Linkage

Matthias Merzenich finds a true-period-14 glider gun in Conway’s Game of Life (\(\mathbb{M}\)).

Simon Tatham asks for links of collected knowledge on Conway’s nimbers, after discovering that the all-ones nimbers appear to generate the multiplicative group of their subfields, which would lead to a canonical choice of primitive polynomial for \(GF(2^{2^n})\). I pointed him to my Karatsuba-like implementation.

The cultural divide between mathematics and ai (\(\mathbb{M}\)). Ralph Furman reflects on differences observed at the 2025 Joint Mathematics Meeting.

A failure to communicate (\(\mathbb{M}\)). Lance Fortnow finds it difficult to write a popularly-accessible summary of the recent breakthough by Ryan Williams (space complexity is at most roughly the square root of time complexity). He tries turning to AI and gets a pile of baloney in response.

The area of the Pythagoras tree (\(\mathbb{M}\)), a fractal tree-like 2d shape with a square base made by attaching two smaller copies to the top of the base, rotated by \(45^\circ\) and scaled by \(1/\sqrt2\). Counted with multiplicity, the area diverges (there are \(2^i\) squares of area \(1/2^i\)) but taken as a union it has an unexpectedly rational area with an unexpectedly large number of digits.

Charles Corderman’s computer (\(\mathbb{M}\)), a 37-bit machine controlled only by a light pen and hacked together out of DEC PDP parts, on which he discovered the switch engine Game of Life pattern in 1971. Adam P. Goucher reconstructs what he can from the limited information still available.

Doubts cast over D-Wave’s claim of quantum computer supremacy (\(\mathbb{M}\)), NewScientist. “D-Wave’s claim that its quantum computers can solve problems that would take hundreds of years on classical machines have been undermined by two separate research groups showing that even an ordinary laptop can perform similar calculations.”

Fractal Kitty pen-plots Voronoi diagram generative art, resembling to me an aerial view of a narrow channel carved through crystalline rock, opening out as it progresses downward.

EATCS interviews Antoine Amarilli (\(\mathbb{M}\)), about “CS theory vs practice, (not) reading papers, (not) having impact, and modernizing our research practices in TCS”.

Monash University network admins make faculty home pages inaccessible from off-campus, totally missing the point of what these pages are generally used for. In response, David Wood moves his page off-campus.

Interview with Judith Butler (\(\mathbb{M}\)). On a random scattering of topics, but the pull quote is “If you sacrifice a minority like trans people, you are operating within a fascist logic”.

Voronoi conjecture for five-dimensional parallelohedra (\(\mathbb{M}\)), Alexey Garber, newly published in Inventiones Mathematicae. A parallelohedron is a polyhedron whose translated copies tile space face-to-face. There are five types of these in three dimensions, all of which are zonohedra, but in higher dimensions they get more complicated. For instance the 4d regular 24-cell is a parallelohedron but not a zonohedron. The Voronoi conjecture relates parallelohedra to plesiohedra, the Voronoi cells of symmetric point sets. The Voronoi cells of a lattice are parallelohedra, but contrary to what MathWorld says, not all parallelohedra are Voronoi cells. The ones that are Voronoi cells have a special property: each face is perpendicular to the line connecting its center to the center of the whole parallelohedron.

According to the Voronoi conjecture, every parallelohedron has an affine transformation taking it to this special form. For instance, in two dimensions this implies: every centrally symmetric hexagon has an affine transformation taking it to a hexagon inscribed in a circle. This has long been known for up to four dimensions but open in higher dimensions. The linked paper finally proves it in five dimensions. It turns out to be much easier to count Voronoi parallelohedra than arbitrary parallelohedra, so one consequence is that we now know exactly how many combinatorially distinct five-dimensional parallelohedra there are: 110,244 of them.

The authors regret <insert corrigendum text> (\(\mathbb{M}\), archived, via).

FBI and Indiana University disappear and unperson Xiaofeng Wang (\(\mathbb{M}\), via, see also, see also, see also). Wang was James H. Rudy professor of computer science, engineering and informatics, director of the Center for Security and Privacy in Informatics, Computing, and Engineering, associate dean for research, ACM Fellow, IEEE Fellow, AAAS Fellow, etc. This does not appear to be immigration-related; he was placed on leave by Indiana two weeks before his house was searched, and the search was by FBI not ICE. Still, because of the current political situation, uninformed speculation is running wild. I do not want to add any of my own but this situation bears continued attention.

Arc diagram (\(\mathbb{M}\)), a graph drawing style in which vertices are placed on a line and edges are drawn as semicircles, now another Wikipedia Good Article.