Wikipedia’s article on rigid analytic geometry links to an interesting survey paper by Brian Conrad on the subject. Rigid analytic geometry is the attempt to translate the theory of complex analytic geometry to the p-adics. The theory is surprisingly complicated.

You know, mathematical terminology cannot be parodied. Mathematicians have invented groups, semigroups, quasigroups, pseudogroups, and two mostly-unrelated concepts both known as groupoids. They have invented both formal groups and quantum groups, neither of which are kinds of groups. And while the study of groups is a branch of algebra, most groups are not, in fact, algebraic.

Continuing the architectural theme, Isabel at God Plays Dice has a post on the ultimate fate of the real world Königsberg bridge problem. Königsberg had seven bridges, and in 1736 Euler proved it was impossible to find a path that allowed you to cross each bridge exactly once.

In World War II, several of the bridges were bombed, and later some were replaced. In present-day Königsberg, now Kaliningrad, there are now only five bridges, and you can now find a path that allows you to cross each bridge exactly once.

Now that this is primarily an architecture blog, here’s Falkirk Wheel, a science-fiction-looking rotating boat elevator in Scotland.

Actual math content soon.

A. J. Berrick has an interesting paper explaining how a topologist thinks about group theory. Topology and group theory are connected throught the fundamental group. For every group, topologists can construct a space with that group as its fundamental group. Some of these can be very complicated, even for comparatively uncomplicated groups. For example, perfect groups lead to very scary-looking constructions.

The paper is A topologist’s view of perfect and acyclic groups.

I have just learned from multiple Google searches that a) apparently I think Hilbert is spelled Hibert (with no l), but b) Google is smart enough to correct me. Next year I’m letting Google do my taxes.

There is a new site, outofprintmath, that is collecting information on which out-of-print books the mathematical reading public would like to see brought back in print. At the moment there are 67 books listed, many of them are surprisingly well-known. I had no idea so many classic texts were out of print. For example, Curtis and Reiner’s Methods of Representation Theory, Kuratowski’s Topology, and Riordan’s Combinatorial Identities are all out of print.

Timothy Chow tells the story behind the site’s creation here.

Todd at Topological Musings has posted an elementary proof of the Hairy Ball Theorem: the theorem that all vector fields on a even-dimensional sphere must vanish somewhere. The elementary proof is by Milnor.

The intersection of two interstate highways, I-95 and I-695 near Baltimore, is topologically non-trivial; it features a non-trivial braiding. Unfortunately, the interchange is scheduled to be redesigned.

Via Low-Dimensional Topology.