Linkage
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Modern CPUs have \(\mathbb{F}_2\) polynomial multiplication as a single operation (\(\mathbb{M}\)). This should be useful for other kinds of bit-hacking, not just algebraic computation.
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Richard Palais’s historic role in promoting the use of computers in mathematics (\(\mathbb{M}\)).
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Emily Fox on why hash tables are good, actually, despite theoretical misgivings.
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All polyhedral manifolds are connected by a 2-step refolding (\(\mathbb{M}\)), new preprint by Alice Zhang and a big team of coauthors.
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Wikipedia’s list of works entering the public domain next year (\(\mathbb{M}\)), with details depending on local laws. See also a related list in an annoying advent-calendar format (via). The mathematical works I saw listed include Julian Coolidge’s A Treatise on the Circle and the Sphere and L. E. Dickson’s History of the Theory of Numbers (v1, v2, v3) under life+70 rules, but these are already online as out-of-copyright at the Internet Archive.
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While looking up polar zonohedra for a new Wikipedia article on zonoids (\(\mathbb{M}\)), I learned that some people use the word “zome” for a geodesic-dome-style building in the shape of a zonohedron. George Hart also provides examples in his 2021 “The Joy of Polar Zonohedra. If you take enough generators, these shapes converge to the surface of revolution of a (scaled) sine curve, as Coxeter knew, and this sort of convergence of zonohedra to something is exactly what defines the zonoids. It seems to be the case that the revolved sine curves are the extreme case of surfaces of revolution that are zonoids, and that any symmetric surface of revolution that curves more gently in the middle (like a lemon, the surface of revolution of a circular arc) should also be a zonoid, but I haven’t found a reference saying so or clarifying what the right formalization of curving more gently might be.
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On several irrationality problems for Ahmes series (\(\mathbb{M}\)). Terry Tao describes a new preprint on infinite series of unit fractions.
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The provenance of our copies of Euclid’s Elements (\(\mathbb{M}\)).
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The Depths of Wikipedians (\(\mathbb{M}\), via, via2, via3), interview with Annie Rauwerda on the state of Wikipedia by Asterisk magazine. “A conversation about yogurt wars, German hymns, tropical cyclones, and the people who make Wikipedia function”.
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Progress on the formalization of the proof of Fermat’s last theorem (\(\mathbb{M}\)), with interesting background on shaky proofs in its foundations in crystalline cohomology.
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New Zealand halves its funding for basic research and cuts all such funding in social science and humanities (\(\mathbb{M}\), via).
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Intriguing and now-lost string art by Kurt Mahler at Australian National University. Update: replicated and extended.
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Mapmatics by Paulina Rowińska (\(\mathbb{M}\)), reviewed by The Aperiodical just in time for holiday gift-giving to people who love both mathematics and maps.