Here’s a round-up of maths news stories from this month we haven’t otherwise covered on the Aperiodical (not including, of course, the important enneahedron news Christian just posted about).
You're reading: Posts Tagged: knot theory
Double Maths First Thing: Issue D
Double Maths First thing is much less effort than an advent calendar.
Hello! My name is Colin and I am a mathematician, on a mission to spread joy and delight, like a sort of Father Christmaths.
I’m sure December is a conspiracy in which Big Diary manipulates time so there are far too many places to be and far too little time to get from one to the other (the eldest currently needs to teleport from water polo to scouts.)
This week’s links
I have a difficult relationship with Quanta magazine. On one hand, it’s putting out articles about lots of great maths and computing; on the other, it insists on horrible clickbait titles, to the point that in my head it’s really called FizzBuzzFeed. In any case, here’s a piece about knots and the Menger sponge
Obviously, Matt Parker lives on YouTube, where clickbait is a survival strategy; he did a nice video about probabilities and multiple dice a while back; Dr Drang has done some more analysis.
You know what’s really good at grabbing my attention without making me sigh? A fantastic first sentence. How about:
You might think it’s unlikely for any interesting mathematics to arise from incense appreciation…
This article does exactly what it says on the incense tin. Excellent stuff.
In historical maths, Walter Van Assche has uncovered some 16th century Chebyschev polynomials, and — some years ago — Ron Doerfler has had a look at Heaviside operator calculus, which is a fantastic, unrigorous mess that just works. I strongly approve.
That’s all I’ve got this week! In the meantime, if you have friends and/or colleagues who would enjoy Double Maths First Thing, do send them the link to sign up — they’ll be very welcome here.
If you’ve missed the previous issues of DMFT or — somehow — this one, you can find the archive courtesy of my dear friends at the Aperiodical.
Meanwhile, if there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website. You can also just reply to this email if there’s something you want to tell me.
Until next time,
C
Aperiodical News Roundup – March/April 2024
Here’s a round-up of mathematical news from the last couple of months.
Awards
The 2024 Abel Prize has been awarded to Michel Talagrand, “for his groundbreaking contributions to probability theory and functional analysis, with outstanding applications in mathematical physics and statistics.”
This year’s Turing Award has been given to Avi Wigderson, “for foundational contributions to the theory of computation, including reshaping our understanding of the role of randomness in computation, and for his decades of intellectual leadership in theoretical computer science.” Widgerson is a previous recipient of the Abel Prize.
Mathematical Discoveries
Nature magazine reports the discovery of a natural metabolic enzyme capable of forming Sierpiński triangles. Fractals are everywhere!
Quine’s New Foundations for set theory, in which the axiom of choice is false, has been formally proved in Lean to be consistent (PDF).
Another unreasonably effective application of maths: knot theory can be used to reveal points where spacecraft can switch between intersecting orbits using minimal fuel.
Other news
And finally, there have unfortunately been two deaths in maths education. First, maths education stalwart and generally lovely person Sue de Pomerai has died. Sue worked at MEI, FMSP and AMSP, and made a huge contribution to maths promotion in the UK. Also Hugh Burkhardt, pioneering mathematics education researcher and former Director of the Shell Centre for Mathematical Education.
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).
Tie, tie, tie a tie / Fly, fly, fly as you might
Novel knot news now! You might already be aware that there are 85 ways to tie a tie. Well, cast that preconception aside because there are actually loads.
Ghost Diagrams
Yet another fun toy for you. Give a computer a set of tiles defined by what their edges look like, can you fit them together? That problem is undecidable, since you can encode Turing machines as sets of tiles, but it turns out it’s fun to watch a computer try.
Ghost Diagrams asks you for a set of tiles (or it’ll make some up if you didn’t bring one) and shows you its attempts to make them fit together. It’s very pretty, and quite mesmerising. Sometimes it looks even better when you turn on the “knotwork” option.
Paul Harrison created Ghost Diagrams while writing his PhD thesis, Image Texture Tools: Texture Synthesis, Texture Transfer, and Plausible Restoration. He’s written a short blog post about the program.
Here are a few patterns I liked: 1, 2, 3, 4, 5.
via John Baez on Google+.
Tying knots in light
According to this post on phys.org, which reports on this paper in science journal Nature, there’s some beautiful physics which results from tying knots in light. It opens, “New research published today seeks to push the discovery that light can be tied in knots to the next level.” Between us, I wasn’t actually aware of the discovery that light can be tied in knots (and I’ve done a fair amount of knot theory, and observed a decent quantity of light) – but apparently it’s something scientists have been exploring for years.
A spinning optical soliton (wave pulse) can spontaneously create knotted and linked structures, as the soliton curves around in space, and while previously it’s been observed after engineering them to happen, now the knots are forming spontaneously, like ” those annoying knots that you always get in electrical cables.” (see: here). The paper suggests similar behaviour might be seen in other types of wavefronts, such as superfluids and trapped matter waves. For anyone who got lost around ‘soliton’, rest assured it involves the use of lasers. Obviously.
More information
Beautiful physics: tying knots in light on phys.org.