It seems that when you play around with the Math Genealogy Project, starting at some contemporary mathematician and going backwards through their advisor, advisor's advisor, etc., you tend to arrive at a famous mathematician once you get back to around the late 1700s. Does this indicate there were relatively few active mathematicians back then, and if so how many were there? Or is it perhaps an artifact of the tendency to keep better track of famous mathematicians' students?

Here is a more difficult follow-up question: What percentage of mathematicians from the late 1700s have some of their work preserved until the present day? One difficulty in answering this is that a mathematician who has none of their work preserved is much more likely to have their name be forgotten altogether, in which case we might not know of their existence in the first place. Still, I think it should be possible to provide a reasonable estimate.

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    $\begingroup$ The science of population genetics is concerned with very similar questions, of course, in a very different context: what can we infer from present populations (and the fossil record) about past interrelatedness? There are interesting mathematical results about ancestral lines - what percentage of a population can be expected to have living ancestors this or that many generations later; what can you expect to see when you track lineages back from the present. I wish somebody could tell us e.g. what the Moran model would say about the question. $\endgroup$ – Bence Mélykúti Sep 13 '18 at 8:21

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