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”.
A more complicated pattern in the primes
Terry Tao continues his quest to find all theorems which sound a bit like the twin prime conjecture, with a paper co-authored with Tamar Ziegler which shows that for certain sets of polynomials \(P_i\), there are infinitely many pairs of natural numbers \(n,r\) such that all the \(n+P_i(r)\) are prime.
Tao has, as usual, written a post on his blog announcing the result, and the paper itself is on the arXiv, titled “Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors”.
There should really be more women maths professors
University of Sydney professor Nalini Joshi has given a talk to the National Press Club of Australia calling attention to the lamentable dearth of women at the top level of maths in Australia. The problem isn’t just limited to maths, either, Joshi says – women aren’t being allowed to reach the top of the hierarchy in fair proportions in any science subjects.
Watch the video of Nalini’s speech – it’s really powerful. That link also contains an article written in advance of the speech which sums up the main points and stats.
Andrew Hacker and Simon Jenkins both make part of their living from occasionally trotting out variations on an article claiming maths is a bit rubbish, really, and people who are good at maths are meanies for imposing it on everyone else. Simon Jenkins titled the 2016 edition of his rant “Our fixation with maths doesn’t add up”, published in the Guardian, and Hacker took it to the next level with a book titled “The Math Myth: And Other STEM Delusions”.
Their trolling is as effective as ever, promoting much indignant tweeting and blogging, but this latest round of know-nothingism has produced a few really good counterpoints. Responding to Jenkins’s piece, Timothy Gowers says “Maths isn’t the problem – the way it’s taught is”, while Marcus du Sautoy has performed a neat judo move to switch the framing, laying out the evidence against the idea that you can be born without a “maths brain”. In the States, Evelyn Lamb has picked apart Hacker’s book with a fine-toothed comb, pointing out the many, many errors and disingenuities – “It doesn’t add up”. Evelyn has also picked one of the particularly fishy examples from Hacker’s book for closer inspection.
The Leech lattice is the best way of packing 24-dimensional spheres
Thomas Hales spent the better part of two decades proving that he’d found the best way of packing spheres in three-dimensional space. We wrote about the completion of that project in 2014.
Now Maryna Viazovska has shown that the best way of packing 8-dimensional spheres is the \(E_8\) lattice and, with Henry Cohn, Steve Miller, Abhinav Kumar, and Danilo Radchenko, that the Leech lattice is the best way of packing spheres in 24 dimensions. Gil Kalai has written a good blog post announcing the result and giving a brief history of the field.
Andrew Wiles wins the Abel prize 2016
Andrew Wiles has been awarded this year’s Abel prize, for his proof of Fermat’s last theorem. There’s a load of information and explanation on the Abel prize website, so just go there. The citation (PDF) outlines what was so great about what Wiles did, or you can watch Alex Bellos explain it all as part of the video of the announcement ceremony.