Euphemia Haynes - trailblazer and educator

Euphemia Haynes (September 11, 1890 – July, 25 1980) was a mathematician and educator, who became the first African American woman to earn a Ph.D. in mathematics when she graduated from the Catholic University of America in 1943, at the age of 53.

She was born into a prominent fourth generation black family in Washington, D.C. Her father worked as a dentist and invested in black-owned businesses. She was valedictorian of her graduating class of M Street High School in 1907, and went on to graduate from Washington D.C. Miner Normal School with distinction in 1909 and shortly thereafter began her long career in the Washington, D.C., school system.

While teaching she continued her own education to better serve her students and the larger community. In 1914, she graduated from Smith College with a major in mathematics and minor in psychology. In 1930, she earned her master's degree in education from the University of Chicago, with her thesis, "The Historical Development of Tests in Elementary and Secondary Mathematics." That same year, recognizing the importance of math education, she founded a new department at her alma mater, the Miner's Teachers College, to address the needs of young teachers learning how to teach mathematics: Division of Mathematics and Business Education, where she continued to serve as professor and chair of the department until she retired in 1959.

In addition to her duties to the college, she also taught in the public schools, moving through a variety of positions as she was needed. She taught elementary classes as well as high school mathematics, serving different schools throughout the district. She also occasionally taught part-time at Howard University.

In 1943, she became the first African American woman to earn a Ph.D. in mathematics when she graduated from the Catholic University of America. She was 53 years old, and her dedication to mathematics and the students of Washington, D.C., was as strong as ever. Continually frustrated by the lack of opportunities for black students to pursue academics instead of vocational training, she pushed for desegregation of the school system. In 1960, she joined the District of Columbia Board of Education, where she continued her mission to improve conditions for all students. In 1966, she became the first woman to serve as chair of the Board of Education.

Throughout her life, her devotion to education was equaled only by her devotion to her religious beliefs. In 1934 she helped found the Catholic Interracial Council of the District of Columbia, an  organization that sought to increase cooperation and understanding between African Americans and whites and advance the cause of social justice and equality for African Americans. She was the first vice-president of the Archdiocesan Council of Catholic Women, and belonged to and served on the boards of several social welfare and civil rights organizations, including the Executive Committee of the DC Health and Welfare Council, the NAACP, the Urban League, and the AAUW.

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Cathleen Morawetz - relentless problem solver

"Her courage and determination in tackling a hard problem relentlessly are characteristic of the finest problem solvers," Peter Sarnak, Professor, School of Mathematics at the Institute for Advanced Study, describing mathematician Cathleen Morawezt.

So often I write about women who've had to overcome multiple setbacks and fight for their place in history against incredible odds. In the case of Cathleen Morawetz (May 5, 1923 – August 8, 2017), it almost seems as though she was destined to take up a career in mathematics. Her parents met at Trinity College Dublin where her mother had recently switched majors from mathematics to history, and where her father John L. Synge began his life-long career in mathematical physics. As you would expect, both supported her interests in math and science from an early age. When she was still a very young child, her answer to the perennial question adults ask children "What would you like to be when you grow up?" was "I want to be a mathematician!" She said later that she didn't really know what a mathematician did, but she knew she wanted to be one just like her dad.

Growing up in a supportive home isn't enough to ensure a successful career, though. She needed the support of a wide variety of people along the way. When she was considering becoming a teacher in India after earning her bachelor's at the University of Toronto in 1945, a chance encounter with family friend and mathematician Cecilia Krieger steered back toward mathematics. Krieger encouraged her to apply for a scholarship to attend MIT to continue her studies.

But even having a master's degree isn't enough to ensure a successful career. When she was looking for a job in the post-war technology boom, she was told that companies didn't hire women. Luckily, her blessed father pulled a few strings and got her a job editing a mathematics manuscript on supersonic flow and shock waves by Richard Courant and Kurt Otto Friedrichs. This turned out to be more than simply an temporary gig to help pay the bills. It formed the foundation of her future research as well as introducing her to Richard Courant, the influential German American mathematician who founded the Courant Institute for graduate studies in applied mathematics at New York University.

Years later she would be the first to point out how fortunate she was to find that initial position at Courant, where she spent the the next six decades working through some rather hairy mathematical problems. During her first years, it was a fortuitous position which allowed her to work part-time and paid her enough to afford childcare and housekeeping help while also giving her the freedom to focus solely on her research when she was in the office. Like many women then, and now, she had to deal with inappropriate questions from colleagues about her ability to juggle motherhood and a career, often not even bothering to disguise the judgment that she was harming her children by being away from them. When asked if she found herself distracted at work worrying about her children, she quipped, "No, I’m much more likely to worry about a theorem when I’m with my children."

