Paul Erdős died in 1996, but his most recent paper is from 2015, nearly 20 years later! There's a writeup at simonsfoundation.org/2015/12/1; the paper itself is math.ucsd.edu/~ronspubs/pre_tr

It's about Egyptian fractions – representations of rationals as sums of distinct unit fractions – and is motivated by the conjecture that it's always possible for all denominators to be semiprime. That's still open, but they prove that every integer has a representation with all denominators products of three primes.

A comparison of two parallel Canadian grant funding tracks shows that when reviewers are told to focus on the investigator rather than the proposed investigation, they are significantly more biased against women: cbc.ca/news/health/cihr-gender

Choose a random graph with countably infinite vertices by flipping a coin to decide whether to include each edge. Or, construct a graph with binary numbers as vertices, with an edge \(x\)—\(y\) when \(x<y\) and the \(x\)th bit of \(y\) is one. Or, construct a graph on primes congruent to 1 mod 4, with an edge when one is a quadratic residue mod the other. They're all the same graph, the Rado graph (en.wikipedia.org/wiki/Rado_gra)! It has many other amazing properties. Now a Good Article on Wikipedia.

Elsevier news roundup: German, Hungarian, and Swedish academics have been cut off from Elsevier journals after subscription negotiations broke down (nature.com/articles/d41586-019). Negotiations with the University of California are ongoing after a missed deadline (insidehighered.com/quicktakes/). Access to Germany was restored (nature.com/news/german-scienti) but without any long-term agreement. And the editorial board of _Informetrics_ resigned to protest Elsevier's open access policies (nature.com/articles/d41586-019).

The list of accepted papers from this year's Symposium on Computational Geometry just came out: eecs.oregonstate.edu/socg19/ac

Four of Conway's five $1000-prize problems (oeis.org/A248380/a248380.pdf) remain unsolved:

*The dead fly problem on spacing of point sets that touch all large convex sets, en.wikipedia.org/wiki/Danzer_s

*Existence of a 99-vertex graph with each edge in a unique triangle and each non-edge the diagonal of a unique quadrilateral, en.wikipedia.org/wiki/Conway%2

*The thrackle conjecture, on graphs drawn so all edges cross once, en.wikipedia.org/wiki/Thrackle

*Who wins Sylver coinage after move 16? en.wikipedia.org/wiki/Sylver_c

0xDE boosted

Three-regular, each 5-bit label appears exactly once, each vertex is the sum (xor) of its neighbors.

0xDE boosted

Finished my stained glass course, and the Menger sponge piece I was making over the course of it. Really, really happy with the results, and to have learned about this medium; the whole process was interesting and I wrote about it (with lots of pictures) here:

joshmillard.com/sgmenger/

#art #fractal

Did you know that two different graphs with 81 vertices and 20 edges/vertex are famous enough to have Wikipedia articles?

The strongly regular Brouwer–Haemers graph (en.wikipedia.org/wiki/Brouwer%) connects elements of GF(81) that differ by a fourth power.

The Sudoku graph (en.wikipedia.org/wiki/Sudoku_g) connects cells of a Sudoku grid that should be unequal. Sudoku puzzles are instances of precoloring extension on this graph.

Unfortunately the natural graphs on the 81 cards of Set have degree ≠ 20...

"Ancient Turing Pattern Builds Feathers, Hair — and Now, Shark Skin": _Quanta_, quantamagazine.org/ancient-tur and original article in _Science Advances_, doi.org/10.1126/sciadv.aau5484

Researchers at the University of Florida led by Gareth Fraser and his student Rory Cooper used reaction-diffusion patterns (also named "Turing patterns" after Turing's early work; see en.wikipedia.org/wiki/Turing_p) to model the distribution of scales on sharks, and performed knockdown experiments to validate their model in vivo.

The Cal Poly ag students have started selling these blood oranges at the local farmer's market, as they do every year around this time, only $1 for five. In the summer they sell sweet corn on the cob.

How to handle journal referees who ask authors to add unjustified citations to their own papers? Is their misbehavior protected by the anonymity of peer review or can they be publicly named and shamed? retractionwatch.com/2019/02/07

_Quanta_ writes up recent progress on the Erdős–Szemerédi sum-product problem (en.wikipedia.org/wiki/Erd%C5%9), that any set of numbers must either have many distinct pairwise sums or many distinct products: quantamagazine.org/the-sum-pro

Progress: "many" increased from \(\Omega(n^{4/3 + 1/1509})\) to \(\Omega(n^{4/3 + 5/5277})\).

Hannah Bast's slides on the European Symposium on Algorithms 2018 Track B experiment (two independent program committees decided on the same set of papers and then the conference accepted the union of their acceptances): ad-publications.informatik.uni

Some conclusions: the initial scoring is remarkably consistent, and per-paper discussions to reconcile differences of scoring are useful, but the final decision on which "gray zone" papers to keep is random and could be replaced by a simple threshold.

Somehow I missed this when it came around last October, but Rod Downey, a New Zealand-based theoretical computer scientist who co-founded the theory of parameterized complexity, has won the Rutherford Medal, New Zealand's highest science award: radionz.co.nz/national/program

Holes and their reflections. (The reflections are in the curved surface of an espresso portafilter.)

Creating a 3D-printable Lorenz attractor: mathvis.academic.wlu.edu/2017/

From Elizabeth Denne's "Visions in Math" blog which, sadly, seems to have gone on hiatus after publishing this in 2017.

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