Spring break brought a lot of time to catch up on my reading this year. Best of all, one my reserves
Love and Math - Edward Frenkel came into the library before we left for the break. Overall, it was good read and led me to think more about abstract algebra than I usually do in my day job. The book interleaves Frenkel's autobiography with some of the math he was encountering along the way described in broad and fairly accessible strokes. I found this fascinating from several angles. There are the lengthy descriptions of growing up in 1980's russia pre-glasnost. One of the hardships he had to overcome was antisemitism that prevented Frenkel from attending the premier university for theoretical math and instead he ended up in an oil and gas applied math program, sneaking into the lectures with other fellow Jews.
On the flip side the description of his math education was quite positive. By 16 he was done with what we consider the normal elementary math sequence and had found a math mentor who introduced him to abstract algebra. Prior to that he was more interested in quantum physics (although I think the divide between the two is overstated) He then moved to college and was taken in wing by a very strong group of math professors and fellow students. Its hard to imagine a similar environment here in the U.S.
Also interspersed are longer discussions about topics such as loop theory and symmetries. These are done at the descriptive level and not suitable for really learning the subject. But its so rare to find any such material and it was great as a tour of what topics concern modern mathematical research. I found the descriptions of the Langland Program to be especially interesting. http://en.wikipedia.org/wiki/Langlands_program
In sum, I'd definitely recommend this to others. One of Frenkel's main goals is to give a clearer picture of what mathematicians really do and here he succeeds brilliantly. For future years I'm going to think about how I could connect material such as this to the fifth graders. So few kids at this point have any idea of the general terrain of mathematics and what a further career might concern. More immediately, they know they will study trigonometry and calculus eventually but at this point they couldn't really tell you what they concern in even very general terms. This is quite different from how we approach almost every other subject in the primary grades.