The job of a theoretical mathematician wasn't one that attracted many women, perhaps due to the expectation that mathematicians would stay in the office late into the night working through theorems -- a prospect that likely wasn't appealing to most people who had interests outside of mathematics. But because of the job flexibility at Courant, she was able to find a balance that worked for her. It was during this period that she came up with her first major breakthrough. Her research on the mathematics involved in transonic flow -- where both subsonic and supersonic sound waves exist simultaneously -- proved that engineers attempting to design airplane wings that eliminated shock waves altogether were impractical because changes in alignment and wind gusts could not be controlled, and instead the focus should be on designs that minimize the impact of shock waves.

"One of my daughters said to me that the problem of being a mathematician is that you're on stage all the time in the sense that you're constantly trying to achieve something in the form of proving a theorem. That's unending. You compete against yourself as well as others and it provides a special fascination in life."

As her children (four in all) grew up, she was able to take on more duties at Courant, including teaching. But she continued her research developing detailed mathematical models, many of which are still used in aerodynamics, acoustics, and optics. It was the research -- the unending work on trying to prove a theorem -- that fascinated her from the beginning. She realized early on in her career that her passion was for theoretical mathematics, and not in the actual work of applying it engineering or accounting. Her talent was in thinking about abstract concepts and then finding ways to express that using mathematics.

Over the course of her career she was awarded numerous award and honors. She was often the first woman to have earned that recognition, but she never stopped thinking about what a privilege it was and how she could use her position to encourage other women to pursue a career in mathematics. In 1998, at the age of 75, she received the National Medal of Science from President Bill Clinton, saying "It's a tremendous moment for me. And I hope it will draw attention to the idea that women can do math and will have some influence on women all the way from grade school to graduate school and beyond."

Cathleen Morawetz's story isn't one of overcoming hardships, but it is inspirational nonetheless because it shows us what women can achieve when given the chance, and echoes many of the modern day calls for a better work-life balance for all researchers, regardless of gender or parenting-status. She was given the early support she needed to take a chance on a difficult career, and then she found a place that enabled her to do her best work while also helping her to maintaining a life outside of research.

You can watch a series of fascinating interviews with her from 2010 and 2012 on the Simons Foundation.

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SRPS Women in STEM: Carolyn Eisele - mathematics historian

Carolyn Eisele (June 13, 1902 – January 15, 2000) was a mathematician, math educator, and a brilliant math historian, whose greatest contribution to the field was her research on the "mathematical method" devised by 19th century philosopher, mathematician and scientist, Charles Peirce. Through her diligent and detailed study, she brought about a better understanding of his philosophy of pragmatism, inspired by his study of mathematics.

Here's where I admit it had never occurred to me that there was such a thing as a math historian. Sure, I know there are science historians, so I don't know why I never thought the same could be applied to the study of mathematics. So you can imagine that when I first read about Carolyn Eisele my inner history nerd was immediately intrigued.

Carolyn Eisele didn't set out to become a math historian. Sure, she was a remarkable young woman who excelled at mathematics at a time when there were few women attending college, much less studying math or science. She graduated from Hunter College in 1923, and earned her master's in mathematics and education from Columbia, graduating Phi Beta Kappa in 1923.

She would have gone on to earn a Ph.D. at Columbia as well, but they didn't offer that level of education to women. (!!) So instead she took differential geometry classes at the University of Chicago and the University of Southern California. Sadly, she wasn't able to earn her degree due to a family illness that forced her to return to New York.

She returned to her alma mater Hunter College as a mathematics instructor, where she stayed for her entire career.

In 1947, though, her life took an unexpected and fortuitous turn. While doing research at the Columbia University library for a new class she was to teach -- history of math -- she came across a manuscript by Charles Sanders Peirce discussing his interpretation of Fibonacci's Liber Abaci -- a document published in 1202 offering evidence of the superior efficiency of doing calculations using Arabic numbers compared to Roman numerals.

The most important aspect of her research was her analysis of Peirce's mathematical method -- his application of mathematical principles to his philosophical work. She saw that his work on mathematics and science and his work on philosophy and history were not two distinct aspects of his intellect, but instead they worked together to inform his entire world-view.

