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One might suppose that the Rubik’s cube toy invented by Ernö Rubik in 1974, however ingenious, is geometrically too simple to present much of an analytical challenge. Nevertheless, finding the minimum number of moves to solve the cube from any position was a hard-won achievement to which numerous mathematicians contributed. After Kloosterman, the upper bound continued to come down by successive degrees as new insights and tools were brought to bear. Michael Reid showed in 1995 that the final answer could not be less than 20, but it took 15 years more to prove that 20 moves would always suffice. That proof was presented in July, 2010 in a paper by Tomas Rokicki, Herbert Kociemba, Morley Davidson and John Detridge. Their approach combined careful problem analysis with a highly efficient approach to searching solution paths on the computer. Even then, the parallel processing power of cloud computing was needed to complete the demonstration in mere weeks rather than decades or centuries. (For more information, please see the source article at NextBigFuture.)

According to Wikipedia, eight grandmasters resided in Reykjavik in 2005, among a population of 110,000, which works out to better than one grandmaster per 14,000 inhabitants. The global average is about one grandmaster per five million population. American chess legend Bobby Fischer was one of the eight; he died in 2008.

The elementary particles that make up ordinary matter are the electron and the quark. The neutrino is also an elementary particle, but is not a constituent of matter. The other particles mentioned are not elementary, all being combinations of quarks. Any particle composed of multiple quarks is, by definition, a hadron. The hadrons are divided into two groups: the mesons, each formed from a quark and an antiquark, and the baryons, each a combination of three quarks or three antiquarks. Because there are many possible ways of combining three quarks, the baryons are a diverse family, but two of its members are the familiar proton and the neutron, which make up the nuclei of atoms. These, together with the much lighter electron, account for virtually all directly detectable matter. However, scientists now widely accept that most of the matter in the universe — about three-quarters — is of a type not directly detectable. The actual composition of this ‘dark matter’ is far from settled, but it appears unlikely that it can be explained in terms of the familiar ingredients of ordinary atoms.