# Mathematician of the Month

Mathematics Department Student Success

## Vito Volterra

Vito Volterra was an Italian mathematician and physicist known for his significant contributions to mathematical biology and integral equations. He was recognized as one of the founders of functional analysis. Throughout his professional life, Volterra made groundbreaking advancements in various fields, including developing theories to model biological systems and studying integral equations. His work has had a lasting impact on the fields of mathematics and physics, solidifying his reputation as a pioneering figure in the scientific community.

**Jaime Escalante**

He’s likely the most well known Hispanic math educator in the United States. Escalante was a Bolivian math teacher who was the subject behind the hit movie, “Stand And Deliver.” He moved to the United States in the 1960s. In 1974, he started teaching at Garfield High School in East Los Angeles, which consisted of predominantly Hispanic students and was also known for drugs and violence. Despite the challenges, Escalante continued to have faith in his students and created an advanced mathematics program. In 1982, his largest class of students passed the advance placement Calculus test. However, the company later disqualified some of the students’ test scores and accused them of cheating. Escalante fought for his students and they once again took and passed the test.

He was awarded the Presidential Medal of Excellence and was inducted into the National Teachers Hall of Fame. He passed away in 2010. In 2016, the U.S. Postal Service honored him with a stamp.

## International Peace Month

*Larry Liebovitch is a professor in the Department of Physics and the Department of Psychology at Queens College, and at the Physics Program of the Graduate Center, City University of New York. He is also a core faculty member of the Sustaining Peace Project at the Earth Institute’s Advanced Consortium on Cooperation, Conflict, and Complexity (AC4). He recently developed a mathematical model simulation of sustainable peace in a society. In this mathematical model, users respond to a series of questions about a community by plugging in values for different factors that research suggests are important to sustaining peace. Examples of these factors include the degree to which leaders model peaceful values and the degree to which information flows freely between members of all groups in a society. The model then shows where the system of factors might end up over time — heading to war or situated in peace — offering a tool for the public to think about possible paths to sustaining peace.*

In thinking through all the different factors that are important to sustaining peace in a community, we found that there are many things that interact with each other, so it can be very hard to think through all the details. For example, if a factor such as “good governance” interacts with a factor such as “equitable distribution of resources,” and interacts with three more things, where does the whole system wind up?

One of the things you can do in a mathematical model is write down equations that represent all these interactions. Once you have equations, there are very standard methods to solve these equations. So, in a way, you just use these methods and then you can see where the whole system is going to wind up. So, the purpose was to see when we have all these interactions, if they’re all happening simultaneously, what happens at the end? What values do all these different factors achieve due to the influence of the other factors? In other words, how do all these pieces interact as a system to sustain peace?

The purpose of putting the math model on the web and GitHub was to provide people an opportunity to play with it. So they could say, ‘Well, what happens if we increase the value of this variable (like tolerance education) or we increase the value of this interaction?’ and see how that will affect levels of peacefulness in the community.

## French American Heritage Month

Benoit Mandelbrot was a Polish born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as “the art of roughness” of physical phenomena and “the uncontrolled element in life”. He referred to himself as a “fractalist” and is recognized for his contribution to the field of fractal geometry, which included coining the word “fractal”, as well as developing a theory of “roughness and self-similarity” in nature.

## Caribbean American Heritage Month

Lucy Campbell was born in Barbados. Her father was from Barbados and was a math professor with a PhD in the area of math called group theory. Her mother was a teacher from Ghana. Lucy also lived in Ghana and in the UK before moving to Canada. She is an applied mathematician, so her research involves using mathematical and computational methods to solve problems in science. Her main interest is in geophysical fluid dynamics, which is the study of the movement of air and water in the atmosphere and oceans. She is particularly interested in understanding how waves in the atmosphere interact and affect the general circulation of the atmosphere and influence weather and climate.

## Asian American and Pacific Islanders Heritage Month

Dr. Kamuela Yong, the first Native Hawaiian to earn a Ph.D. in applied mathematics, serves as an associate professor of mathematics at the University of Hawai‘i–West O‘ahu. Recognized for his exceptional teaching, he received the 2019 Frances Davis Award for Excellence in Undergraduate Teaching and the 2020 University of Hawai‘i Regents’ Medal for Excellence in Teaching. Dr. Yong is a co-founder of IndigenousMathematicians.org, where he is building a global community for Indigenous mathematicians. Integrating Pacific ancestral knowledge, such as navigation, into his curriculum, he authored the freely available trigonometry textbook “Trigonometry Through Wayfinding and Navigation Across the Pacific. Dr. Yong’s research interests include mathematical modeling of biological, ecological, and epidemiological systems using diffusion.

