’re leaving Springer and setting up a new journal called Algebraic Combinatorics. The new journal will follow the principles of Fair OA – the key points are that the journal will be free to read, fees will be low, and acceptance won’t depend on ability to pay.

Hugh Thomas, one of the editors of Algebraic Combinatorics, said of the move,

“There wasn’t a particular crisis. It has been becoming more and more clear that commercial journal publishers are charging high subscription fees and high Article Processing Charges (APCs), profiting from the volunteer labour of the academic community, and adding little value. It is getting easier and easier to automate the things that they once took care of. The actual printing and distribution of paper copies is also much less important than it has been in the past; this is something which we have decided we can do without.”

Another victory for fair and sensible maths publishing, brought about by a small group of OA advocates set up by Mark Wilson and including Timothy Gowers. There’s much more about what’s happened and why you should support the new journal on Gowers’s weblog.

Algebraic Combinatorics lives at algebraic-combinatorics.org (can you believe that was available?!)

2017 LMS prize winners announced

The London Mathematical Society has announced the winners of its various prizes and medals for this year.

Here’s a summary of the more senior prizes:

  • Alex Wilkie gets the Pólya prize for “his profound contributions to model theory and to its connections with real analytic geometry.”
  • Peter Cameron gets a Senior Whitehead prize for “his exceptional research contributions across combinatorics and group theory.” Peter has written a rare horn-tooting post on his excellent blog about winning the prize.
  • Alison Etheridge gets a Senior Anne Bennett prize “in recognition of her outstanding research on measure-valued stochastic processes and applications to population biology; and for her impressive leadership and service to the profession.”
  • John King gets a Naylor prize for “his profound contributions to the theory of nonlinear PDEs and applied mathematical modelling.”

The Berwick prize goes to Kevin Costello, and Whitehead prizes go to  Julia Gog, András Máthé, Ashley Montanaro, Oscar Randal-Williams, Jack Thorne, and Michael Wemyss.

Read the full announcement at the LMS website.

Laws of mathematics not as immutable as we thought, in Australia

Australian PM Malcolm Turnbull said, as part of a speech proposing a law to force tech companies to give the government access to encrypted messages,

“The laws of mathematics are very commendable, but the only law that applies in Australia is the law of Australia.”

The problem is that the end-to-end encryption schemes used by messaging apps make it practically impossible for the makers of the app to read messages, even if they really want to.

New Scientist writer Jacob Aron has seen the positive side of Turnbull’s comments:

The curious mathmo talks to David Roberts

Way back at the end of last year I put out a call to mathematicians I know: hop on Skype and chat to me for a while about the work you’re doing at the moment. The first person to answer was David Roberts, a pure mathematician from Adelaide. 

We had a fascinating talk about one thread of David’s current work, which involves all sorts of objects I know no more about than their names. I had intended to release this as a podcast, but the quality of my recording was very poor and it turns out I’m terrible at audio editing, so instead here’s a transcription. Assume all mistakes are mine, not David’s.

If you’ve ever wanted to know what it’s like to work in the far reaches of really abstract maths, this is an excellent glimpse of it.

DR: I’m David Roberts, I’m a pure mathematician, currently between jobs. I work – as far as research goes – generally on geometry and category theory, and the interplay between those two. And also a little bit of logic stuff, which I thought I’d talk about.

13532385396179 doesn’t climb to a prime

Someone called James Davis has found a counterexample to John H. Conway’s “Climb to a Prime” conjecture, for which Conway was offering \$1,000 for a solution.

The conjecture goes like this, as stated in Conway’s list of \$1,000 problems:

Let $n$ be a positive integer. Write the prime factorization in the usual way, e.g. $60 = 2^2 \cdot 3 \cdot 5$, in which the primes are written in increasing order, and exponents of $1$ are omitted. Then bring exponents down to the line and omit all multiplication signs, obtaining a number $f(n)$. Now repeat.

So, for example, $f(60) = f(2^2 \cdot 3 \cdot 5) = 2235$. Next, because $2235 = 3 \cdot 5 \cdot 149$, it maps, under $f$, to $35149$, and since $35149$ is prime, we stop there forever.

The conjecture, in which I seem to be the only believer, is that every number eventually climbs to a prime. The number 20 has not been verified to do so. Observe that $20 \to 225 \to 3252 \to 223271 \to \ldots$, eventually getting to more than one hundred digits without reaching a prime!

Well, James, who says he is “not a mathematician by any stretch”, had a hunch that a counterexample would be of the form $n = x \cdot p = f(x) \cdot 10^y+p$, where $p$ is the largest prime factor of $n$, which in turn motivates looking for $x$ of the form $x=m \cdot 10^y + 1$, and $m=1407$, $y=5$, $p=96179$ “fell out immediately”. It’s not at all obvious to me where that hunch came from, or why it worked.

The number James found was $13\,532\,385\,396\,179 = 13 \cdot 53^2 \cdot 3853 \cdot 96179$, which maps onto itself under Conway’s function $f$ – it’s a fixed point of the function. So, $f$ will never map this composite number onto a prime, disproving the conjecture. Finding such a simple counterexample against such stratospherically poor odds is like deciding to look for Lord Lucan and bumping into him on your doorstep as you leave the house.

A lovely bit of speculative maths spelunking!

via Hans Havermann, whom James originally contacted with his discovery.

Right answer for the wrong reason: cellular automaton on the new Cambridge North station

Cambridge North is a brand new train station, and the building’s got a fab bit of cladding with a design ‘derived from John Horton Conway’s “Game of Life” theories which he established while at Gonville and Caius College, Cambridge in 1970.’

One problem: that’s Wolfram’s Rule 135, not the Game of Life. You can tell because of the pixels.

Rule 135 is a 1-dimensional automaton: you start with a row of black or white pixels, and the rule tells you how the colour of each pixel changes based on the colours of the neighbouring pixels. The Cambridge North design shows the evolution of a rule 135 pattern as a distinct row of pixels for each time step. Conway’s Game of Life follows the same idea but in two dimensions – a pixel’s colour changes depending on the nearby pixels  in every compass direction.

Either way, it’s a lovely pattern. I suspect the designers went with Rule 135 instead of the Game of Life so that they’d get a roughly even mix of white and black pixels, which is hard to achieve under Conway’s rules.

Just in case gawping at train stations is your cup of tea, here’s a promotional video with lots of lovely panning shots of the design:

EDIT: James Grime has now also done a video, which can be seen here:

More information

Delayed £50m Cambridge North railway station opens on BBC News.

Cambridge North Station information from Atkins Group, the design consultancy responsible for the station building.

Press release from Greater Anglia trains.

The Game of Life: a beginner’s guide by Alex Bellos in the Guardian.

Brought to our attention by @Quendus on Twitter.