Reprinted from the Newsletter of the Association for Women in Mathematics, Vol. 23, No.4 (July/August 1993), 11-12.
In 1840, Florence Nightingale begged her parents "to let her study mathematics instead of doing worsted work and practicing quadrilles." Her mother "did not approve, home duties were not to be neglected for mathematics." She assumed that her daughter's destiny was marriage, "and what use were mathematics to a married woman?" Her father, who loved math and had communicated that love to his daughter, nevertheless urged her to study more appropriate subjects (for a woman), "history or philosophy, natural or moral. Florence expressed her preference for mathematics by saying, "I don't think I shall succeed so well in anything that requires quickness as in what requires only work."  Her parents finally granted permission. Years later, her mathematical approach saved the British army at Scutari during the Crimean war and provided the data that led to hospital reforms. 
Only after long emotional battles was Florence permitted to have tutors in mathematics. (One of her tutors was J.J. Sylvester.) She learned arithmetic, geometry, algebra, and before her involvement with nursing, spent her time tutoring children in these subjects. In the British Museum, one can read lesson plans in her handwriting (including story problems based on the lives of the children she was tutoring) for teaching arithmetic and geometry. She includes reminders to tell pupil teachers "to write notes of all the lessons they will give through the next week--the must never give them unprepared--of what they will say...tell them you prepare yourself."
Her lesson plans show concern about the education of girls. "Girls' arithmetic has been neglected--their geography should be made arithmetical." She made notes to ask such questions as:
How high is the reindeer? Are you as high? How high are you? 3 feet--how much is that? a yard-- are you a quadruped? How far is the topmost point of Europe from the Equator? How far do you come to school? Two miles-- now, if you were to walk two geographical miles a day, how long should you be walking to the equator? 
Clearly, she espoused teaching by questioning. In later years, when she wrote on nursing, she expressed the hope that the memory of Socrates would help her with the art of questioning, so that "those who read may learn not of me but of themselves."
Florence Nightingale's interest in mathematic extended beyond th subject matter itself, as shown in letters to her sweetheart during 1846. For example, in May she wrote, "There is a most lovely character given of D'Alembert's the great mathematician's lightheartedness...It says that it is the exclusive privilege of the exact science, to enjoy everyday some new truth which comes to reward one's work." Again, in August: "The loss of power of the high priest...the inconsiderate 'following of the leader' of the people, are everyday feelings in our hearts, just as is the jealousy, which brought under a different system of police, Abel to the grave." Her letters how her sense of humor. In September after attending a political speech, she wrote: "I have invented a new system of Logarithms (finding the capacities of arithmetic not sufficiently extensive) to count the number of times 'Imperial Majesty' occurs in the speech...." 
Nightingale helped to promote what was then a revolutionary idea (and a religious one for her) that social phenomena could be objectively measured and subjected to mathematical analysis. Her work with medical statistics was so impressive that she was elected (in 1858) to membership in the Statistical Society of England. One of the pioneers in the graphic method of presentation of data, she invented colorful polar-area diagrams to dramatize medical data.  Although other methods of persuasion had failed, her statistical approach convinced military authorities, Parliament, and Queen Victoria to carry out her proposed hospital reforms.
During the American Civil War, Nightingale was a consultant on army health to the United States government. She also responded to a British war office request for advice on army medical care in Canada. Her mathematical activities included ascertaining "the average speed of transport by sledge" and calculating "the time required to transport the sick over the immense distances of Canada."
Florence Nightingale was a feminist, of course. It is amusing to see that she dedicated Introductory Notes on Lying in Institutions to the shade of Socrates' mother. She fought for the privilege of studying math, for the right to be a nurse, and for every woman's right "to bring the best that she has, whatever that is to the work of God's world... to do the thing that is good, whether it is 'suitable for a woman' or not." She cautioned against extremism, "which urges women to do all that men do...merely because men do it, and without regard to whether this is the best that women can do."  She was a true mathematician in her love for reasoning, always questioning assumptions and taking great care in the process of reaching conclusions.