Asian American and Pacific Islander Heritage Month
In honor of Asian American and Pacific Islander Heritage Month, we would like to recognize the accomplishments of Mathematicians.
Asian American and Pacific Islander Heritage Month
Shing-Tung Yau is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathematics at Tsinghua University.
Yau was born in Shantou, China, moved to Hong Kong at a young age, and to the United States in 1969. He was awarded the Fields Medal in 1982, in recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors to the development of modern differential geometry and geometric analysis. The impact of Yau’s work can be seen in the mathematical and physical fields of differential geometry, partial differential equations, convex geometry, algebraic geometry, enumerative geometry, mirror symmetry, general relativity, and string theory, while his work has also touched upon applied mathematics, engineering, and numerical analysis.
Katsumi Nomizuwas a Japanese-American mathematician known for his work in differential geometry. Nomizu was born in Osaka, Japan on the first day of December, 1924. He studied mathematics at Osaka University, graduating in 1947 with a Master of Science then traveled to the United States on a U.S. Army Fulbright Scholarship. He studied first at Columbia University and then at the University of Chicago where in 1953 he became the first student to earn a Ph.D. under the thesis direction of Shiing-Shen Chern. The subject was affine differential geometry, a topic to which he would return much later in his career. He presented his thesis, Invariant affine connections on homogeneous spaces in 1953.
Katsumi Nomizu was well known for his devotion to meticulous exposition in a very formal style and to high-quality teaching at the undergraduate level. His 1966 text, Fundamentals of Linear Algebra includes these words in the dedication, “It is my hope that this book will continue to serve those students of mathematics and science for whom a more than rudimentary background in linear algebra is an indispensable part of their training.”
Over the course of his career, Katsumi Nomizu was influential in determining the course of differential geometry by stressing what he called the structural approach. In 1965, he edited the Proceedings of a United States-Japan Seminar in Differential Geometry that he helped to organize for the National Science Foundation. He was invited to visiting positions in Berlin, Bonn, Strasbourg, and Rio de Janeiro. Among his nearly one hundred papers and articles and seven books, he had twenty-three co-authors from Belgium, Brazil, China, Germany, Italy, Japan, Poland, Yugoslavia and the U.S.
Dr. Kamuela Yong is an associate professor of mathematics at the University of Hawai‘i–West O‘ahu. He is the first Native Hawaiian to earn a Ph.D. in applied mathematics. Dr. Yong’s research interests include mathematical modeling of biological, ecological, and epidemiological systems using diffusion. Dr. Yong is the 2019 recipient of the Frances Davis Award for Excellence in Undergraduate Teaching and the 2020 recipient of the University of Hawai‘i Regents’ Medal for Excellence in Teaching.
In his words, “Math is all around us,” Yong said. “Applied math really helps to explain how things work everyday—everything from business decisions to even architect decisions.”
Arab American Heritage Month
Arabic mathematicians have always been remembered for developing algebra and trigonometry, combining Greek geometry with Indian and Babylonian ideas, re-introducing zero to modern civilization, and contributing through applied mathematics in astronomy.
Muslim mathematician and astronomer whose major works introduced Hindu-Arabic numerals and the concepts of algebra into European mathematics. Latinized versions of his name and of his most famous book title live on in the terms algorithm and algebra.
In the 12th century a second work by al-Khwārizmī introduced Hindu-Arabic numerals and their arithmetic to the West. It is preserved only in a Latin translation, Algoritmi de numero Indorum (“Al-Khwārizmī Concerning the Hindu Art of Reckoning”). From the name of the author, rendered in Latin as Algoritmi, originated the term algorithm.
Finally, al-Khwārizmī also compiled a set of astronomical tables (Zīj), based on a variety of Hindu and Greek sources. This work included a table of sines, evidently for a circle of radius 150 units. Like his treatises on algebra and Hindu-Arabic numerals, this astronomical work (or an Andalusian revision thereof) was translated into Latin.
Al-Khwārizmī’s contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry.
Abu Kamil Shuja’ ibn Aslamwas a prominent mathematician of Islamic Golden age who is considered the first mathematician to use irrational numbers as solutions and coefficients to equations methodically. Fibonacci later embraced this method; it made Abu Kamil harbinger of algebra to Europe. His contribution to algebra and geometry were plenty. He effortlessly worked on algebraic equations having powers higher than x2, solved sets of non-linear simultaneous equations with three unknown variables, exemplified the rules of signs for expanding the multiplication, and always computed all possible solutions to some of his problems. One of his strengths was to write the issues rhetorically, rather than to use mathematical notation. It made it understandable even to ordinary people.
