Linkage for the Ides of March

I am quite amused by the description of “some unimpressed Wikipedia editor” (\(\mathbb{M}\)) who didn’t think the evidence for or against the Kummer–Vandiver conjecture in algebraic number theory is particularly strong, but I am unable to explain why it is so amusing. (No, it wasn’t me.)

Yuansi Chen’s preprint, “An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture” is described less technically by Gil Kalai and now Quanta (\(\mathbb{M}\)). It doesn’t quite solve the Bourgain slicing conjecture, that high-dimensional convex bodies of unit volume have cross-sections of constant volume, but it reduces the dependence on dimension from a power of \(d\) to something smaller.

Inside Higher Ed on arrests of US-based Chinese researchers for supposed instances of grant fraud (\(\mathbb{M}\)) that turn out to mean participating in official university-level collaborations with Chinese universities, taking notes at someone else’s talk, and serving as a peer reviewer: “Is it making major cases out of minor issues? Is it ethnic profiling?” The answers seem obvious.

Oscar Wilde wrote The Ballad of Reading Gaol while staying with Bob Ross (\(\mathbb{M}\), also, also), as I learned from this Banksy video.

De quinque corporibus regularibus (\(\mathbb{M}\)). A 15th-century book on the mathematics of polyhedra by painter Piero della Francesca, lost for centuries except through a plagiarized translation by Luca Paciola, and rediscovered in the Vatican Library in the 19th century. Its contributions include the volume of bicylinders (independent of previous work by Archimedes and Zu Chongzhi) and a novel formula for the height of an irregular tetrahedron. Now a Good Article on Wikipedia.

British Universities are in negotiations with Elsevier (\(\mathbb{M}\)). Elsevier claim that because they have added many new open-access journals, there is more content to justify higher subscription prices. (Yes, that is blatant double-dipping.) The University of California system hasn’t been a subscriber to Elsevier since the end of 2018 and we’ve been doing fine without.

Building mechanical computers out of graphene nano-origami (\(\mathbb{M}\), via).

The latest wrinkle in crumple theory (\(\mathbb{M}\), via). Siobhan Roberts in the NYT on how paper crumples, based on a new study in Nature Communications led by Jovana Andrejevic. It builds on previous studies showing logarithmic growth of total crease length on repeated re-crumpling, but gains more insight by looking at the distribution of sizes of unfolded areas, and the ways those areas fragment into smaller areas, rather than just their total perimeter.

Since I saw it a year ago and again this week, I wondered: how can I see Los Angeles from my neighborhood, 65km away? (\(\mathbb{M}\)) Doesn’t the earth’s curvature get in the way? Isn’t the horizon typically 5km away?

It isn’t refraction.

I live on a hill. Many LA skyscrapers are on another hill. Both are around 100m high, and the land between is low and flat. That turns out to be almost exactly the right altitude for mutual visibility, even though a single hill would have to be 400m high to see as far.

ISO obstructs adoption of standards by paywalling them (\(\mathbb{M}\)); in particular the ISO 8601 date format standard is not public. This makes these standards problematic when individuals, rather than deep-pocketed corporations, need to follow them. RFC 3339 could be used in place of ISO 8601 in many uses, but is too restricted for some (can’t handle BC). Are there other good alternatives?

A large sockpuppet ring has been caught adding citations of Stephen Wolfram’s works to Wikipedia (\(\mathbb{M}\)). A typical addition: equivalence of the Riemann hypothesis to a tag system, a trivial corollary of Minsky’s proof of universality of tag systems. They’ve been going at it for years, so it will take significant effort to clean up. Technical information that might point to who did this (e.g. an overenthusiastic fan or corporate publicists) is private.

Hilbert’s Tenth again (\(\mathbb{M}\)). Matiyasevich famously proved undecidability of Diophantine equations over integers in the 1970s, but the same question over rationals remains open. A new paper by Prunescu makes progress by proving undecidability of exponential equations over rationals. As Richard Lipton explains in this blog post, a key step, parameterization by integers of rational solutions to \(x^y=y^x\), comes from a 30-year-old recreational-mathematics article by Márta Svéd.

Internet Archive Scholar (\(\mathbb{M}\)), a new full-text database of “over 25 million research articles and other scholarly documents preserved in the Internet Archive”.

Sample pages from the gorgeous-looking new book Illustrating Mathematics, edited by Diana Davis (\(\mathbb{M}\), via).