I enjoy talking about Pythagoras when I teach the Pythagorean theorem. I sometimes mention Descartes when introducing Cartesian coordinates. And Leibniz and Newton are mentioned in many calculus classes. But all of these famous mathematicians accessible to high school students are male.
What female mathematician can I introduce to my high school students? And what mathematical concept did she work with?
Emmy Noether comes first to mind, as one of the most influential mathematicians in abstract algebra, specifically in the development of Noetherian rings (along with many properties of ideals).
One aspect of her work that high school students might like is from another area, analysis. Noether's theorem says that every symmetry of the laws of nature (or the universe) gives rise to a Conservation Law.
So, energy is conserved because of time symmetry (meaning that the laws of nature don't change after time).
Momentum is conserved because of translation symmetry (meaning that the laws of nature are the same at every point).
Angular momentum is conserved because of rotation symmetry (meaning that the laws of nature are the same in every direction).
Edit: Recently I've learned that, in quantum mechanics, Noether's theorem has quite a few more implications. For instance, the fact that the phase factor is redundant (i.e. the direction of the complex number that you square to get a probability) gives rise to conservation of charge, and quite a few other things get conserved in QFT.
Julia Robinson! I recommend her for a high school audience for a few reasons:
Mathematical reasons: She is best known for her work towards the solution of Hilbert's 10th Problem, regarding an algorithm for solving Diophantine Equations. High school students can absolutely recognize and solve particular Diophantine Equations. Furthermore, and more relevant to Robinson's work, I believe high school students can appreciate (upon seeing examples) the subtle dependence of such equations on their coefficients.
For instance, ask a high school algebra student to experiment and find all the solutions to, say, $6x+15y=33$. Then, ask them to solve $6x+15y=34$. What changes? Give them some random coefficients for $ax+by=c$. What would they do? Can they generalize to more variables?
Then, work with them on a quadratic equation, something like $x^2+1=y^2$. Can they find any solutions? What about $3x^2-5y^2=2$? Do they see how hard it is to get a general method?
Then, you can start to talk about what Hilbert's 10th Problem says. This can facilitate several interesting discussions for a high school audience
(I understand this doesn't really address the full depth of Hilbert's 10th, but if you're looking to pique the interest of a high school audience, I believe this should suffice.)
Historical reasons: Julia Robinson is one of the more notable and renowned mathematicians (no need for "female") of the 20th century, especially in America. Despite this, she had difficulty securing an academic position. But despite that, she went on to obtain such a position and became the first female president of the AMS. Along the way, she devoted much of her time to other interests, including political campaigns.
Surely, she can spark many interesting discussions for a high school audience!
Florence Nightingale, elected to the Royal Statistical Society and (honorarily) to the American Statistical Association, for her work on the importance of statistical data and statistical graphics.
Her statistics and her graphics persuaded the British government to improve sanitation in military hospitals, saving many soldiers' lives.
She was a statistician rather than a mathematician, but since statistics is part of high school math classes, she seems worth talking about.
Perhaps not strictly a mathematician in the traditional sense, but I think Ada Lovelace might be a great woman to start with in today's digital world. She even has an important programming language named after her: Ada.
Augusta Ada King, Countess of Lovelace (10 December 1815 – 27 November 1852), born Augusta Ada Byron and now commonly known as Ada Lovelace, was an English mathematician and writer chiefly known for her work on Charles Babbage's early mechanical general-purpose computer, the Analytical Engine. Her notes on the engine include what is recognised as the first algorithm intended to be carried out by a machine. Because of this, she is often described as the world's first computer programmer.
Or, if you choose to go with the ancients, I'd suggest Hypatia:
Hypatia (/haɪˈpeɪʃə/ hy-PAY-shə; Ancient Greek: Ὑπατία; Hypatía) (born c. AD 350 – 370; died 415) was a Greek Alexandrine Neoplatonist philosopher in Egypt who was one of the earliest mothers of mathematics. As head of the Platonist school at Alexandria, she also taught philosophy and astronomy.