Roshidi Rashed is a mathematician, philosopher, and historian of science. He is well known for his work on illuminating the works of medieval Arab mathematicians and physicists. He highlights through his work the unrecognized Arabic scientific tradition. It is through the numerous publications that he has highlighted the immense contributions of the Arabic world to the development and formalization of mathematics.
There was a time when the Arab world was far ahead from all its peers. Thousands of years ago, it had tremendous technological advantages over the west in many fields, but the most prominent among them was in Mathematics. It is impressive to note that in the medieval period, the task of translating the work of Greek and Hindu mathematicians was almost an industry in its own right. The tradition has continued and even today, many Arabic mathematicians show the way in this field.
Women’s History Month
In honor of Women’s History Month, we would like to recognize the accomplishments of a group of Female Mathematicians.
Iranian-born Maryam Mirzakhani was one of the greatest mathematicians of her generation, making exceptional contributions to the study of the dynamics and geometry of mathematical objects called Riemann surfaces.
She was a professor at Stanford University and held a Ph.D from Harvard University. In 2014, she was the first and only woman, and first Iranian, to be awarded a Fields Medal (also known as the International Medal for Outstanding Discoveries in Mathematics) for “her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces”. In 2005, as a result of her research, she was honored in Popular Science’s fourth annual “Brilliant 10” in which she was acknowledged as one of the top 10 young minds who have pushed their fields in innovative directions.
Her work had a huge impact in shaping her field and has opened up new frontiers of research that are just starting to be explored. She shows us that, even in a male-dominated field, women can be role models and lead the way forward with their discoveries.
Mary Cartwright was a British mathematician and a woman of many firsts! She was not only the first woman to obtain a first in her university degree, but also one of the first mathematicians to study what is now known as chaos theory. She was the first woman to receive the Sylvester Medal (awarded for the encouragement of mathematical research), the first woman to be President of the Mathematical Association and the first woman to be President of the London Mathematical Society.
Thanks to her bravery in daring to defy the status quo, her work has gone on to strongly influence the modern theory of dynamical systems, and she even has a mathematical theorem named after her.
Mary Jackson, also known as Mary Winston, was an American mathematician and aerospace engineer who in 1958 became the first African American female engineer to work at the National Aeronautics and Space Administration (NASA).
In 1951, she started working at the National Advisory Committee for Aeronautics (NACA), where she was a member of its West Area Computing unit – the West Computers, comprising African American female mathematicians – and Jackson’s supervisor was Dorothy Vaughan. The women provided data that were later essential to the early success of the U.S. space program. At the time, NACA was segregated, with Black employees required to use separate bathrooms and dining facilities. In1958, she became the first Black female engineer at NASA, which had been established earlier that year; NACA had been incorporated into it.
Jackson worked as an aerospace engineer for some 20 years. Much of her work centered on the airflow around aircraft. Despite early promotions, she was denied management-level positions, and in 1979 she left engineering and took a demotion to become manager of the women’s program at NASA. In that position, she sought to improve the opportunities for all women at the organization. She retired in 1985.
Jackson’s contributions to the space program received greater recognition after her death in 2005. She and other West Computers – including Dorothy Vaughan and Katherine Johnson – were the inspiration for Margot Lee Shetterly’s book Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race, which was made into an acclaimed film; both were released in 2016.
Black History Month
In honor of Black History Month, we would like to recognize the accomplishments of a group of African-American Mathematicians.
Fern Hunt attended Bryn Mawr College, earning an AB in mathematics in 1969. She went on to earn a master’s degree and PhD in mathematics from the Courant Institute of Mathematics at New York University. Her PhD thesis (1978) Genetic and Spatial Variation in some Selection-Migration Models was advised by Frank Hoppensteadt.
Fern lectures at colleges and universities in order to encourage students in mathematics. She uses her experiences of the setbacks she experienced as a black woman in mathematics to mentor minority students interested in mathematics. In 1998 she was an instructor at a summer workshop for women entering PhD programs in mathematics run by the Edge Foundation (Enhancing Diversity in Graduate Education).
In 2000, Hunt received the Arthur S. Flemming Award for her contributions to probability and stochastic modeling, mathematical biology, computational geometry, nonlinear dynamics, computer graphics, and parallel computing. From 1988 to 1991, she was a member of the Graduate Record Examination Mathematics Advisory Board. She has been a member of the Bryn Mawr College board of trustees since 1992 and the Biological and Environmental Research Advisory Committee for the Department of Energy since 1994.
Hunt was included in the 2019 class of fellows of the American Mathematical Society “for outstanding applications of mathematics to science and technology, exceptional service to the US government, and for outreach and mentoring”. The Association for Women in Mathematics has included her in the 2020 class of AWM Fellows for “her exceptional commitment to outreach and mentoring; for her sustained efforts to make the AWM organization more inclusive; for her service to higher education and government; and for inspiring those underrepresented in mathematics with her work in ergodic theory, probability, and computation.”
