March is National Women's History Month, a good time to reflect in our classrooms on the achievements and accomplishments of women in mathematics and statistics. In 2001, the percentages of female students taking the AP Calculus and AP Statistics Exams were 45.5 percent and 50 percent, respectively. But how many of these students know of the roles that women have played in the development of calculus, statistics, and mathematics in general, or the influence that these subjects had in the lives of female mathematicians? We present here a brief profile of just a few outstanding women mathematicians. Sources for additional information are presented at the end of the article.
Maria Gaetana Agnesi (1718-1799)
Agnesi was exposed to mathematics from a very early age. By the age of 20 she had started work on her most important contribution to mathematics, the book Analytical Institutions, which focused on differential and integral calculus. Originally intended as a textbook for her brothers, this work was eventually published in 1748 to wide acclaim, and was later translated into English. Early sections contained elementary problems on maxima, minima, tangents, and inflection points. Also described in the text was a cubic curve now known as the "Witch of Agnesi," the name coming from a mistranslation of the original Italian that appeared in the English edition. Today this curve is a common example found in many calculus texts. The Canadian composer Elma Miller has even written a work called "The Witch of Agnesi" for B-flat clarinet, bass clarinet, horn, percussion, viola, and double bass. The piece was first performed in late October 1989 in Toronto. Despite its premiere performance so near Halloween, the inspiration for the piece was the curve described by Maria Agnesi.
Sophie Germain (1776-1831)
Germain taught herself mathematics by using books from her father's library. In the book Women in Mathematics, Lynn Osen says that Germain "spent the years of the Reign of Terror studying differential calculus" while confined to her home. During a lifetime of research in mathematics, she made important contributions to the areas of number theory and mathematical physics, including being one of the first mathematicians, male or female, to provide a partial solution to Fermat's Last Theorem for a large class of exponents. Sophie Germain's Theorem was still being used 150 years after her death in investigations of Fermat's famous conjecture. A prime number n when 2n+1 is also prime is now called a Sophie Germain prime. There are applications for Sophie Germain primes in number theory and even in cryptology for digital signatures based on the Diffie-Hellman key agreement algorithm, so finding large Sophie Germain primes is actually a worthwhile pursuit. They even make an appearance in the Tony award-winning play Proof. The largest known Sophie Germain prime, as of August 2001, is 109,433,307 x 266452 -1, a number with 20,013 digits.
Florence Nightingale (1820-1910)
Nightingale is most remembered for her work as a nurse in reforming hospital sanitation methods, yet she was also a pioneer in the applications of statistical analysis and methods of data presentation in medicine. She was an innovator in the collection, tabulation, interpretation, and graphical display of descriptive statistics. For example, Nightingale developed the "polar-area diagram," a precursor of the pie chart, to dramatize mortality rates due to unsanitary hospital conditions during the Crimean War. In 1858 she became the first woman to be elected a Fellow of the Royal Statistical Society, and in 1874 became an honorary member of the American Statistical Association. Karl Pearson acknowledged Nightingale as a "prophetess" in the development of applied statistics.
Sofia (or Sonya) Kovalevskaya (1850-1891)
Kovalevskaya was an influential mathematician, writer, and advocate of women's rights in the nineteenth century. She claimed to have been introduced to differential and integral calculus at the age of 11 by studying her father's old calculus notes that were papered on the nursery wall as a substitute for regular wallpaper. She went on to become the first woman to be granted a Ph.D. in mathematics when she was awarded her doctorate from Göttingen University in 1874. Many colleges and universities in the United States now hold annual Sonya Kovalevskaya Math Days for high school girls to celebrate mathematics.
Sibner was an aspiring actress as a young woman. Later, as a fine arts student at City College in New York City, she took a required calculus course, loved the subject, and immediately changed her major to mathematics. She received her Ph.D. in 1964 from the Courant Institute of Mathematical Sciences and today is a noted researcher and professor of mathematics at Brooklyn Polytechnic University.
In 1962, Gloria Hewitt became only the third African-American woman to receive a Ph.D. in mathematics. In a 1995 interview with Shannon Hensley, a student at Agnes Scott College, Hewitt referred to her college years at Fisk University when asked at what point she realized her interest in pursuing a career in mathematics: "I remember when I took calculus in college the only book I took home over the Christmas holidays was my calculus book. I wanted to do those word problems. I worked on one problem for the whole two weeks before I solved it. It wasn't that hard, but I just didn't understand the process involved. When the light dawned, I was so happy! I don't believe I ever felt so rewarded. It was a major breakthrough. I was hooked. After that, to the amazement of my fellow students, I recall sitting on campus doing calculus problems for recreation." Hewitt, a professor of mathematics at the University of Montana and a dedicated mathematics educator, was also a reader and Table Leader for the grading of the AP Calculus Exam for 12 years, and a member of the AP Calculus Test Development Committee from 1991 until 1995.
Additional information about these six women and many more profiles of women mathematicians can be found at the Web site on Biographies of Women Mathematicians at Agnes Scott College.
Grinstein, Louise S. and Paul J. Campbell. Women of Mathematics: A Biobibliographic Sourcebook, Greenwood Press, 1987.
Morrow, Charlene and Teri Perl. Notable Women in Mathematics: A Biographical Dictionary, Greenwood Press, 1998.
Murray, Margaret A.M. Women Becoming Mathematicians, MIT Press, 2000. Osen, Lynn. Women in Mathematics, MIT Press, 1992.
Parker, Marla. She Does Math! Real-Life Problems from Women on the Job, Mathematical Association of America, 1995.
Larry Riddle is a professor of mathematics at Agnes Scott College in Decatur, Georgia. He started grading AP Calculus exams shortly after beginning his teaching career, and nineteen years later is now in his fourth year as the Chief Reader for AP Calculus.