The latest “This Week’s Finds” by John Baez discusses Felix Klein and his “Erlanger Programm”, which essentially was the idea that geometry should be understood as the study of Lie groups G, their subgroups H, and coset spaces G/H. This, supplemented with Cartan’s notion of a connection, allowing things that only locally look like G/H, is very much at the heart of our modern view of geometry. John gives links to quite a few things worth reading by and about Klein here. Another very interesting document is Klein’s own history of 19th century mathematics “Development of mathematics in the 19th century”.
I’m very much looking forward to the next installment of TWF, where John promises some insights into Hecke algebras. He also has a wonderful posting that generated an interesting discussion at the n-category cafe on the topic of mathematical exposition, entitled Why Mathematics Is Boring.
I wrote a bit about the LHC Theory Initiative here last year. They have just announced the award of two graduate fellowships and say that they will be awarding postdoctoral fellowships in the future. Unclear from this if they were successful in their efforts to get NSF funding, the solicitation of applications for the fellowship just mentions an older grant to Johns Hopkins.
NPR has run a two part series on the LHC (here and here). The first part features CERN theorist Alvaro de Rujula. I had the great pleasure of taking a particle theory course from him when I was a student at Harvard a very long time ago. He cut an impressive figure, and provided a survey of the subject that was both enlightening and entertaining.
Scott Aaronson provides quotes from someone else (Gian-Carlo Rota) whose lectures I attended around the same time, including one that ends “You and I know that mathematics, by definition, is not and never will be flaky”. I kind of agree with the sentiment in the full quote, but my experience with Rota back then was a rather weird one. For some misguided reason I had decided that since category theory was the most abstract kind of mathematics I had heard of, it would be a good idea to take a course on it. The only course on the subject was a graduate course down at MIT offered by Rota, so I started going down there to sit in on it. A few lectures into the course Rota all of a sudden announced that he had decided that only those students actually enrolled for credit should be taking the course, and that the several of us who were just auditing should leave. So we did, somewhat mystified (it’s not like the room was over-packed or anything). To this day, I still don’t know what that was about. Perhaps Rota knew that he was doing me a favor by stopping me from thinking about category theory at that point in my education, when in retrospect it seems likely that it really would have been somewhat of a waste.
There’s a lot more about Rota at this web-site. His capsule reviews in the back of the journal he edited, Advances in Mathematics, provided outrageous entertainment for many years (although some might at times think that they were, well, flaky…).