It was through her meticulous research to understand his philosophy that she was able to make it more accessible to a wider audience. That's what historians do, really. She wasn't a stereotypical brilliant mathematician working in a laboratory in some college math department, trying to solve complex problems and writing equations on a chalkboard. She was a brilliant mathematician working in the library, reading about someone else's complex ideas and thinking about how best to share her findings with the world. This kind of work requires a level of mathematic genius that in some ways may be even more impressive, since she had to be able to understand and interpret the ideas of another mathematics genius.

Read more about the importance of her pioneering research on Charles Peirce's works [PDF].

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Charlotte Angas Scott - trailblazing mathematician

Charlotte Angas Scott (June 8, 1858 - November 10, 1931) was the first British woman to receive a doctorate in mathematics, and one of the eight founding faculty at Bryn Mawr College.

Charlotte grew up in a somewhat unusual home in Lincolnshire, England, in the mid-1800s. Her father, a minister, and mother both believed in the value of education for girls as much as boys, and made sure Charlotte had tutors for all subjects, including math and science, starting at a very young age. So it's no surprise that she earned a scholarship to the recently opened women's Girton College, where she excelled in her studies.

In 1880, she obtained special permission to take the Cambridge Mathematical Tripos Exam -- the exam required to qualify for a bachelor's degree. Until then, only men were admitted, and even after she placed 8th overall she wasn't granted a degree, or allowed to attend the ceremony. Instead, she received a certificate and attended a special dinner in her honor at Girton. Even though she had to endure these insults, her performance opened the door to the Tripos for other women, the first of her many trail-blazing feats throughout her remarkable life.

Even so, in 1882, she was finally awarded her Bachelor of Science, and by 1885 she had earned her doctorate. During this time she taught other young women attending Girton, and reinforced her belief in the value of equal educational access for women.

In 1885 she was selected as one of the eight founding faculty members at the new American college for women, Bryn Mawr, where she served as Associate Professor of Mathematics. This was the role she had hoped for, and her entire career at Bryn Mawr was dedicated to improving the standards for women's education. In addition to serving as mentor to many of the women in mathematics who would go on to do great work, she was also responsible for setting the admission requirements for arithmetic, algebra, and geometry, and convinced the college to administer an entrance exam for math and science.

She also continued her own research, specializing in the planar geometry, and wrote and published over 30 papers as well as the text An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry in 1894. In 1899 she was made co-editor of the American Journal of Mathematics, and her paper "A Proof of Noether's Fundamental Theorem" was published, quickly becoming the first research paper written in the US to find critical acclaim in Europe. (You might recognize the name Noether. In this case, it's referring to Max Noether, father of brilliant mathematician Emmy Noether.)

You can read more about her life and work at Biographies of Women Mathematicians.

And for even more info about her, check out Math History [PDF].

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Maria Reiche - The Lady of the Lines

Maria Reiche (15 May 1903–8 June 1998) was a German mathematician, archaeologist, and translator who studied the Nazca Lines in Peru. Known as the "Lady of the Lines," she helped educate people about these remarkable geoglyphs, and worked hard to gain government recognition and preservation for them.

She was born in Dresden, Germany, where she attended Dresden Technical University studying mathematics, astronomy, geography and foreign languages. After graduation, she moved to Peru to work as a nanny and teacher for the children of the German consul in Cuzco. Once her position there ended, she stayed in Cuzco, working as a teacher as well as a technical translator. (She spoke five languages!)

In 1940, she became an assistant to an American historian, Paul Kosok, who was studying the mysterious lines in the Nazca desert. Together, they worked to map the lines and discover their meaning. In 1946, she began to map the lines and determined there were 18 different animals and birds represented. After Paul Kosok left Peru, she remained to continue her research. She used her mathematical knowledge to analyze how the Nazca people could have created these images on such an enormous scale. To get a better look at the lines, she enlisted the help of the Peruvian Air Force to take photographic surveys from above.

As increased development began to damage the lines (a highway was built right through one of the images), she turned her attention to education and preservation efforts. She even went so far as to hire private security to protect the lines, until the Peruvian government finally agreed to limit public access to these important heritage sites.

The image at the top is from the fantastic Good Night Stories for Rebel Girls (Amazon/Library) by Elena Favilli & Francesca Cavallo, with the illustration by Gaia Stella. I was fortunate enough to be able to interview Elena and Francesca while they were running their Kickstarter for this excellent book.

Read more about her life and work in the excellent obituary in the Independent

Check out this biography, Maria Reiche by Wilfredo Gameros

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Sylvia Serfaty - Mathematician

"It's really beautiful to observe, as you progress in your mathematical maturity, how everything is somehow connected. There are so many things that are related, and you keep building connections in your intellectual landscape." 

