…are condemned to repeat it.” (George Santayana.) I doubt there exist many people capable of rediscovering stochastic calculus but it is surprising how many “financial mathematicians” claim to know it while demonstrating utter ignorance of the foundations. The 2004 paper “A short history of stochastic integration and mathematical finance the early years, 1880–1970″ by Protter and Jarrow documents the history of mathematical finance in great detail. I am convinced that knowing the events leading to discoveries of certain difficult to understand mathematical facts makes the facts themselves much more natural and accessible. If you have ever been puzzled by, say, Itō isometry or Doob-Meyer decomposition, the paper will show all the gradual refinements the ideas underwent. There are also also all kinds of less mathematical stories in the text – like how American and European options got their names.
In conclusion, here is another, less famous, part of the quote above: “…when experience is not retained, …, infancy is perpetual.”
