*Mathematicians Under the Nazis*is a long, meticulous and painstakingly researched book about the history of German mathematics, mathematical institutions, and mathematicians during the Nazi era.

The book does a good job of dispelling a number of impressions that one might have of Mathematicians and Nazis. First, there is one reading of Segal's book that can be construed as the history of the petty bickering among the mathematicians in Nazi Germany. German mathematicians quarreled incessantly. Many of them spent a lot of time jockeying for power. Almost none were above political quarrels or denunciations. Many of them got truly swept up in Naziism. Many had little problem with the initial full-scale of removal of Jews from universities. This was especially true in Gottengen, which was a mathematical powerhouse and also a bastion of right-wing activity. Segal traces much of this attitude to the idea of the good German university professor as a civil servant who was in some way beholden to the state.

Secondly, lest one get the impression that the German state was efficient, Segal clears much up there too. First there were many overlapping bureaucracies, all of which competed for resources, and all of which were driven to backstabbing to get ahead.

In the "total state" as Nazi Germany was, there was a push to make all the country's institutions hierarchical. That is, there would be a leader of each institution with a clear command structure. The Nazi state was interested in this, and other types of existing hierarchies mattered little to them. In an attempt to get ahead then, there were various mathematicians who attempted to ingratiate themselves as "fuhrer" of German mathematics.

One of the main contenders for this position was perhaps the most colorful character in the story. Ludwig Bieberbach, who was a rather respected mathematician, attempted to Nazify mathematics itself. In a series of articles, Bieberbach identified a style of mathematics that he thought was Aryan and another that was Jewish. Racially typologizing mathematics was part of a tradition that went back at least as far as Felix Klein, and was used by many, especially Oswald Spengler in his famous

*Decline of the West*. This generated something of a small research program in "Nazi Mathematics".

Segal's book is rife with detail, and tells the stories of many of the Jewish and German mathematicians who were impacted by Naziism, like Courant, Landau, Suss, Blaschke, . . . The Book also details the many mathematical institutions in Nazi Germany, such as Nazi mathematics camps, and mathematics in concentration camps.

The book is long and detailed and was an enlightening read.