How differently do mathematicians and historians think? It would seem the factor is about a billion.
I went to a lecture today by a history professor. His abstract had raised the question, “How many people alive today are descendants of Genghis Khan?” The answer he gave in the lecture was, around 16 million.
That was the word he used, simply “descendants”. However, after a question it emerged that he actually meant not just descendants but descendants in a direct male line, male to male to male to male (hence all with the same Y chromosome).
This is a sensational, spectacular, supernova kind of a difference. Suppose Genghis Khan lived 30 generations ago. In principle each of us has up to 2^30 ≈ 1 billion ancestors back then. (The actual number will be less because of overlaps and limited population size.) If one of your ancestors was Genghis Khan or William the Conqueror or Attila the Hun, that’s not very remarkable. But if your father’s father’s father’s … father was Genghis or William or Attila, that’s astonishing.
To this historian, the distinction was evidently a footnote.
[27 September 2016]