The concept of the professional mathematician came relatively late to European history. (This truism is expressed in history of mathematics code as "Fermat was a lawyer.") After the ingenious dabblers had had their due, an array of institutions, titles, degrees, prizes and professorships secured mathematics as a professional endeavor. Among its other consequences, the rise of professional mathematics created a new set of formal barriers to women. I will summarize the experiences of three who succeeded in the new atmosphere: Sophie Germain, Sofia Kovalevskaia, and Alicia Boole Stott. These 19th-century mathematicians came from different countries, were of three distinct generations and hailed from contrasting economic backgrounds. I am uniting them here not merely to pay homage to exceptional talent, luck, and resources, but to highlight commonalities in their experiences as women. I wish to pose an important and difficult question: What do these women's experiences tell us about the construction of mathematical knowledge?