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Welcome to the 214th edition of Carnival of Mathematics!
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Welcome to the 214th edition of Carnival of Mathematics, meta-hosted by the remarkable

In order to appear cool and up-to-the-minute I thought I should ask ChatGPT to do the traditional Carnival honours and provide some facts about the number 214. Here's a screenshot:

ChatGPT on 214  

I thought yada yada yada ... WAIT A MINUTE! 214 is the sum of WHAT?

So is 214 actually the sum of the first 23 anything? I'll append your valid answers to this page if you email me them (no, not you, ChatGPT!)

So straight to submissions! Well, here's a ChatGPT gem from Tony Mann which I wanted to submit but hesitated because it's on Facebook and I'm never sure what that means in terms of durability/accessibity.

Three breakthroughs in mathematics in March: on 16th Gil Kalai's Combinatorics and More posted rumours of a big announcement from a Cambridge seminar and added the big reveal the day after: a reduced upper bound for Ramsey numbers that has been sought since 1935. Timothy Gowers, who was at the seminar, reported on Twitter that there was the same feeling as at Andrew Wiles's history-making 1993 gig.

Perhaps unfairly, the huge significance of an upper bound reduction from \(4^k\) to \((4-\varepsilon)^k\) was never going to hold the headlines in competition with The Hat, announced a few days later. This from the University of Waterloo was closely followed by a 3D-printout at from Dave Richeson (divbyzero); an interactive Hat tiler from; a complete github monotiling bundle from Christian Lawson-Perfect; quilting instructions from fractalkitty; and a slew of first-rate blog explanations: The Aperiodical, Gödel's Lost Letter, Gil Kalai again, ...

And the third announcement? Two high school girls coming up with a trig proof of Pythagoras. One that didn't depend (circularly) on \(\cos^2x+\sin^2x=1.\) This was a bit more low-key because the actual proof wasn't available. There was just a Guardian article and a regional AMS talk. But Youtube channel MathTrain cleverly reverse-engineered the proof from pictures of slides from the AMS talk. Then for good measure, Akshar Varma on mathstodon produced a diagrammatic version.

More trig: it was the day formerly known as Pi day on the 14th. Ioanna Georgiou had this very nice podcast about Archimedes, as seen through the lens of her clever popular mathematics writing (see here). More directly Pi-related was an announcement on twitter by John C. Beach regarding calculations encoded by the Egyptians. He has this follow-up. Andrius Kulikauskas submits a very different take on geometry: A Geometry of Moods, Evoked by Wǔjué Poems of the Táng Dynasty.

Patrick Honner also goes from a poem to geometry: "Neg-a-tive b, plus or minus / The square root of b squared / ...", a quadratic formula mnemonic, apparently. Why is cubic less accessible than quadratic to algorithmic solution? This is a contribution to Quanta magazine's teaching wing: Quantized Academy, and very beautifully done it is too, with some well-judged self-test questions at the end. But I can't let him get away with "But unlike the quadratic formula, [the cubic formula] has no catchy tune to sing along to". Who does not know Tartaglia's timeless aria "Quando che’l cubo con le cose appresso"? An English translation by Kellie Gutman helpfully brought to us by

Quanta magazine is a force of nature (at least in mathematics; some of their physics coverage has been controversial). Magazine, Academy, Podcasts, ... Super-explainer Steven Strogatz hosts The Joy of Why (a play on one of his book titles) and in "Is There Math Beyond the Equal Sign?" talks to category theorist Eugenia Cheng (author of The Joy of Abstraction). Listen to the audio — a transcript is helpfully provided, but the spoken word here brings everything to life.

No transcripts for Youtube clips, normally, but polymathematic's explantion of intransitive dice is wonderfully visual and provides a beautiful little case study in applied probability.

Bartosz Ciechanowski has a "weekend hobby" which would be a full-time job for lesser mortals. So lesser am I that full-time is just assimilating his incredibly rich and interactive description of the mechanics of riding a bicyle. In awe!

Some nice submissions on factoring: John D Cook has this on Conway's method, with lots of useful pointers to related things; Matt Henderson has a cute gif on twitter for visualising factoring; and he has another gif: a way of telling if a maze is divisible by two! Meanwhile, if you want to divide into two equal factors and don't trust ChatGPT (I don't), well, has just what you need.

Richard Fisher trusts ChatGPT because he used it "to research trusted sources and calculate parts of" The numbers that are too big to imagine, a well-written BBC Future stroll through the mathematics of big. "For the sake of clarity", the BBC primly points out, "[we don't] use generative AI as a primary source or to replace the journalism needed for our articles." Let's see how long that lasts.

Jay Daigle certainly isn't taking ChatGPT on trust and his blog has a couple of very thorough explorations of its implications for mathematics and mathematics education. One of the great things about doing Mathematics Carnival is the serendipidous blog reading entailed. The actual submission from Jay Daigle's blog was on Euler's method for getting approximate evaluations of ODE solutions and how this is a different way of looking at the Riemann integral and the Fundamental Theorem of Calculus. Daigle's blog posts tend to finish with a step back: "what's this actually amount to?" which I find refreshing.

Thanks for reading! Submit here to Carnival 215, to be hosted by Cassandra at Cassandra Lee Yieng’s Blog.

Email me what 214 is the sum of the first 23 of!