As a Neoplatonist philosopher, she belonged to the mathematic tradition of the Academy of Athens, as represented by Eudoxus of Cnidus; she was of the intellectual school of the 3rd century thinker Plotinus, which encouraged logic and mathematical study in place of empirical enquiry and strongly encouraged law in place of nature.
Recent scholarship has determined that certain important commentaries were indeed written by Hypatia:
Hypatia also wrote commentaries on the Arithmetica of Diophantus, the Conics of Apollonious and edited part of her father's Commentary on the Almagest by Ptolemy.
Hypatia also met with a rather unfortunate end:
According to the only contemporary source, Hypatia was murdered by a Christian mob after being accused of exacerbating a conflict between two prominent figures in Alexandria: the governor Orestes and the Bishop of Alexandria.
More details @ Events leading to her murder. She was at times something of a popular romantic icon as well. See: In the 19th century, interest in the "literary legend of Hypatia" began to rise.
Perhaps the dramatic aspects of Hypatia's life could be deemed distractions from her accomplishments in mathematics, when dealing with HS students. On the other hand, since her story is interesting and provocative, it might well serve to foster students' interest in her accomplishments.
Sophie Germain and her work on Fermat's Last Theorem.
Any Living One who is friendly enough to come talk with them.
Seriously, learning about "people in books" can sometimes be inspiring. But actual live role models are best. Write a local college, university, or business to find a woman who self-identifies as a mathematician. Invite her to your school to spend some time with your students. You want a real person who happens to be a mathematician, a woman, and reasonably happy about that arrangement.
I feel awkward about leaving out women who might be working as mathematics instructors in your school, because I think they count as part of the community, too. But students are used to the whole "female high school teacher" archetype, and you seem like you want to adjust their view of normal jobs for women mathematicians, so you are better off finding someone new.
Maryam Mirzakhani, who just won the Fields Medal, and also was the first Iranian student to win a gold medal in the IMO in 1995 with a perfect score.
My colleague Mohammad Javaheri was on Iran's IMO team with her in 1995. He told us the other day that after Maryam won the gold, when the rest of the team went up to congratulate her she said "next, the Fields Medal". Nineteen years later, she did it!
(I'm not sure what else to say that would be interesting to high school students...as moduli spaces of Riemann surfaces may not be so interesting to them...)
Edit (Jan 2018) I recommend checking Annie Perkins' page:
The Mathematicians Project: Mathematicians Are Not Just White Dudes
If you scroll down, then you will find a section entitled Women (alphabetical by last name).
There are some great sources/names there, and - as a bonus - the project keeps evolving!
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Edit: Marjorie Rice has recently passed away; for more on her life, see the Quantum story here.
I think Marjorie Rice is a great example of an amateur mathematician who managed to make nontrivial discoveries with regard to tessellations. Interestingly, her notation was deciphered by a female professor of mathematics, Doris Schattschneider (also here), who helped to lead the development of Geometer's Sketchpad. (Perhaps you use this piece of software in your school?)
Another great choice is Mary Dolciani (also here) who was a Ph.D mathematician especially known for her teaching abilities, and a prolific writer of textbooks and curricula (e.g., through the School Mathematics Study Group, SMSG, which developed New Math). I included a bit about her in an earlier MESE answer.
Vi Hart, the self-termed Mathemusician. I especially enjoy her Doodling in Math Class YouTube series.
Sonya Kovalevsky, correspondent of Weierstrass, for example.
If your main interest is to provide a role model that students can identify with, you might want to look at Danica McKellar. According to her Wikipedia entry:
McKellar studied mathematics at UCLA, graduating summa cum laude in 1998.
As an undergraduate, she coauthored a scientific paper with Professor Lincoln Chayes and fellow student Brandy Winn entitled "Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on $\mathbb{Z}^2$." Their results are termed the 'Chayes–McKellar–Winn theorem'.
[...]
