# What female mathematician can I introduce to my High School students?

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?

• See the book Women in Mathematics by Lynn M. Osen for several good examples. Apr 20 '14 at 23:03
• What do you say about Pythagoras? I'd want to emphasize that stories about him are less reliable than stories about Johnny Appleseed.
– user173
Apr 21 '14 at 2:10
• Apr 21 '14 at 5:02
• Few if any of the results that high school students will rely on are attributable to women. You can't much work around that because it's a feature of the syllabus, the difficulty of modern mathematics, and the small number of pre-modern female mathematicians. I can't think of an example not of the form, "here is an impressive female mathematician, here is why her work was important, but you won't be using that". AP classes might get near, but for example Emmy Noether's work starts after an average undergraduate algebra syllabus stops. Apr 21 '14 at 13:29
• Also there was no Fields medal when Noether was under 40. You don't need to manufacture a female Fields medalist, as Noether was clearly a more important mathematician than the average Fields medalist. Apr 21 '14 at 16:19

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.

• Noether's theorem is probably going to seem quite mind-blowing to anyone who isn't able to follow its mathematical derivation. Which could be a good or bad thing. ;-) Apr 21 '14 at 0:53
• Even if you can't follow the derivation of Noether's theorem the examples are still pretty cool. It's pretty intuitive once it's pointed out that momentum should be related to shift symmetry and angular momentum to rotational symmetry (and then you can blow their minds with time shift symmetry and energy). Apr 21 '14 at 16:21

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

• Solving equations in integers (Why have mathematicians been interested in solving them since pretty much antiquity? Where do they appear in real life?)
• Algorithms and decision procedures (What is an algorithm? What makes one better than another? Do we care about how efficiently they can run, or how easy they are to describe/implement?)
• Logic and philosophy of mathematics (What does it mean to prove something? What does it mean to disprove something? What does it mean to prove that there is no procedure that could solve every Diophantine equation?)

(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!

• Another good J.R. topic is one of the "positive aspects of a negative solution": there is a polynomial whose positive values are exactly the primes.
– user173
Apr 21 '14 at 5:36
• +1: It is hard for me to imagine anyone who would not regard Julia Bowman Robinson as being an inspirational figure in one manner or another. May 20 '14 at 17:39

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.

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.

• I recommend against discussing Hypatia, since we have nothing written by her. How would you answer the OP's question: What mathematical concept did she work with?
– user173
Apr 21 '14 at 3:00
• My citations explain that. BTW, recent scholarship has determined that certain important commentaries were indeed written by Hypatia. See 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. Apr 21 '14 at 3:04
• @DanNeely - where someone tried to insist she was murdered for being a woman in science - that contention is absurd to anyone who knows anything about the ancient Greeks, and perhaps bringing her up will open the door to educating kids about good History and the role of women in the ancient world, which seems to be related to what the OP is interested in. Otherwise, why the question at all? Apr 21 '14 at 21:50
– user1167
Apr 22 '14 at 9:14
• For another influential female computer scientist, there is Grace Hopper: smbc-comics.com/?id=2516 Apr 23 '14 at 17:36

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.

• It is worth noting that according to some sources (en.wikipedia.org/wiki/Pie_chart) she popularised / invented the use of pie charts.
– Rune
Apr 21 '14 at 19:44
• @Rune, she popularized/invented a variant of pie charts -- a creative variant that worked for her, but not a format I would advise students to use. If I showed those charts in a class, I would ask: "How else might you present this data to make it clear and visually striking?"
– user173
Apr 21 '14 at 19:59
• +1 Florence Nightingale was one of the first people to successfully use statistics and data visualisation to bring around a direct change in government policy which saved lives and changed the history of war and medicine. It's a perfect example of how maths can change the world, with loads to interest children (war and nursing and surprising counter-intuitive facts: she proved that more soldiers were dying of infections in dirty field hospitals than from battle, which led to modern nursing). She was genuinely one of the top pioneers in her field (nothing to do with her gender). Apr 22 '14 at 14:17
• Brilliant idea. There is vast potential here for interdisciplinary ideas, and a good reminder that not all of the people who developed statistics and probability were into gambling! Apr 27 '14 at 15:17
• @user867 I agree, not all of the pioneer statisticians were into gambling -- some were into eugenics!
– user173
Apr 28 '14 at 0:27

Sophie Germain and her work on Fermat's Last Theorem.