One of the things that fascinates me most about science and math is the line that can be drawn through history connecting researchers, each building on the work of those who came before. And then how their own work builds on what they have learned and what others are learning. It's all very exciting to me, even though I know it's a lot of hard, often lonely, work.

I recently read an interview with Sylvia Serfaty, and while I can't say I understand what she's working on, I find it immensely interesting to just listen to her talk about the process of mathematical research. And how she came to realize that this was her passion.

When she was in high school, her math teacher was giving out challenging problems for the students to solve. Sylvia took hers home and wrestled with it for a while and eventually came up with a solution. As it turns out, it was a different, more abstract solution than the one her teacher was expecting. How exhilarating it must have been to realize she had a natural aptitude for solving problems and that this might be her calling in life!

But she makes it clear she was not math prodigy. She really dislikes that stereotype of math researchers as savants, and instead makes it clear that she and others like her put in long hours of hard work, much like practicing for musicians honing their craft. Actually, this is something I see quite often in my research of women in STEM -- they emphasize the time and effort required to reach their goals.

Sylvia's work included taking on the problem of using math to analyze superconductors -- to determine the relationship between the magnetic field of the superconductor and the vortices that appear. This took her decades to solve. She first took on this problem in 1998 as a post-doc, and continued to work on it off and on over the next 18 years. In that time, she earned the European Mathematical Society prize in 2004, and then in 2012, she shared the Poincaré Prize with Nalini Anantharaman, another remarkable female mathematician, making them the only two women awarded that honor. So far.

She is also an outspoken proponent of increasing outreach to bring more women and minorities into STEM fields, because everyone sees the world a little bit differently and that changes how they approach problems and come up with different answers. "That’s why you need people with different points of view, to think of different perspectives and find different roads."

You can read a fantastic interview with her from earlier this month.

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Kickstart This! African American Women Mathematicians Activity Book

Like many of you, I saw the film Hidden Figures and cheered and cried with the amazing women whose stories had been shamefully neglected for far too long. As someone with more than a passing interest in women's history, I was also more than a little frustrated and disappointed that the stories of these women and others weren't routinely taught in school when I was a kid. Heck, they haven't been taught in most schools in the nearly-30 years since I graduated.

I sometimes wonder if learning about the endeavors of women in math and science would have changed the career trajectories of some of my classmates. Would more of us have actually considered a career in STEM? Would we have stuck with science and math even when it got "hard?" It's difficult to tell. If nothing else, learning about the contributions of these women and others who came before them would have given us a richer understanding of the complex history of the eras in which they lived.

Over the last couple of years, there has been a concerted effort to tell the stories of important women in history whose work has overlooked, if not completely dismissed, for decades or even centuries. Most of the women newly-celebrated worked in the fields of medicine or science, with only a few representing mathematics, and even fewer still were African American women.

Until now, that is. Dr. Shelly Jones is committed to sharing the stories of these math pioneers in her work with students and teachers around the country. As someone who works with a diverse population, she knows the importance of creating a more accurate and representative picture of influential mathematicians, which was more than just a bunch of white men with a smattering of white women.

So, as you can imagine I was thrilled to learn about her African American Women Mathematicians Activity Book. It looks like a fun activity book for middle-grade students, including puzzles that will encourage students to learn more about these women's lives and work. This is an especially important age when it comes to determining whether a student with pursue a career in STEM, and it's when the interest in math peaks for many girls. Perhaps by showing them examples of smart women who did great work, more will be inspired to follow in their footsteps.

The project is already 66% (that's 2/3rds in fractions) funded, with only a week left, but it still needs your help to get off the ground. Dr. Jones was kind enough to answer a few of my questions about her work in teaching mathematics as well as explaining the importance of the African American Women Mathematicians Activity Book.

SRPS: First, can you tell us a little about yourself? What's your background? What inspires you?

SJ: Currently, I am an Associate Professor of Mathematics Education at Central Connecticut State University (CCSU) in New Britain, Connecticut. I teach undergraduate mathematics content and methods courses for pre-service teachers as well as graduate level mathematics content, curriculum and STEM courses for practicing teachers. I am interested in and conduct research on culturally relevant mathematics, making mathematics and music connections, and the effects of college students’ attitudes and beliefs about mathematics on their success in college.

Before CCSU, I was a Mathematics Teacher and then Supervisor in three Connecticut K-12 school districts and then the Assistant Director for Mathematics at The Project to Increase Mastery of Mathematics and Science (PIMMS) at Wesleyan University. I have been an educator for over 25 years.

