Linkage for the end of the year

Everipedia is the Wikipedia for being wrong. Linked not to diss a rival encyclopedia but to explain why Wikipedia’s strict standards for including only information that can be verified in reliable published sources (especially when it’s about a living person) are important.

Recent gossip on Mochizuki’s purported proof of the abc conjecture, and more gossip. The story that his work has already been accepted to the journal that he’s the editor-in-chief of turns out to be exaggerated, but he did submit it there. And commenters are starting to point to specific points in the proof that seem problematic.

The matroid parity problem, a powerful algorithmic problem on matroids with many applications in combinatorial optimization and graph drawing, among them finding large planar subgraphs and embedding graphs onto surfaces of maximum genus. New Wikipedia article.

Keevash’s solution to the combinatorial design problem. It’s a couple years old, but still a breakthrough: almost all parameters for combinatorial designs have solutions.

Chopstick sleeve origami art exhibit. Who could resist playing with the convenient piece of paper left over from wrapping your chopsticks? Not me.

Partisan gerrymandering with geographically compact districts. Why looking at the shapes of congressional districts is inadequate as a test for whether they’re unfairly drawn — you have to look more carefully at the distribution of people and their preferences within those shapes. From a preprint by Boris Alexeev and Dustin Mason.

Hexaflexaflakes (G+). Vi Hart cuts through some baloney regarding the number of folds needed to achieve a given degree of symmetry in paper snowflakes.

Platonic solids on their summer holiday (G+, from “You’re All Just Jealous Of My Jetpack” webcomic). With bonus hosohedron. It’s now the summer holidays in the southern hemisphere, right?

Use of free textbooks is rising, but barriers remain (G+). The Chronicle of Higher Education discusses factors behind the slow uptake of free textbooks (now up to 9% from a previous 5%) and efforts by publishers to recapture that market by publishing value-added non-free versions of the same texts.

Google Maps’s moat. How integrating lower-level data such as the shapes of buildings and the precise locations of businesses lets Google maps build higher-level constructs such as “areas of interest” (business corridors within cities), and what this says about their dominance in mapping.

Vanishing line on Conway’s game of life. If you start with one-cell-thick infinite line of live cells in Conway’s game of life, it behaves like a one-dimensional cellular automaton whose time-space diagram looks like a Sierpinski triangle, but if it’s finite then it shrinks from its ends, and the Sierpinski triangle (at a larger scale) gets frozen into the debris left behind as it shrinks.

Chaos Train (G+). An amusing exercise on quantifier ordering by Joel David Hamkins. See also his three-quantifier Monkey Madness.

Science YouTubers attempting a graph theory puzzle (G+). It’s the classic three utilities puzzle, on a mug. (The mug itself is available for purchase.)

Enumerative Combinatorics, volume 1, second edition (via David Roberts and Luis Guzman). Free online almost-final copy of Stanley’s classic book.