I’m slowly working to (sort of) recreate Martin Gardner’s cover images from Scientific American, the so-called Gardner’s Dozen.
This time it’s the turn of the March 1964 issue. In the article ‘The remarkable lore of the prime numbers’, later included as chapter 9 in Martin Gardner’s Sixth Book of Mathematical Games from Scientific American, Gardner describes how Stanislaw Ulam in a boring meeting doodled a grid of numbers, spiralling out, then circled the primes. “To his surprise the primes seemed to have an uncanny tendency to crowd into straight lines.” These Ulam sprials, discovered the year before, contain lines related to prime-generating functions, which I have written about recently.
The UK Government have announced the new set of King’s Birthday Honours. Here’s our selection of particularly mathematical entries for this year. If you spot any more, let us know in the comments and we’ll add to the list.
Philippa Bonay, Director, Operations, Office for National Statistics. Appointed OBE for Public and Charitable Services.
Anne Davis, Professor of Mathematical Physics, University of Cambridge. Appointed OBE for services to Higher Education and to Scientific Research.
Paul Fannon, Fellow, Christ’s College, Cambridge, and Volunteer, United Kingdom Mathematics Trust. Appointed OBE for services to Education.
Ian Hall, Professor of Mathematical Epidemiology and Statistics, University of Manchester and Senior Principal Modeller, UK Health Security Agency. Appointed OBE for services to Public Health, to Epidemiology and to Adult Social Care, particularly during Covid-19.
David Marshall, Lately Director of Census, Northern Ireland Statistics and Research Agency (now Northern Ireland chief electoral officer). Appointed OBE for services to Official Statistics and Census-taking in Northern Ireland.
Bruno Reddy, Founder and Chief Executive Officer, Maths Circle, Ampthill, Bedfordshire, and creator of Times Tables Rock Stars. Appointed OBE for services to Education.
Sam Rose, Deputy Director, Data and Analysis Division, Department for Transport. Appointed OBE for services to Advanced Analytics
Matthew Woollard, Professor of Data Policy and Governance, UK Data Archive, University of Essex. Appointed OBE for services to Data Science
George McMath, Lately Deputy Principal, Northern Ireland Statistics and Research Agency, Northern Ireland Civil Service. Appointed MBE for services to the Northern Ireland Census.
Get the full list from gov.uk. Spot anyone we’ve missed? Let us know in the comments.
A few weeks ago I heard someone casually refer to ‘that formula of Euler’s that generates primes’. I hadn’t heard of this, but it turns out that in 1772 Euler produced this formula:
.
Using this, , which is prime. , which is also prime. is another prime. In fact this sequence of primes continues for an incredible forty integer inputs until . It might generate more primes for higher inputs, but what’s interesting here is the uninterrupted sequence of forty primes.
This got me wondering. Clearly is prime because 41 is prime, so that much will work for any function
for prime , since . Are there other values of that generate a sequence of primes? Are there any values of that generate longer sequences of primes?
I wrote some code to investigate this. Lately, I’ve taken to writing C++ when I need a bit of code, for practice, so I wrote this in C++.
I figured the cases where is prime but isn’t weren’t that interesting, since is trivially prime. In fact, when for any prime , but saying so doesn’t seem worth the effort.
So I kept track of the primes whose functions generate more than one prime, and the lengths of the sequences of primes generated by each of these. This produced a pair of integer sequences.
I put the primes that work into the OEIS and saw that I had generated a list of the smaller twin in each pair of twin primes. I was momentarily spooked by this, until I realised it was obvious. Since and , any prime this works for will generate at least a twin prime pair .
What about the lengths of the sequences of consecutive primes generated? The table below shows the sequences of consecutive primes generated for small values of . Most primes that generate a sequence produce just two, and definitely stands out by generating forty.
I was pleased to see this sequence of lengths of primes generated was not in the OEIS. So I submitted it, and it is now, along with the code I wrote. (I discovered along the way that the version where sequences of length one are included was already in the database.)
Anyway, I amused myself by having some C++ code published, and by citing Euler in a mathematical work. Enjoy: A371896.
With the emphasis on occasionally, I’m occasionally working to (sort of) recreate Martin Gardner’s cover images from Scientific American, the so-called Gardner’s Dozen.
This time I’m looking at the cover image from the November 1959 issue. The column is ‘How three modern mathematicians disproved a celebrated conjecture of Leonhard Euler’, about the so-called Euler’s Spoilers, the story of three mathematicians – Parker, Bose and Shrikhande – who had disproved a conjecture of Euler’s about Latin squares. The column was reprinted as chapter 14 in his New Mathematical Diversions from Scientific American.
A few months ago a group of us launched a membership club, The Finite Group, which you can join!
A big update is the lineup — your membership now supports the work of and gives you access to content from mathematician and TikTok star Ayliean MacDonald, as well as Chalkdust’s Matthew Scroggs and The Aperiodical’s Katie Steckles and me. Membership gives you access to a chat community and monthly livestreams. For a taste of the livestreams, check out this π minute video!
The big news is that the next livestream will be free to view live online on 27th March from 5-6pm GMT. All four of us will be working through the recent ‘100 Mathematical Conventions Questions’ quiz that’s been dividing (a small subset of) the internet. The stream will be available live, and a recording will be available to members afterwards.
You know how loads of things in maths are named for the wrong person? In 1996, a fun quiz appeared in The Mathematical Gazette based on history of maths misconceptions. It contained a series of questions where the obvious answer is not correct, such as “Who discovered Cramer’s rule?”, “Did Pascal discover the Pascal triangle?” and “Who first published Simpson’s rule?”
I was looking for a demo to show my students that generative AI programs are not producing accurate knowledge when I thought of this quiz. I put its questions to ChatGPT to see how it did. The point of the exercise is that these systems just parrot back words from their training data without any concept of truth, so if the training data is full of misconceptions, so too will be the responses. But these are misconceptions from the 1990s, so how much influence will they have on the responses?
Stephen Wolfram has announced version 14 of Mathematica, which will be available immediately both on the desktop and in the cloud. The latest version has 6602 built-in functions, and is accompanied by significant documentation and online tutorials to help people learn how to use it.
A new mathematical modelling competition, open from 1st Feb, invites predictions for when cherry trees will blossom in five cities in the USA and Japan, with cash and prizes awarded for a compelling narrative and reproducible analysis containing any data and code used. (via IMAmaths on X)
Science is reporting that a group of mathematicians are producing “low-quality papers” that repeatedly reference their work, distorting citation metrics apparently in an attempt to raise their institution’s rankings. As a result of this practice,
publishing analytics company Clarivate has excluded the entire field of math from the most recent edition of its influential list of authors of highly cited papers, released in November 2023.
Claire Voisin has been awarded the Crafoord Prize in Mathematics by the Royal Swedish Academy of Sciences — the first woman to win this award in mathematics. (via European Mathematical Society on Mastodon)