Hunt’s work earned her recognition by Mathematically Gifted & Black as a Black History Month 2017 Honoree.
Jesse Ernest Wilkins Jr. was an African American nuclear scientist, mechanical engineer and mathematician. A child prodigy, he attended the University of Chicago at the age of 13, becoming its youngest ever student. His graduation at a young age resulted in him being hailed as “the Negro Genius” in the national media.
Wilkins had a widely varied career, spanning seven decades and including significant contributions to pure and applied mathematics, civil and nuclear engineering, and optics. Wilkins was one of the African American scientists and technicians on the Manhattan Project during the Second World War. He also conducted nuclear physics research in both academia and industry. He wrote numerous scientific papers, served in various important posts, earned several significant awards and helped recruit minority students into the sciences.
In 1940, Wilkins completed his AB in mathematics at the University of Chicago. He went on to an MS and PhD in mathematics at the same institution, which he completed in 1941 and 1942.
In 1944 he returned to the University of Chicago where he served first as an associate mathematical physicist and then as a physicist in its Metallurgical Laboratory, as part of the Manhattan Project. Working under the direction of Arthur Holly Compton and Enrico Fermi, Wilkins researched the extraction of fissionable nuclear materials, but was not told of the research group’s ultimate goal until after the atomic bomb was dropped on Hiroshima. Wilkins was the co-discoverer or discoverer of a number of phenomena in physics such as the Wilkins effect and the Wigner–Wilkins spectra.
In 1970 Wilkins went on to serve Howard University as its distinguished professor of Applied Mathematical Physics and also helped found the university’s new PhD program in mathematics. During his tenure at Howard he undertook a sabbatical position as a visiting scientist at Argonne National Laboratory from 1976 to 1977. From 1990 Wilkins lived and worked in Atlanta, Georgia as a Distinguished Professor of Applied Mathematics and Mathematical Physics at Clark Atlanta University, and retired again for the last time in 2003.
Throughout his years of research Wilkins published more than 100 papers on a variety of subjects, including differential geometry, linear differential equations, integrals, nuclear engineering, gamma radiation shielding and optics, garnering numerous professional and scientific awards along the way.
Annie Jean Easley was an American computer scientist, mathematician, and rocket scientist. She worked for the Lewis Research Center (now Glenn Research Center) of the National Aeronautics and Space Administration (NASA) and its predecessor, the National Advisory Committee for Aeronautics (NACA). She was a leading member of the team which developed software for the Centaur rocket stage and was one of the first African-Americans to work at NASA. Easley was posthumously inducted into the Glenn Research Hall of Fame in 2015. On February 1, 2021, a crater on the moon was named after Easley by the IAU.
In 1955, Easley read a story in a local newspaper about twin sisters who worked for the National Advisory Committee for Aeronautics (NACA) as “computers”. She applied for a job the next day and was hired two weeks later – one of four African Americans out of about 2500 employees. She began her career as a computer at the NACA Lewis Flight Propulsion Laboratory (which became NASA Lewis Research Center, 1958–1999, and subsequently the John H. Glenn Research Center) in Cleveland, Ohio. Later after electronic computers started being used at NASA her title changed to mathematician and computer technician. After receiving her degree Easley also had to complete specialization courses at NASA in order to be considered a professional at NASA. Easley was denied financial aid that other employees received for education, without explanation from the agency. She also noted that she did not feel that her pay was very high when she first started with two years of college. Although she was promised a GS-3 in her interview, her first paycheck was a GS-2, and when she questioned it, she was told there were no more GS-3s available.
Easley lived in a time where women and African-Americans were facing discrimination from society, although she prided herself in her work ethic and achieved her goals nonetheless. She also experienced some discrimination related to being an African-American during her career, especially with the picture-cutting incident at her work, when her face was cut out from a picture to put it on display. In her 34-year career she worked in four different departments: the Computer Services Division, the Energy Directorate, the Launch Vehicles Group and the Engineering Directorate, although none of her moves were due to promotions, which she recognized may have been due to her race or sex.
Throughout the 1970s, Easley advocated for and encouraged female and minority students at college career days to work in STEM careers. She tutored elementary and high school children as well as young adults who had dropped out of school in a work-study program.
National Braille Literacy Month
Lev Semenovich Pontryagin was a Soviet mathematician. He was born in Moscow and lost his eyesight completely due to an unsuccessful eye surgery after a primus stove explosion when he was 14.
Despite his blindness he was able to become one of the greatest mathematicians of the 20th century, partially with the help of his mother Tatyana Andreevna who read mathematical books and papers (notably those of Heinz Hopf, J. H. C. Whitehead, and Hassler Whitney) to him. He made major discoveries in a number of fields of mathematics, including algebraic topology and differential topology. Pontryagin authored several influential monographs as well as popular textbooks in mathematics.
