Mathematics in War and peace

Stephen Ahearn 1994 has an article in the August-September 2005 issue of The American mathematical monthly, dealing with the origins and significance of some mathematical metaphors in War and peace. Tolstoy spoke of history as “continuous,” in the mathematical sense, and held that the accounts of historians who treated it as a sequence of discrete events or as a reflection of the wills and acts of a small number of “great men” are false or, at best, rough approximations. He summarizes his own method thus:

Only by taking infinitesimally small units for observation (the differential of history, that is, the individual tendences of men) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.

Ahearn points out that Tolstoy probably adopted this view as a result of conversations with a friend, Sergei Urusov, who was a mathematician with an interest in history.

I was especially moved to see that Ahearn dedicated the paper to the memory of my colleague John Mohan.

Ahearn, Stephen T. “Tolstoy's integration metaphor from War and peace.” The American mathematical monthly 112 (2005), 631-638.