Helmut Hasse and Emmy Noether are two of the giants of 20th century algebra and number theory. Noether, who was 16 years older, had already begun her revolutionary work on abstract algebra by the time Hasse came into prominence in the early 1920s. Their correspondence resulted from Hasse's interest in Noether's new ideas, but it quickly blossomed into a full-blown conversation about mathematical ideas. The letters are reproduced here with extensive annotations that include extensive discussion of the mathematics.
The correspondence covers two periods that are particularly interesting. The first is the time during which Brauer, Noether, and Hasse worked on their famous theorem about division rings over number fields (which some would call the Albert-Brauer-Hasse-Noether theorem to highlight the fact that A. Adrian Albert also played a part). The second is the period of Noether's last letters, written just before her untimely death in 1935. They give us at least a hint of her feelings on being forced to leave Germany and some idea of how she reacted to the American mathematics community when she arrived here to teach at Bryn Mawr.
A final section of the book includes a few letters notifying Hasse of Noether's unexpected death and some correspondence between Hasse and Noether's brother Fritz, who was then a professor in Tomsk, Siberia. An index of names mentioned, an extensive bibliography, and short biographies of the many mathematicians who are mentioned are provided to round off the volume.
Some of the correspondence between Hasse and Fritz Noether concerns Emmy Noether's papers, which were apparently sent from Bryn Mawr to Tomsk, but may never have actually arrived there. In any case, Noether's papers have been lost. As a result, most of Hasse's letters to her are not available (he did keep copies of a few of them). So what we have here, with a very few exceptions, are Noether's letters to Hasse. They offer a valuable window into the mind of one of the century's most influential algebraists. For historians of mathematics, this is an indispensable book, which every serious research library will need to have. But I suspect it might also interest algebraists and number theorists, since it gives them a glimpse of how some of the most important ideas in their fields were developed.
This book actually has two titles on the cover; the one given above and Helmut Hasse und Emmy Noether: Die Korrespondenz 1925–1935. The German title is perhaps more accurate, since the only part of the book that is in English is the introduction (and even that shows signs of having been written originally in German). The authors say that they "have abstained from translating the Hasse-Noether letters. In our opinion," they add, "the impulsive and unmistakable distinctive style of Emmy Noether can best be appreciated in her original language. Nevertheless, if there is some demand then we may offer English translations some time in the future."
Fernando Q. Gouvêa is professor of mathematics at Colby College. He is very interested in the history of algebra and number theory in the early twentieth century. This book made him feel sorry that he didn't take that third semester of German.