Links

In 1906, famous composer John Philip Sousa took to Appleton’s Magazine to pen an essay decrying the latest piratical threat to his livelihood, to the entire body politic, and to “musical taste” itself. His concern? The player piano and the gramophone, which stripped the life from real, human, soulful live performances. “From the days when the mathematical and mechanical were paramount in music, the struggle has been bitter and incessant for the sway of the emotional and the soulful,” he wrote. “And now in this the twentieth century come these talking and playing machines and offer again to reduce the expression of music to a mathematical system of megaphones, wheels, cogs, disks, cylinders, and all manner of revolving things which are as like real art as the marble statue of Eve is like her beautiful living breathing daughters.” —“100 Years of Big Content Fearing Technology—in its own words,” Nate Anderson, Ars Technica

In the classic cosy catastrophe, the catastrophe doesn’t take long and isn’t lingered over, the people who survive are always middle class, and have rarely lost anyone significant to them. The working classes are wiped out in a way that removes guilt. The survivors wander around an empty city, usually London, regretting the lost world of restaurants and symphony orchestras. There’s an elegaic tone, so much that was so good has passed away. Nobody ever regrets football matches or carnivals. Then they begin to rebuild civilization along better, more scientific lines. Cosy catastrophes are very formulaic—unlike the vast majority of science fiction. You could quite easily write a program for generating one. —“Who Reads Cosy Catastrophes?” by Jo Walton, Tor.com

The specific aim of the Polymath Project was to find an elementary proof of a special case of the density Hales–Jewett theorem (DHJ), which is a central result of combinatorics, the branch of mathematics that studies discrete structures (see ‘Multidimensional noughts and crosses’). This theorem was already known to be true, but for mathematicians, proofs are more than guarantees of truth: they are valued for their explanatory power, and a new proof of a theorem can provide crucial insights. There were two reasons to want a new proof of the DHJ theorem. First, it is one of a cluster of important related results, and although almost all the others have multiple proofs, DHJ had just one — a long and complicated proof that relied on heavy mathematical machinery. An elementary proof — one that starts from first principles instead of relying on advanced techniques — would require many new ideas. Second, DHJ implies another famous theorem, called Szemerédi’s theorem, novel proofs of which have led to several breakthroughs over the past decade, so there is reason to expect that the same would happen with a new proof of the DHJ theorem. —“Massively Collaborative Mathematics,” Timothy Gowers & Michael Nielsen, Nature