While I was away partying at Amherst, Andre LeClair and his grad student appear to have solved high-temperature superconductivity. There are three major papers:
http://arxiv.org/abs/0805.4182, "A model of a 2d non-Fermi liquid with SO(5) symmetry, AF order, and a d-wave SC gap," Eliot Kapit and A. LeClair
http://arxiv.org/abs/0805.2951, "A unique non-Landau/Fermi liquid in 2d for high Tc superconductivity," Eliot Kapit and A. LeClair
http://arxiv.org/abs/0805.4200, "On the New Model of Non-Fermi Liquid for High Temperature Superconductivity," Henry Tye
High-temperature superconductors are a class of materials (doped cuprate compounds) that are superconductors -- i.e. transmit currents without resistance -- at much higher temperatures than conventional superconductors (mostly metals). Why they do this -- or, indeed, why they become superconductors at all -- has been one of the big open questions in theoretical condensed matter physics for 20 years.
I don't yet know what the response to these papers will be; however, if their analysis is correct, they appear to constitute an explanation of high-temperature superconductivity. I wonder about the opacity of the titles. Andre LeClair is a mathematical physicist at Cornell; I met him briefly when I visited Cornell as a prospective grad student, and he strongly discouraged me from working with him on the grounds that most of his recent research projects hadn't worked out.