Their research revealed a new surprise: the woman is the great-great-great-great-great-great-great grandmother of UK Foreign Secretary Boris Johnson.
The body was uncovered in 1975 while renovations were being done on Basel's Barfüsser Church.
She was buried right in front of the altar, clearly well fed, and wearing good quality clothes.
This was obviously the body of a wealthy lady of Basel.
But who was she exactly, and when did she die?
There was no gravestone to indicate her identity, but initial testing of her wooden coffin suggested it dated from the 16th Century.
Another clue: her body was riddled with mercury - a standard treatment for syphilis from the late 15th to the 19th Century. Highly toxic mercury treatment was more often a kill than a cure and it was this that preserved her body.
But that still left open the question of who she was.
Basel in the 16th and 17th Centuries was a wealthy trading city; its port on the river Rhine was a key hub for moving goods across Europe, and it remains so today.
Local historians knew that members of Basel's wealthy families were buried in and around the Barfüsser Church.
Some were clearly named in records, some had clearly marked gravestones.
But not the mummy. It only became clear in 2017, in newly discovered archives, that the mummy had been uncovered once before, in 1843.
Those records led historians to suspect the mummy was a member of a well-established Basel family, the Bischoffs.
Using the most up to date methods, scientists were able to extract DNA material from the mummy's big toe.
This was compared, by scientists working independently from one another, with DNA taking from living descendants of the Bischoff family.
The results were clear, showing a 99.8% probability that the descendants and the mummy were all from the same maternal line.
Now the scientists and the historians were sure: the mummy was none other than Anna Catharina Bischoff. Born in Basel in 1719, she died there in 1787.
Once her identity had been established, genealogists were able - with the help of the efficient records of births, marriages, and deaths which tend to be kept by the wealthier classes - to trace more of Anna Catharina's descendants.
She had seven children. Only two survived childhood, but one daughter, also Anna, married a certain Christian Hubert Baron Pfeffel von Kriegelstein. Five generations of von Pfeffels later, and we find Marie Luise von Pfeffel marrying one Stanley Fred Williams.
Their daughter Yvonne married Osman Wilfred Johnson Kemal… and their son, Stanley Johnson, is British Foreign Secretary Boris Johnson's father.
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