Here’s a round-up of all the mathematical news from the last couple of months we didn’t otherwise cover here.
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Exciting new maths of 2024
Over at the Finite Group, members (including me and Katie) have been discussing what in maths news has excited us this year. Here’s a summary.
Brayden Casella and fellow authors claimed that there exists a non-terminating game of Beggar-My-Neighbour, solving one of John H. Conway’s anti-Hilbert problems. Beggar-My-Neighbour is a card game similar to War in which two players deal cards onto a shared pile, aiming to win all the cards into their hand. Matthew Scroggs made a bot: Beggar-my-neighbour forever. In other game theory news, Othello is solved.
Jineon Baek claims a resolution to the moving sofa problem. This considers a 2D version of turning a sofa around an L-shaped corner, attempting to find a shape of largest area. (There are some nice animations at Wolfram MathWorld.) Baek offers a proof that the shape above, created by Joseph L. Gerver in 1992, is optimal.
The Great Internet Mersenne Prime Search (GIMPS) announced a new Mersenne prime: \(2^{136,279,841}-1\). You can get maximum excitement about this news from Ayliean on TikTok, and join in the fun by signing up to record yourself saying a chunk of the prime for the Say The Prime project.
One thing that’s new, apart from the prime itself, is that the work was done on a network of GPUs, ending “the 28-year reign of ordinary personal computers finding these huge prime numbers”. Also this was the first GIMPS prime discovered using a probable prime test, so the project chose to use the date the prime was verified by the Lucas-Lehmer primality test as the discovery date. In other computation news, the fifth Busy Beaver number has been found, as well as 202 trillion digits of pi.
A new elliptic curve was discovered, breaking a record set in 2006 and pushing at the limits of current methods for finding them. Here’s some background on the curves and some of the characters involved.
This year also saw a proof of the geometric Langlands conjecture, and this article explains why this is such a big deal.
We’re all still excited about the discovery of the aperiodic monotiles, and the result passed peer review and was published this year.
And finally, it may not be top research news, but 2024 was also the year that Colin Beveridge started his Double Maths First Thing newsletter. Subscribe to the newsletter here, and check out the archive of past issues here at The Aperiodical.
Finite Group is a friendly online mathematical discussion group which is free to join, and members can also pay to access monthly livestreams (next one Friday 20th December 2024 at 8pm GMT and recorded for viewing later). The content isn’t at the level of the research mathematics in this post, but we try to have a fun time chatting about interesting maths. Join us!
Double Maths First Thing: Issue 0
Double Maths First Thing is Colin’s weekly news round-up. Or round-down, if the fractional part is smaller than a half. You can sign up to receive it in your inbox on a Wednesday morning here.
Hello! My name is Colin and I am a mathematician. Welcome to issue 0 of Double Maths First Thing, in which I highlight some of the mathematical things that have caught my eye this week.
Let’s talk about \( \pi \) and powers
First up, a nod to physicists Arnab Priya Saha and Aninda Sinha for doing something with no real application: they “accidentally discovered a new formula for pi”. There’s a bit about it in Scientific American, a Numberphile video, and a paper in Physical Review Letters (open access). I’ve not worked through it in detail, but it’s got a Pochhammer symbol in it, so it must be good.
I promise this isn’t always going to be about pi, but I also stumbled on a proof that pi is irrational — again, I’ve not worked through the details, but it looks like it would be accessible to a good A-level class with a bit of hand-holding.
Via reddit, a surprisingly tricky problem with a lovely twist in the tail: show that \( 3^k + 5^k = n^3 \) has no solutions for \( k > 1 \). (There’s a hint and a spoiler over on mathstodon.)
Somewhere to visit: W5, Belfast
I’ve recently been on holiday in Northern Ireland. We visited W5 in Belfast, which is a pretty cool science museum — lots of hands-on stuff, including a build-your-own Scalextric-style car, bottle rockets and a green-screen bit where you can present the news about the alien invasion. On the minus side… there are lots of missed opportunities for highlighting the maths that underpins it all. Still, it’s a fun half-day if you’re all Titanic-ed out.
Maths in the news
In the proper news, the Guardian had a long read about Field’s Medallist Alexander Grothendieck; although it too is a bit maths-light, it’s understandable given quite how heavy Grothendieck’s maths is. Katie Steckles also pointed me at the devastating news that UK railcard discounts are dropping from 34% to 33.4%, which strikes me as the sort of thing that probably costs more to implement than it could possibly save the train operators.
Upcoming maths
If you’re in the market for more maths, I can heartily recommend both the Finite Group, whose next livestream is on Friday September 13th, and Big MathsJam, which is a gathering of amazing geeks the first weekend of November. Early-bird tickets are (just about) still available; I have mine already. There’s also a day of recreational maths lectures in memory of David Singmaster on Saturday September 21st in London or online, and a New Scientist event about how maths explains the world the following Saturday, also in London.
That’s all for this week! If there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website.
Until next time,
C
Aperiodical News Roundup – June/July 2024
Here’s a round-up of some news we didn’t cover on the Aperiodical in the last couple of months.
The Indiana Pi Legislation
This is a guest post by Storm Reinbolt, outlining a historical mathematical incident which almost caused a misdefinition!
π is an irrational number that is equal to 3.1415926535 (to 10 digits). Things could have been different, however, if Dr. Edward J. Goodwin succeeded in passing Indiana Bill No. 246. This bill would have completely changed π and mathematics as a whole.
