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-they 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 mathematics extended
beyond the 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 show 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.
1. Woodham-Smith, C., Florence Nightingale. New York: Atheneum. p. 37.
2. Pickering, G. Creative Malady. New York: Oxford University Press,
1974. p. 100.
3. Nightingale Papers, Vol. X. British Museum Additional Manuscript
#43402, 1850. pp 84-89.
4. Ibid. p. 85.
5. Nightingale, F., Introductory Notes on Lying-in Institutions. London:
Longmans, Green, 1871. Dedication.
6. Letters. British Museum Additional Manuscript #46176. 1846.
7. Cohen, I.B., "Florence Nightingale," Scientific American.
March 1984, pp. 128-136.
Reprinted with permission of the author from the Newsletter of the Association
for Women in Mathematics, Vol. 23, No.4 (July/August 1993), 11-12.