Linkage

Dozens of the world’s most cited scientists stop falsely claiming to work in Saudi Arabia (\(\mathbb{M}\)). Perhaps relatedly, Clarivate has tightened its checks for fraudulent citation practices and removed a greatly expanded number of researchers from its highly cited researcher lists.

After learning about the existence of plesiohedra, Jim Propp wants to know about stegohedra, ankylohedra, and icthyohedra. One possibility for stegohedra: a polyhedron with triangular faces each of which has exactly one concave and two convex dihedrals.

A photograph of George Green? A case study in historical misconception (\(\mathbb{M}\)). Peter Rowlett does some sleuthing and discovers that a purported photo of the British mathematician is really of an American wagon maker and civil war soldier.

Research papers containing hidden prompts directing artificial intelligence tools to give them good reviews (\(\mathbb{M}\), via). The prompts were “concealed from human readers using tricks such as white text or extremely small font sizes”. The link gives no explicit examples but some can be found in the comment thread.

Interpreting hat color puzzle states as orientations of hypercube graphs.

The most useless data visualisation ever (\(\mathbb{M}\)): a bar chart of US GDP by year that shows a single bar of a fixed size, with only the scale markings changing if you use a slider to view different years.

Hexagonal box (not actually hexagonal).

Measuring the impact of early-2025 AI on experienced open-source developer productivity (\(\mathbb{M}\)). METR ran a controlled experiment with 16 experienced open-source developers on 246 programming tasks. The developers predicted that the use of AI would speed up their work by 25%, and after the experiment judged that it had sped it up by 20%. But when actually measured, the use of AI slowed down their work by 19%.

Record lattice sphere packings discovered (\(\mathbb{M}\)). The proof “utilizes a stochastically evolving ellipsoid that accumulates lattice points on its boundary, while containing no lattice points in its interior”, reviving an old but abandonded idea of Minkowski.

BusyBeaver(6) is really quite large (\(\mathbb{M}\), see also). The previous bound of roughly \(10\uparrow\uparrow 15\) is improved to at least \(2\uparrow\uparrow2\uparrow\uparrow2\uparrow\uparrow9>2\uparrow\uparrow\uparrow 5\), while \(BB(7)>2\uparrow^{11}2\uparrow^{11}3\), as expressed in Knuth’s up-arrow notation. Meanwhile the smallest \(n\) for which ZFC cannot determine \(BB(n)\) has been reduced from 643 to 588, but there’s a lot more room for improvement.

Carleson’s theorem formalized in Lean (\(\mathbb{M}\)). This is the one about pointwise almost everywhere convergence of Fourier series of \(L^2\) functions, for which Wikipedia states “there are still no easy proofs”.

The vigorous and long-running academic debate about precisely what shape the polyhedron depicted in Dürer’s Melencolia I is (\(\mathbb{M}\)). For another one sort of like this, see the debate on whether the sphere in Da Vinci’s Salvator Mundi is hollow or solid, and what it is made of.

The new diamond open access journal Annals of Formalized Mathematics publishes its first issue (\(\mathbb{M}\)). I’m particularly interested in Karayel’s “Derandomization with pseudorandomness”. It looks like it will be an interesting journal.