Fact: Pietro Agnesi was not a professor, or even a mathematician. As far as we know, he never even lived in Bologna. He was born into a family of wealthy silk merchants, but he may never have worked in the family business. Pietro Agnesi enjoyed socializing with scholars and noblemen. Some believe he educated Maria, and her younger sister, Teresa, to increase his own popularity in the upper class.
The myth that Maria's father was a professor continues to be published on the Internet (see About.com, for example) and in print references. [Wikipedia originally had it wrong, too, but they have since updated their information. However, there are other errors in their entry that I'll be addressing later.] This particular myth minimizes Maria's accomplishments in the field of mathematics--it's not as impressive for an 18th-century woman to have excelled in math if her father was a mathematician.
Here's another fact: By age fourteen, Maria Gaetana Agnesi was tackling tough problems in geometry and ballistics—the science of the flight patterns of bullets and cannonballs. (The following image is courtesy of Florida's Educational Technology Clearinghouse.)
For an explanation of this drawing, along with original source information, see the description at the bottom of this page.
Ballistics was a most unusual topic for an eighteenth-century girl to study--few girls could even read or write at that time! Maria was likely fascinated by math, and that's why she focused on it the way she did. Not because of her father's knowledge of the subject. However, he was the one who allowed her to study and he provided her with the best tutors.
Have you come across this myth about Maria? If so, please post a comment telling me where. I'll try to contact the source to set the record straight.