A conversation about mathematics inspired by Lewis Carroll’s Game of Logic. Presented by Katie Steckles and Peter Rowlett.
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Mathematical Objects: Universe of cake
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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!
Review: Mapmatics by Paulina Rowińska
This is a review of the book Mapmatics: How we Navigate the World through Numbers by Paulina Rowińska. We were kindly sent a copy of the book to look at, and Elinor Flavell shares her thoughts.
Do you love maps? Do you hate maps? Have you never given much thought to maps but are now worried that it might be good to know how to navigate if your phone dies? Well, Mapmatics is for you!
Do you know a geography nerd who is always bringing up maps? Do you know someone who always seems to get lost, despite it being easier than ever to get around? Or do you have that one friend who still doesn’t believe that everything can be related to maths? Well, Mapmatics is for them!
Mapmatics is for everyone!
Mapmatics is for you, and for anyone in your life who would like to more deeply understand the connections between maths and the world around them. On the surface Mapmatics is a book about how we create and use maps to interpret the world around us. But Rowińska shows that the reason we can do all of these things with maps is because of mathematics.
Over eight chapters, Rowińska talks us through problems that humans have wrestled with through the centuries – from “how can we take a 3D globe and turn it into a 2D map?” to “how can we map the inside of our planet without actually going to the centre of the earth?”. And with each problem she takes us through the underlying mathematics. Each chapter explores a different aspect of maps, and includes a diverse range of topics, from gerrymandering to the London Tube map.
Rowińska does a great job at explaining some rather complicated ideas while talking about lots of other researchers, giving you plenty of resources to go and learn more about a certain subject, if you so wish; and she includes some very helpful diagrams! She is very good at defining and explaining geography jargon in terms which a geography novice such as myself could understand. However, I would have found it helpful to include a glossary in the book so I could refer back to them. I also found it rather refreshing that in her examples she does not stick to the gender neutral “he” when talking about a random person experiencing something.
I have two primary criticisms of the book: Rowińska starts off the book by talking about her first experience of maps, but I would love to know more about her link to maps and geography and what prompted her to write the book in the first place. Secondly, I would love to see even more diagrams – in colour- in the book as I think this would support some of the more difficult mathematical ideas included. However, I realise this is the eternal struggle between author and publisher.
This book would suit anyone who loves understanding the mathematics behind things that we use every day. From a technical point of view, I would recommend having at least done mathematics in your final years of secondary school, as some of the mathematics presented would be challenging otherwise.
Overall, this is an engaging book that covers a huge variety of applications – from earthquakes to animation, and will be of interest to anyone who likes to understand the intersection between maths and other topics.
Mapmatics, at Pan Macmillan
Mapmatics, at Bookshop.org
Mapmatics, at Waterstones.com
Mathematical Objects: An object with Tai-Danae Bradley
A conversation about mathematics inspired by … an object. Presented by Katie Steckles and Peter Rowlett, with special guest Tai-Danae Bradley.
Katie mentions Peter’s The unplanned impact of mathematics, free to read at Nature.
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Mathematical Objects: Borges’ Library of Babel
A conversation about infinity inspired by The Library of Babel by Jorge Luis Borges. Presented by Katie Steckles and Peter Rowlett.
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Mathematical Objects: Parallelepiped with Ayliean MacDonald
A conversation about mathematics inspired by a very special parallelepiped. Presented by Katie Steckles and Peter Rowlett, with special guest Ayliean.
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Aperiodical News Roundup – October 2024
Here’s a roundup of some of the maths-related news from this month we didn’t otherwise cover here!