Louis Antoine was a French mathematician who discovered Antoine’s necklace, which J. W. Alexander used to construct Antoine’s horned sphere. He lost his eyesight in the first World War, at the age of 29.
In 1919, Antoine began his doctorate in mathematics at the University of Strasbourg. Antoine was assisted by his friends during his studies, who produced braille copies of mathematical papers. Antoine developed a system of braille mathematical notation, with the assistance of a student at École Normale Supérieure. Antoine discovered Antoine’s necklace in 1921. He submitted his thesis in 1921. In 1922, Antoine became an assistant lecturer at the Faculty of Sciences in Rennes. He subsequently became a professor of Pure Mathematics at Rennes in 1925.
Emmanuel Giroux is a blind French geometer known for his research on contact geometry and open book decompositions. Giroux has Marfan syndrome, because of which he became blind at the age of 11. He earned a doctorate from the École Normale Supérieure in Paris in 1991 under the supervision of François Laudenbach
He has been the director of the Unit of Mathematics, Pure and Applied (UMPA) at the École normale supérieure de Lyon. In 2015, he left Lyon to co-direct the Unité Mixte International of the Centre national de la recherche scientifique and the Centre de Recherches Mathématiques, in Montreal, Quebec, Canada.
Giroux is known for finding a correspondence between contact structures on three-dimensional manifolds and open book decompositions of those manifolds. This result allows contact geometry to be studied using the tools of low-dimensional topology. It has been called a breakthrough by other mathematicians. In 2002 he was an invited speaker at the International Congress of Mathematicians.
Human Rights Month
Katherine Johnson was an American mathematician whose calculations of orbital mechanics as a NASA employee were critical to the success of the first and subsequent U.S. crewed spaceflights. Her social influence as a pioneer in space science and computing is demonstrated by the honors she received and her status as a role model for a life in science. Johnson was named West Virginia State College Outstanding Alumnus of the Year in 1999. President Barack Obama presented her with the Presidential Medal of Freedom, one of 17 Americans so honored on November 24, 2015. She was cited as a pioneering example of African-American women in STEM. President Obama said at the time, “Katherine G. Johnson refused to be limited by society’s expectations of her gender and race while expanding the boundaries of humanity’s reach.” NASA noted her “historical role as one of the first African-American women to work as a NASA scientist. She was also featured in Vanity Fair for being a Human Rights activist in 2016.
Lee Lorch was an American mathematician, early civil rights activist, and communist. His leadership in the campaign to desegregate Stuyvesant Town, a large housing development on the East Side of Manhattan, helped eventually to make housing discrimination illegal in the United States but also resulted in Lorch losing his own job twice. He and his family then moved to the Southern United States where he and his wife, Grace Lorch, became involved in the American civil rights movement there while also teaching at several Black colleges. He encouraged black students to pursue studies in mathematics and mentored several of the first black men and women to earn PhDs in mathematics in the United States. After moving to Canada as a result of McCarthyism, he ended his career as professor emeritus of mathematics at York University in Toronto, Ontario.
Kandalla Balagopal was a human rights activist, mathematician and lawyer who was known for his work on the issue of civil liberties and human rights. He was a staunch civil liberties activist in Andhra Pradesh. He had broken away from the Andhra Pradesh Civil Liberties Committee (APCLC), with which he was associated since its inception in ‘80’s, on the issue of violence perpetrated by the erstwhile CPI-ML Peoples War. He was a writer on people’s issues and had recently written about the developments on the Maoist front in west Bengal. Balagopal was a mathematician, he began his career as a teacher in Warangal but soon turned full-time human rights activist. He was a Mathematics professor at Kakatiya University before quitting in 1985. He did his PhD in Kakatiya University. He chose to become a lawyer much later, after getting fully associated with the human rights movement.
Robert Parris Moses
Robert Parris Moses is an American educator and civil rights activist, known for his work as a leader of the Student Nonviolent Coordinating Committee on voter education and registration in Mississippi during the Civil Rights Movement, and his co-founding of the Mississippi Freedom Democratic Party. He is a graduate of Hamilton College and completed a master’s in philosophy at Harvard University. Since 1982 Moses has developed the nationwide Algebra Project in the United States. He has received a MacArthur Fellowship and other awards for this work, which emphasizes teaching algebra skills to minority students based on broad-based community organizing and collaboration with parents, teachers and students. He currently runs the Algebra Project, which is a continued effort to improve math education in poor communities with the goal of sending more students to the workforce. Starting as a civil rights leader and transitioning into an advocate for the poor through his work with the Algebra Project, Moses has revolutionized the ideal of equal opportunity and has played a vital role in making it a reality.