>>What if Galileo's daughters, rather than being put in a convent, were able to marry and participate in the society of the Renaissance? By all accounts, they were as brilliant as their father.<<

Alternately: in our world, convents were one of the few places that educated women (unless your family had private tutors).

What about a Rennesance convent that was a way for brilliant women to be educated and do work as brilliant polymaths?