Carnival of Mathematics #233

Welcome to the 233rd Carnival of Mathematics!

Who can forget 233, the 6th Fibonacci prime? Hey, not all numbers are interesting. Don’t ask me about the smallest positive uninteresting number. You can’t make it interesting with your feeble mind tricks! Anyway, on to the fun.

Provers and Shakers

The big discovery this month was a new largest known prime number, $2^{136279841} - 1$, as reported by the Great Internet Mersenne Prime Search. It has been 6 years since a new Mersenne prime was discovered. One new facet is that it was discovered by a NVIDIA A100 GPU, and confirmed the next day by an H100. Apparently this computation was done in the cloud during periods of GPU under-utilization. It was widely covered by not-so-mainstream news, for example by Stand-up Maths and John D. Cook, as well as Tom’s Hardware, I assume because they love GPUs.

A slightly less popular math result was the disproof of the bunkbed conjecture, by (and blogged by) Igor Pak, Nikita Gladkov, and Aleksandr Zimin. The news was also covered on YouTube by Trefor Bazett.

Audio

The Carry the Two Podcast published a timely episode called Mathematics and Political Geography about redistricting and how to identify communities of interest, as well as about polling sites. It was interesting to hear from Ranthony Clark on how they used agglomerative hierarchical clustering to identify communities of interest, despite my own reservations about clustering as implicit model selection. But it seems like they did enough manual human review to make it sensible. I also was pleased to hear from Mason Porter about another technique I’m skeptical of, peristence homology, to study polling site locations. I like it when people try things that I’ve seen fail in brand new contexts, because if they succeed we all get to enjoy cool new math.

They have a handful of political math episodes out this October, so listen if you want more.

Video

Sophie Maclean discussed the Condorcet voting paradox in a Numberphile video,

Vi Hart also published a Halloween-themed romp about constructing polylinks with Smarties.

The Stand-up Maths channel also published a fun video about a regular expression that recognizes (non)-primes, based on a blog post from September by Illya Gerasymchuk. It works by looking at the unary representation of the number, and using capturing groups to make the regex engine search for strings whose lengths are multiples of a smaller number, up to the length of the input string. In python:

def is_prime(n):
    return not re.match(r'^.?$|^(..+?)\1+$', '1'*n)

The second half of the regex, (..+?)\1+, matches “some number of a fixed character” (..+), followed by 1 or more copies of that captured group. It wouldn’t be Math $\cap$ Programming without some code.

Bloggers

Mathober was in full swing, and I saw all kinds of posts on Mathstodon with the #mathober hashtag.

Bill Gasarch wrote an article about how Emil Post anticipated Godel and Turing, in response to this Feb 2004 article by John Stillwell. On the same blog (they share it), Lance Fortnow wrote about how more and more Nobel prizes seem to go to folks that are more traditionally associated with computing than the field in question.

Nobel’s will predates Turing and the development of computation as a new field. The importance of computing and artificial intelligence has take on such an importance that the Nobel Prize committees felt they needed to honor it, even if it means broadening the categories and encompassing computer science as a part of physics.

David Eppstein wrote about half-flipped binary tilings of the hyperbolic plane, and Matthew Arcus posted some nice pictures in response.

John D. Cook wrote about the running average of the number of divisors of a number, demonstrating the well-known fact that it grows logarithmically. He also wrote about Shannon’s formula for channel capacity.

Colin Beveridge started writing a newsletter called Double Maths First Thing, which has continued in October and provides a nice suite of links I wouldn’t normally come across.

James Propp wrote a nice article about recreating standard dice with as few pips as possible, which is a strange but fun constraint. Perhaps the best part was the comedic bit he did during his talk at Gathering for Gardner, role playing as an efficiency-obsessed capitalist who views the number of pips on a standard die as unacceptible waste.

Zoe Griffiths wrote a book review of Mapmatics by Paulina Rowinska, which covers everything from cartography to gerrymandering.

In September Terry Tao announced a collaborative project to try to combine proof the Lean proof assistant with modern LLM-based AI tools to try to explore a problem in universal algebra to classify “equational theories for magmas.” This month, he gave an update showing a ton of progress. He had very nice things to say about the contributions of Lean and people using it, but little nice to say about the contributions of AI tools.

Perhaps the only thing that I was expecting to see at this point that has not yet materialized is significant contributions from modern AI tools. They are being used in a number of secondary ways in this project, for instance through tools such as Github copilot to speed up the writing of Lean proofs, the LaTeX blueprint, and other software code, and several of our visualization tools were also largely co-written using large language models such as Claude. However, for the core task of resolving implications, the more “good old-fashioned” automated theorem provers have so far proven superior. However, most of the remaining 700 or so implications are not amenable to these older tools, and several (particularly the ones involving “Asterix” and “Obelix” had stymied the human collaborators for several days), so I can still see a role for modern AI to play a more active role in finishing off the hardest and most stubborn of the remaining implications.