In 1894, Dr. Goodwin, a physician who dabbled in mathematics, claimed to have solved some of the most complex problems in math. Among these was the problem of squaring the circle, which was proposed to be impossible by the French Academy in 1775. This is impossible due to the fact the area of a circle is $\pi \cdot r^2$, where $r$ is the radius, and the area of a square is $s^2$, where $s$ is the length of each side.
This was proven by Ferdinand von Lindemann in 1882, and is what makes squaring a circle impossible.
In order to square a circle, $\pi \cdot r^2$ must be equal to $s^2$. For example, if $r=1$, we would have $\pi \cdot 1^2 = s^2$, or $\pi = s^2$. This would mean that each side of the square is equal to the square root of π, and since π is transcendental, there’s no algebraic expression that could describe π.
Regardless, Goodwin claimed to have done it, and published his paper to American Mathematical Monthly in 1894. It was gibberish, and no amount of understanding in mathematics would make his work comprehensible. He claimed nine different values of π across his many works, with one claim going as far as $9.2376\ldots$, “the biggest overestimate of π in the history of mathematics” (A History of Pi). When his theories weren’t becoming popular, he decided to take them to the Indiana State Legislature on January 18, 1897.
Goodwin had convinced his state representative, Taylor I. Record, to introduce House Bill 246 (Indiana Bill No. 246). House Bill 246 would make Goodwin’s method of squaring the circle a part of Indiana law. However, those in the legislature either didn’t understand or didn’t even glance at the bill – and the House Committee on Canals decided to pass it. Dr. Goodwin’s ridiculous bill was now headed to the senate.
At the statehouse where the senate took up the bill was Professor Clarence Abiathar Waldo, a mathematics professor from New York. When Waldo heard what the bill was about, he was shocked to discover he was in the middle of a debate on a fundamental principle of mathematics. He decided to intervene and talk to the senators about the repercussions the bill would have on everything mathematics, and was able to stop the bill from passing the second chamber.
After Waldo’s intervention, it was clear to everyone that the people involved in the attempted passing of the bill, including Dr. Goodwin, were all wrong, and it was ridiculous to define mathematical truth by law.
Aperiodical News Roundup – June 2022
Community News
The Spectra Math (@LGBTMath) account has announced that the AMS (American Mathematical Society) has instituted a new policy, based on consultations with Spectra, concerning author name changes. The policy is intended to make its journals more inclusive, especially of trans and non-binary researchers. The policy seeks to provide a simple and efficient way for authors to update their name on published articles in a minimally intrusive way that respects the author’s privacy.
‘Author Name Changes’, on the AMS website
The Eindhoven University of Technology has advertised a post for a Full Professor in Applied Algebra and Geometry, which for the first six months of being advertised will only be open to female candidates. The post is part of the Irène Curie Fellowship program, which is dedicated to reaching at least 30% female researchers on TU/e’s permanent academic staff by 2024.
Job advert: Full Professor in Applied Algebra and Geometry
Igalia, contributors to digital maths writing standard MathML, have announce their intent to ship MathML support in Chromium going forward. They claim this announcement is a big step towards having MathML support enabled in Chromium (and hence Chrome) by default. (via Deyan Ginev on Twitter).
Despite previous big promises, the UK government has failed to deliver a promised £300m in funding for pure maths research, as revealed in a recent meeting of the Parliamentary Science and Technology Committee. It’s covered in this Times Higher Ed article (paywalled), or you can watch the proceedings on Parliamentlive.tv (via Protect Pure Maths on Twitter).
Maths Developments
Scientists in Japan have built a tiny Möbius strip from carbon nanotube building blocks (New Scientist article).
In a paper titled ‘The Next 350 Million Knots’, mathematician Benjamin A. Burton at The University of Queensland has enumerated all knots up to 19 crossings, meaning we now have a total of 352152252 known distinct non-trivial prime knots (only infinity to go!) (via Ian Agol).
Google’s Emma Haruka Iwao, architect of a previous large π digit calculation record announcement in 2019, is at it again: the 100 trillionth digit of π in base 10 has been revealed to be (spoiler alert) 0. According to a post on the Google Blog, the calculation took over 157 days and processed around 82,000 terabytes of data.
Events
The ICMS (International Centre for Mathematical Sciences) in Edinburgh has instituted a visiting fellow in music, with the inaugural recipient being Julien Lonchamp, an orchestral composer who has scored a number of short films.
He is interested in how sound and music work at the interface with other disciplines, including visual art and science. He aims to create novel immersive “sound-worlds” by combining a wide range of composition processes in order to communicate abstract or complex ideas.
ICMS press release
If you enjoyed this news item, check out his Soundcloud.
Since these news items are saved up for the end of the month, we can exclusively reveal that registration for the virtual ICM (International Congress of Mathematics) 2022 is both open, and already full. Luckily all lectures will be recorded and made available online afterwards.
And finally
The most important news item of the month was that Guinness has announced the world record for solving three Rubik’s cubes while juggling them was recently smashed by Colombian 19-year-old Angel Alvarado. There’s a video of the new record solve, which took 4:31.01 (beating Angel’s own previous record of 4:52.43, set in May 2021).
Searching for the truth
Earlier today, I tweeted about my exciting new Pi search website, which lets you search for any string of digits within the infinite decimal expansion of π. If you haven’t seen it, go and check it out now.