First, a couple of examples of recent progress in mathematics
- Terry Tao has some new ideas about the Navier-Stokes equation. See his blog here, a paper here, and a story by Erica Klarreich at Quanta here.
- I’ve been hoping to find more time to learn enough to write something intelligible about a major new advance: Peter Scholze’s recent work on the p-adic geometry of Shimura varieties and results linking torsion classes and Galois representations. I’m still far from being up to that task, but Scholze’s Marston Morse lectures at the IAS are a good place to start (see here, here and here). Last week MSRI hosted a very successful week-long “Hot Topics” program on this, see here.
Update: One more, for those of you not getting enough multiverse. Today’s Washington post has an op-ed from Bush speech-writer Michael Gerson (at one point the ninth most influential evangelical Christian in the US, if you believe Wikipedia and Time). The title is Physics is Enjoying a Golden Age (also available here). Gerson thinks physics is in a Golden Age because he has just read Tegmark’s book and is very excited that physics has now become metaphysics, with room for God again:
The point here is not that Tegmark’s theories are broadly accepted, only that such theories are no longer considered absurd. Physics has seen the return of the unseen — parallel universes, infinitesimal strings, floating and colliding branes — that are reasonably inferred without being physically observed. I can think of other creative forces in that category. Not for centuries has physics been so open to metaphysics, or more amenable to an ancient attitude: a sense of wonder about things above and within.