I serve the mathematics education community by presenting at conferences at the local and national levels. I also provide mathematics professional development in K-12 school districts around the country. I am member and volunteer of the Benjamin Banneker Association, a national organization who advocates for the excellence in teaching and learning for African American children. I am a contributing author of a book entitled, The Brilliance of Black Children in Mathematics: Beyond the Numbers and Toward a New Discourse. Recently I completed a study on Using Culturally Relevant Cognitively Demanding Mathematics Tasks in Classrooms in the United States and Abroad. I worked with teachers from the United States, Brazil, Ecuador, and Bermuda.

I have two daughters ages 17 and 23.

SRPS: What motivated you to dedicate your life to math pedagogy -- instructing teachers how to teach math?

SJ: I began my career as a computer programmer but didn't like the isolation of creating and troubleshooting programs. I began to train people on the job and found that I really enjoyed teaching. I always hear people say, "I'm not good at math." I want to change that narrative. I think people are better at math than they think. They are just not good at "school" math. We must change what we consider is math. It is so much more than just symbol manipulation and following mathematical procedures. It is a way of thinking that includes patterns and logic.

SRPS: One of the questions I hear pretty often from school-aged kids is "When will I ever use this in real life?" Is this because students don't see the relevance of math in their lives?

SJ: Yes, students and even some adults don’t see the relevance of mathematics because they don't see the connection to real life. It is up to teachers to help students see the connection between "school" math and real-life math. Much of what we do in real life is mathematical. For example, we estimate time, recipes, and budgets. We do scheduling, plan trips, calculate percentages, use spatial reasoning to decorate rooms and create art. We even use math (fractions) to read music and tune musical instruments. This is just to name a few. The key is to point this out to students when appropriate and to use real-life scenarios as much as possible in our mathematics curriculum.

SRPS: What is the African American Women Mathematicians Activity Book?

SJ: This activity book is being created to honor the important work, accomplishments and everyday lives of African American Women Mathematicians. Although the book is geared to children in grades 3 – 8 it is appropriate for all ages. All of the featured mathematicians will have a profile sketch and a short biography followed by an activity page displaying their math interest or a hobby they enjoy. For example, Evelyn Boyd Granville participated on a team that created computer software for NASA's Project Vanguard and Project Mercury space programs. Her activity page will include a coloring page of a sketch of the Mercury space craft. Whether at home or school, children will enjoy uncovering mathematician's names through word searches, unscrambling math vocabulary words, solving equations to decode a mathematics fact, answering math history trivia to complete a crossword puzzle, and using their math brain to figure out a magic square. The book will also include some coloring pages and an eye spy page where students will locate hidden mathematical objects.

SRPS: There is a distinct lack of African American women in math and science fields, and several prominent physicists -- like Jedidah Isler & Chanda Prescod-Weinstein -- are calling attention to that. Many people talk about the "broken tech pipeline." How do we encourage more girls to even consider a career in math?

SJ: Whenever possible we must provide opportunities for girls and young women to participate in STEM activities. We must encourage them to "try it!" Having role models is another important aspect of getting more girls into STEM fields. My university sponsors a Girls in STEM Day for high school aged girls. In addition, I coordinate an annual CAMPY-on-Campus event at my university. CAMPY is the Connecticut Association of Mathematically Precocious Youth. Every year we host over 100 middle school students of which many are girls. The students spend a full day participating in STEM activities. They also receive a cool mathematics related t-shirt. These types of events are needed to spark students interest in STEM fields.

SRPS: How did you decide which female mathematicians from history to include?

SJ: The activity book will start with the "firsts" African American women to receive doctorate degrees in mathematics. They are Euphemia Lofton Haynes, Evelyn Boyd Granville, Marjorie Lee Brown, Argelia Velez-Rodriguez, Gloria Conyers Hewitt, and Sadie Gasaway. I will also feature more current mathematicians such as Etta Zuber Falconer and Genevieve Knight. Dr. Falconer was a pioneer of the computer science program at Spelman College in Atlanta, Georgia. Dr. Knight was one of the founding members of the Benjamin Banneker Association, Incorporated, an affiliate organization of the National Council of Teachers of Mathematics (NCTM). So far, I have 20 women; however, as I work on this project, I am finding more and more women to include. I will make a final decision at the end of my Kickstarter campaign. I was asked to include some young women mathematicians and so I am looking for those women now.

Check it out: African American Women Mathematicians Activity Book

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