In a famous 1954 speech, Hermann Weyl said of Jean-Pierre Serre, "never before have I witnessed such a brilliant ascension of a star in the mathematical sky as yours." Surely Weyl would have been equally impressed that Serre's star is still burning bright some 50 years later.
Had Weyl lived but a bit longer he would have seen the comet that was Alexandre Grothendieck. It was visibly coming to those who looked in the right place in 1954, arguably brighter than all the other celestial objects in the period 1958-1970, and then occasionally visible (but only by telescope) since. We earthbound mathematicians have trouble understanding Grothendieck, what with his extreme abstraction and his utter independence from examples. At least we see stars moving predictably in circles. What to make of the brief bright comet moving crosswise?
Grothendieck-Serre Correspondence helps us understand both Serre and Grothendieck better. It contains about forty letters in each direction, mostly from the period 1955-1964. There are some easy-to-understand parts about things like getting better jobs and how "szyzygytic" is not quite correctly spelled. Mostly, however, the book documents with detail the creation of very formidable mathematics. Difficulties for readers are alleviated somewhat by twenty-seven pages of endnotes written recently by Serre. The current bilingual edition — original French on the left, a truly excellent translation into English on the right — certainly will help many too.
As a whole, the book gives an insider's view of one of mathematical history's most important research associations. Ironically, Serre and Grothendieck never wrote a paper together. It is overdue and fitting that their signatures have finally appeared together and handsomely on a book cover.
David Roberts is associate professor of mathematics at the University of Minnesota, Morris.