Who is the audience for scholarship in the history of mathematics? Historians of mathematics, perhaps, or maybe some historians of science. But a much larger group is mathematicians and students of mathematics. I talk to mathematicians a lot, and I believe that we are in fact doing something of interest to mathematicians. We have an advantage over historians of other subjects. A distinguished mathematician asked me recently what Euclid had said about a particular result. I doubt that many historians of physics are asked by physicists, “Tell me, how did Aristotle prove that the earth can't move?” Mathematicians use history to enliven the subject, or to motivate topics, or to humanize mathematicians to a general audience, or to justify mathematics to government and public. But is the history right? As historians, we think getting it right matters. Do mathematicians think that?
Now there are a lot of myths out there in the mathematics community. I will walk the reader through seven of the myths I have encountered in my career as a historian of mathematics. I will suggest how to debunk them, and, more important, what is at stake, for the teaching and understanding of mathematics, in getting that particular thing right. At the end, I will bring this together by telling you again how important the historian's work can be.
A.Myth: The social history of mathematics is easy; just determine what nation or group your mathematician comes from and generalize.
Consider how Eric Temple Bell, in his book Men of Mathematics, describes some controversies between the 19th-centurymathematicians Leopold Kronecker and Georg Cantor.