McKellar has authored several mathematics-related books primarily targeting adolescent readers [those in middle-school and high-school] interested in succeeding at the study of mathematics.
Classically speaking, Maria Agnesi is the best classical mathematician to study. She published calculus texts that expanded and reflected upon the works of Leonhard Euler.
Adm. Grace Hopper earned a Ph.D. in mathematics at Yale (1934), helped program the Mark I (1944), developed the first compiler (1952) and some early computer languages, and worked on the development of the UNIVAC I.
Maria Gramegna, the brilliant student of Giuseppe Peano.
When you use matrices to solve systems of differential equations, you rely in many ways to her ideas. She defined the exponential function of a matrix through its power series and used it as we do it now. Though this is not strictly speaking high school mathematics, you can mention her story to every undergraduate.
She also generalized this to infinite systems and integrodifferential equations, and many ideas of her 1910 thesis belong to the foundation of functional analysis.
After that, she became a school teacher and died in an earthquake in 1915.
Grace Chisholm Young seems overlooked so far (13 answer so far) and in my opinion she is worth considering. She worked mostly in real analysis and what is sometimes called classical point set theory (among other things, she's the "Young" in the Denjoy-Young-Saks theorem and she wrote a well known survey paper on nowhere differentiable continuous functions in 1916), and she played a large role in her husband's 200+ papers.
Besides math, she knew 6 languages, completed all the requirements for a medical degree except for residency, had 6 children in a period of 9 years, and wrote a book on reproduction for children. Despite all her activities, she was also very devoted to her children (teaching each to play a musical instrument), who went on to become: both a son and a daughter were fairly well known mathematicians (the son was also a chess grandmaster), a daughter became a medical doctor and the first female member of the Royal College of Surgeons, a son earned a Ph.D. in chemistry at University of Oxford and later pursued public finance and diplomacy, a daughter completed an undergraduate degree in math and was an Associate Professor of French at Bryn Mawr from 1927 to 1935, a son earned an undergraduate engineering degree and was killed as a pilot in World War 1.
I recommend looking through Ivor Grattan-Guinness' 1972 paper A mathematical union: William Henry and Grace Chisholm Young, which contains many interesting details about her life.
Alicia Boole Stott, the daughter of George Boole (Boolean Algebra), had a deep understanding of 4D geometry. She got married and lived the life that entailed back then (1890s and on). Coxeter gives her husband some credit for connecting her to Pieter Schoute. They worked together and published some papers on 4D polytopes. Coxeter's book, Regular Polytopes has a brief biography. Coxeter worked with her later in her life. George Boole's household was rather interesting according to Coxeter. Alicia was introduced to 4D geometry through C.H. Hinton, who married her sister and wrote a book on the fourth dimension.
I think for young girls Ruth Lawrence is a great role model since she got her phd at age of 17:
- At the age of 9, Ruth Lawrence gained an O-level in mathematics, setting a new age record.
- Also at the age of 9 she achieved a Grade A at A-level Pure Mathematics.
- In 1981 Ruth Lawrence passed the Oxford University interview entrance examination in mathematics, coming first out of all 530 candidates sitting the examination, and joining St Hugh's College in 1983 at the age of just twelve.
Another example would be Shelly Harvey from Rice University.
I have several daughters and I like talking to them about my female friends in the computer graphics industry. In particular, an acquaintance of mine, Kelly Ward, who did the physics (and math) for the hair in Disney's Tangled.
A few links:
http://www.gpb.org/blogs/passion-for-learning/2012/06/06/disneys-tangled-an-exercise-in-physics-and-computer-animation http://unc.edu/meet-a-tar-heel/kelly-ward/
More famous for computer science than maths, but a strong mathematician none the less and creator of the Liskov substitution principle (the L in SOLID), Barbara Liskov.
The story of Sarah Flannery may interest high school students, as she worked on non-trivial mathematics related to codes as a sixteen year old.