• Germain primes are a very accessible mathematical starting point.
– jwg
Apr 23 '14 at 5:59
• I remember doing a report on her in 6th grade. But I remember boundary constrained differential equations (well, I didn't know that's what they were at the time). Apr 24 '14 at 10:02
• I often quote Sophie Germain to elementary math students, saying, "Algebra is but written geometry and geometry is but figured algebra," or some slight paraphrase of that. I find this relevant when doing any kind of analytic geometry, and seeing the same facts revealed geometrically as well as in formulas. Jun 15 '17 at 14:02

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...)

• This is especially relevant now. As for the last sentence, it would be worth mentioning that she helped bridge the gap between probability theory and geometry (?) the common pool table analogy seems particularly effective with kids, although she gave her preferred example here Jul 16 '17 at 22:58
• Today's news was heartbreaking. Thanks for the link, Andres. Jul 17 '17 at 1:03

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.

Vi Hart, the self-termed Mathemusician. I especially enjoy her Doodling in Math Class YouTube series.

• I really think this answer needs more attention. Her videos were really inspiring for me in high school.
– DLeh
Apr 23 '14 at 20:13
• They're inspiring for me and I've already graduated from college! Apr 23 '14 at 21:21
• This girl is awsome and very inspiring. She should definitely be a female mathematician model for high school students, firstly because she can easily inspire them, and also because she has worked on things that high school students can understand. I have created an account here, just to upvote your answer Jul 3 '14 at 18:59
• She's working as part of elevr which is a VR research group, of which one part is exploring mathematics via VR. The other women she is working with are all interesting in their own right too. May 17 '17 at 14:26

Sonya Kovalevsky, correspondent of Weierstrass, for example.

• She won the Prix Bordin for her work on what is now known as the Kovalevsky top, and she proved the full version of the Cauchy-Kovalevsky theorem, which stood for nearly 50 years as the central result in the theory of partial differential equations, until the theory of weak solutions came along. Apr 22 '14 at 13:41

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!







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.

• (A recent update on tessellating pentagons!) Aug 13 '15 at 6:19
• (& an even more recent update!) Jul 11 '17 at 23:23

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.

• This was going to be my answer! She was World News' Person of the Week (youtu.be/nXsfBQlXb6Y) and her Math Doesn't Suck book has great reviews. Apr 22 '14 at 7:09
• Winnie Cooper from The Wonder Years! That's pretty awesome (for anyone that still remembers). May 17 '17 at 14:32

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.

• There is also a curve called the Witch of Agnesi.
– kan
Apr 22 '14 at 19:33
• Yes. This is one to mention in calculus class. Although women were not allowed in the university, she learned mathematics from her father, a professor of mathematics at the University of Pisa. In later years, on occasion she would substitute for her father when he was away ... although the rules prohibited women students, there was (through oversight) no rule prohibiting women instructors... Aug 14 '14 at 17:05

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.

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.

• There is something wrong with the sentence "Coxeter gives her husband some credit for connecting her to Pieter Schoute". As Wikipedia shows and is probably well known, Coxeter is a man; however you write feminine adverb "her".
– kan
Apr 22 '14 at 19:32
• @kan Coxeter gives Alicia Stott's husband Walter credit for putting Alicia in contact with Pieter Schoute. The "her" is Alicia Stott in both cases. Apr 22 '14 at 19:54
• That is now very clear. Thanks for the clarification. I am not a native speaker as you probably figured but if you think it is appropriate, you could consider rewording your answer a little bit.
– kan
Apr 22 '14 at 21:05

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.

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.

• Under this answer I thought I'd mention Lisa Sauermann, whose accomplishments (IMO performances) are recent enough that most likely know of her. Apr 21 '14 at 15:34
• RL is fairly controversial as a role model, as many people at the time felt that her father was using her to live out his own dreams of being an Oxford undergraduate (he accompanied her there). (Only she is qualified to give a judgement on that.) Also, while she is clearly very bright, she has not produced any groundbreaking work as an adult. Apr 24 '14 at 13:30
• I'm not sure of the logic behind your first sentence: Does getting a Ph.D at a young age imply one is a great role model? Apr 25 '14 at 16:16

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.

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.

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.

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.

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.

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.

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.

## Shakuntala Devi a.k.a Human Calculator

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.

Other Human calculators

• While perhaps an interesting person, this woman is not a mathematician. Mental calculation is closer to magic (a kind of performance art or theater) than to mathematics. Jan 27 '18 at 13:50

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.

http://youtu.be/rDBdT1Dl_QY?t=55m6s

• The video says "her cult status eclipsed her mathematical achievements" -- if I had time to discuss 30 mathematicians with a class, I wouldn't spend much time on one who requires a proviso like that.
– user173
Apr 24 '14 at 14:07

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.