Readers of The Aperiodical may recall three excellent posts on the Maths of Star Trek by Jim ‘But Not As We Know It’ Grime. At the same time, Jim discussed the topic in glorious audio with Andy Holding and Will Thompson, hosts of the Science of Fiction podcast (worth listening to, but at least visit the page to see a picture of Jim nursing a tribble). As part of this, the hosts asked Jim what uniform colour mathematicians on the Enterprise would wear.
JIM: Science and medics, those are the blue shirts.
HOST: Where do mathematicians go? Scientists?
JIM: That’s right, yes, science.
HOST: You’re safe?
JIM: Yes, I am, I’m in the blue shirt category.
Jim is pleased to say that mathematicians wear blue because, as he explains, gold and red uniformed crew were much more likely to be killed during the famous five-year mission than those in blue. I’ve written in the past about maths and mathematicians being everywhere, for example when asserting that most of the Nobel prizes are for mathematics. Was Jim right about those blue-shirted mathematicians?
Harald Helfgott has announced a proof of the odd Goldbach conjecture (also known as the ternary or weak Goldbach conjecture). This is big news. Like a good maths newshound, Christian Perfect promptly wrote this up for The Aperiodical as “All odd integers greater than 7 are the sum of three odd primes!”
Wait, though, there’s a problem. As Relinde Jurrius pointed out on Twitter, the formulation used in the paper abstract was not quite the same.
The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer $N$ greater than $5$ is the sum of three primes. The present paper proves this conjecture.
The version Christian used makes the assertion using odd primes, whereas the paper abstract only claims “the sum of three primes”. The latter version includes $7$ because $7$ can be written as the sum of three primes, but not odd ones ($7 = 3+2+2$). Certainly, you can see both statements of the weak Goldbach conjecture used (for example, here’s the $\gt 5$ version and here’s the $\gt 7$ version). Are they equivalent?
I have a new toy. ‘Ox Blocks’ box promises “Noughts and Crosses with a novel twist”.
I have moved my blog Travels in a Mathematical World to The Aperiodical!
Since the start of the year, the Math/Maths Podcast has been on hiatus. I’m very much enjoying the extra thesis-writing time but apparently this has left some missing their regular mathematical listen. Not infrequently I get an email from someone wishing me well with my thesis and asking when we’ll be back podcasting. Well, nature abhors a vacuum and here are three offerings that I’m aware are working to fill the void. (Oh, and “pale imitations” – I’m joking, of course!)
My Aperiodical co-conspirators Katie Steckles and Christian Perfect started All Squared, a maths magazine podcast, in February. The description for the first episode (or “number”, as Katie and Christian have it) overtly points out the “unusual paucity of maths podcasts at the moment” and promises “a half-hour podcast featuring maths, guests, puzzles and links from the internet”. The name is designed to be recognisable to mathematicians, who might find themselves reporting that an expression is “all squared”. As someone who named a podcast as overtly as it is possible to be, “Math/Maths”, this obfuscation amuses me. The three episodes so far have been enjoyable with a guest and main topic in each. As far as I’m concerned, this is far more the Aperiodical podcast that should exist than is The Aperiodcast with that third guy.
This one started just before Samuel Hansen and I went on our hiatus, but if you enjoyed the teaching aspects of what we did you can get a lot more on the theme from Craig Barton and his guests on the TES Maths Podcast. Craig promises “to share the latest news, resources and ideas that are relevant to secondary/high-school maths teachers and general number enthusiasts”.
Wrong, but Useful is a new podcast featuring “a mathematical conversation” between Colin Beveridge and Dave Gale that sets out its stall as a response to the lack of Math/Maths episodes. The title is another nod to the mathematically minded without being overt, referring to a quote from George Box and Norman Draper who wrote “essentially, all models are wrong, but some are useful” (Empirical Model-Building and Response Surfaces, 1987). Episode 1 sees Colin and Dave finding their feet in a rambling, wide-ranging mathematically-themed discussion. There were a couple of awkward moments that gave me Math/Maths early episode flashbacks but I’m looking forward to Colin and Dave getting into the swing for the next episode.
I present a new paper, ‘A simple proof that π is rational‘. The abstract is:
The number pi, written using the symbol π, is a mathematical constant that is the ratio of a circle’s circumference to its diameter, and has been claimed since antiquity to be an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, and that therefore its decimal expansion never ends or settles into a permanent repeating pattern. Here a proof is given that π can indeed be expressed as a ratio of two integers, 4/17, a fact that has unbelievably been overlooked until now. Moreover, this proof is understandable to anyone with a basic knowledge of algebra and calculus and arises from simply considering a standard integral at two values of x, x=1/4 and x=1. Of course I doubted the result at first, given that it has been overlooked for so many years, but I have checked the proof and verified it to be correct. This is a crucial and important revelation that will significantly alter all of mathematics.