While in high school Britney Gallivan folded a piece of (very special) paper twelve times, when most people thought it couldn't be folded more than 7 or 8 times, and wrote a paper about it.
Like the amateur mathematician, Marjorie Rice, mentioned in another answer, she shows that people who are deeply engaged in a problem can make advances, and that mathematics has room for new discoveries.
Thanks to Google Doodle, today I learned about Olga Ladyzhenskaya and her fantastic life.
From Wikipedia. Ladyzhenskaya was born and grew up in Kologriv. She was the daughter of a mathematics teacher who is credited with her early inspiration and love of mathematics. In October 1939 her father was arrested by the NKVD and soon killed. Young Olga was able to finish high school but, because her father was an "enemy of the people", she was forbidden to enter the Leningrad University. After the death of Joseph Stalin in 1953, Ladyzhenskaya presented her doctoral thesis and was given the degree she had long before earned. She went on to teach at the university in Leningrad and at the Steklov Institute, staying in Russia even after the collapse of the Soviet Union and the rapid salary deflation for professors.
Ladyzhenskaya was on the shortlist for potential recipients for the 1958 Fields Medal, ultimately awarded to Klaus Roth and René Thom.
Her Mathematical Work. She was known for her work on partial differential equations (especially Hilbert's nineteenth problem) and fluid dynamics.
I think some aspect of the fluid dynamics might be introduced in high school. There is an attempt here. In particular, looking at the male-dominated history of the subject, I feel she should find her place in the photo used in the aforementioned attempt.
Émilie du Châtelet ,(17 December 1706 – 10 September 1749) was a French mathematician, physicist, and author during the Age of Enlightenment. Her crowning achievement is considered to be her translation and commentary on Isaac Newton's work Principia Mathematica. The translation, published posthumously in 1759, is still considered the standard French translation.
Voltaire, one of her lovers, declared in a letter to his friend King Frederick II of Prussia that du Châtelet was "a great man whose only fault was being a woman"
(From Wikipedia)
Ingrid Daubechies, known for Daubechies wavelets and former president of the IMU.
Ruth Moufang, known for Moufang loops.
Mary Somerville (1780-1872) was a self-taught mathematician and an expert on theoretical astronomy. The Dictionary of National Biography (London, 1897) described her as 'the most remarkable woman of her generation'. See this article about her.
The Association for Women in Mathematics has a great annual essay contest. Here is a link. There are some great essays and the subjects run the gamut from industry to academia to the arts.
Her talents eventually earned her a place in the 1982 edition of The Guinness Book of World Records.As a writer, Devi wrote a number of books, including novels and non-fiction texts about mathematics, puzzles, and astrology.
Whitman, Betsey S. Women of Mathematics: A Biobibliographic Sourcebook, Louise Grinstein and Paul Campbell, Editors, Greenwood Press, 1987.
Bailey, Martha J. American Women in Science: A Biographical Dictionary, ABC-CLIO, 1994.
Karen Uhlenbeck ought to be mentioned. She made deep contributions in the theory of minimal immersions (more generally, harmonic maps), gauge theory of Yang Mills equations (the work of Taubes and Donaldson on four manifolds uses her work), wave maps, integrable systems (e.g. solitons, instantons), etc. She is one of the most important researchers in geometrically and physically motivated partial differential equations of her generation. Although her work as such is probably almost completely inaccessible to any but the most exceptional high school students, the study of soap films and minimal surfaces can be presented to high school students, and some part of her work treats themes that can be seen (in some distant way) as emerging from that source. Maybe something could also be said about solitons, which have applications in telecommunications (although Uhlenbeck's work is not oriented towards applications).
Although her mathematics is not the most accessible, she is a model example of a contemporary woman mathematician of the highest level intellectually and professionally. She has also been active in promoting the participation of women in mathematics.
I always make sure to mention Hypatia in my classes and at least show them parts of this video (The Story of Maths - Marcus Du Sautoy BBC). I've linked to the part where she's mentioned.
