Every European alive today is descended from Charlemagne
This is not a romantic exaggeration. It follows from the mathematics of genealogy—and so does something even stranger.
Trace your ancestry back forty generations and you should, in theory, have a trillion slots for ancestors. That is a number vastly larger than the human population that existed a millennium ago. The paradox resolves when you realise that family trees are not trees at all. They are webs. The same individuals occupy multiple slots because distant cousins married and lines looped back on themselves across generations.
In 1999, Yale statistician Joseph Chang calculated the implications. For any large population, there exists a most recent common ancestor of every living person—and that date is surprisingly recent. For people with European ancestry, the shared ancestor of every person now alive probably lived no earlier than around 1400, and possibly as recently as 1000. Charlemagne died in 814. He has living descendants. Therefore, every person of European ancestry alive today is a direct descendant of Charlemagne—and of every other European who lived at that time and left any descendants at all.
This extends globally. Douglas Rohde's computational modelling suggested the most recent common ancestor of all living humans—regardless of geography—probably lived no earlier than around 1400 BC. Geneticist Adam Rutherford uses this result to show that the concept of ethnic or genealogical purity is mathematically impossible. Your ancestors were everywhere. They were involved in every event in human history.