## Arab American Heritage Month

In mathematics, the Arab cipher, or zero, made workable the solution of complicated mathematical problems. The Arab numeral, an improvement on the original Hindu invention, and the Arab decimal system made simpler and more flexible the course of science.^{[2]}

The Arabs invented and developed Algebra and made revolutionary strides in trigonometry. Al-Khwarizmi, credited with the invention of Algebra, was inspired by the need to find a more accurate and comprehensive method to assure the precise divisions of land so that the Koran could be specifically obeyed in the laws of inheritance. The Astrolabe, combining the use of mathematics, geography and astronomy was also devised with religion in view, and was used to chart exactly the time of sunrise and sunset, to determine the time for fasting during the month of Ramadan. The writings of Leonardo da Vinci, Leonardo Fibonacci of Pisa and Master Jacob of Florence show the Arab influence on mathematical studies in European universities.^{[3]}

The reformation of the calendar, with a margin of error of only one day in five thousand years was also a contribution of the Arab intellect. Indeed, in our every day commerce, whether it is in yard goods, lumber, or ingots of gold and silver, we use the weights and measures by which the Arabs of the past conducted the business of their every day life.

## Women’s History Month

In 2019, Karen Uhlenbeck became the first female recipient of the Abel Prize, the highest prize in mathematics (there is no Nobel category for math). The award was in recognition of Uhlenbeck’s pioneering work in geometric partial differential equations and gauge theory, known as the mathematical language of theoretical physics.

Uhlenbeck’s groundbreaking insights have applications in particle physics, string theory and general relativity.

## Black History Month

Dr. Evelyn Granville (May 1, 1924 – June 27, 2023) was the second Black woman to earn a doctorate in mathematics (Yale University, 1949) from an American University. She performed pioneering work in the field of computing. In addition to serving as a department chair of mathematics at Fisk University, she worked as a mathematician for IBM (International Business Machines) focusing on the orbit computations and computer procedures for NASA’s Project Mercury. Two of her Fisk University students, Vivienne Malone-Mayes and Etta Zuber Falconer, also went on to earn doctorates.

## Braille Literacy Month

Nicholas Saunderson (1682–1739), the fourth Lucasian professor of mathematics at Cambridge, was fluent in Latin, French, and Greek, and an accomplished musician. He enjoyed a reputation as an outstanding teacher, noted for both his popular lectures on natural science and his expertise in tutoring mathematics. He wrote two successful mathematics texts, *The Elements of Algebra* and *Method of Fluxions*, and invented a palpable arithmetic which also served as a geoboard. These achievements are especially remarkable considering that he was blinded by smallpox at the age of one. It was said at Cambridge that he was a teacher who had not the use of his eyes but taught others to use theirs.

## Human Rights Month

Lipman “Lipa” Bers is a Latvian American mathematician, born in Riga, who created the theory of pseudo analytic functions and worked on Riemann surfaces and Kleinian groups. He was also known for his work in human rights activism. Bers spent World War II teaching mathematics as a research associate at Brown University, where he was joined by Loewner. After the war, Bers found an assistant professorship at Syracuse University (1945–1951), before moving to New York University (1951–1964) and then Columbia University (1964–1982), where he became the Davies Professor of Mathematics, and where he chaired the mathematics department from 1972 to 1975. His move to NYU coincided with a move of his family to New Rochelle, New York, where he joined a small community of émigré mathematicians. He was a visiting scholar at the Institute for Advanced Study in 1949–51. He was a Vice-President (1963–65) and a President (1975–77) of the American Mathematical Society, chaired the Division of Mathematical Sciences of the United States National Research Council from 1969 to 1971, chaired the U.S. National Committee on Mathematics from 1977 to 1981, and chaired the Mathematics Section of the National Academy of Sciences from 1967 to 1970. He founded the Committee on Human Rights of the National Academy of Sciences and beginning in the 1970s worked to allow the emigration of dissident soviet mathematicians including Yuri Shikhanovich, Leonid Plyushch, Valentin Turchin, and David and Gregory Chudnovsky.

## Native American Heritage Month

Thomas Storer was a member of the Navajo tribe. As a mathematician, he did research in combinatorics. Storer is known as one of the first Native Americans to earn a Ph.D. in mathematics in the U.S. and to reach a position of full professor at a major university. As a child, he learned string figure-making from his grandmother. String figure-making is an activity that has been carried out by many societies of oral tradition; it consists of producing geometrical forms using a string knotted into a loop. Storer became a string figure-making enthusiast and published an article in which he developed formal approaches of string figure-making.

## Filipino American History Month

Dr. Tito Mijares, as a researcher he performs studies in relation to multi-variety hypothesis and analysis, which were published in the Annals of Mathematical Statistics, a global journal. He was born on December 26, 1922.

His accomplishment in statistics made him elected to attachment in international statistical groups such as the Statistical Institute of Asia and the Pacific, International Statistical Institute, and the Institute for Vital Registration and Statistics.

Dr. Mijares was voted to membership in worldwide statistical system in the country. He became Deputy Director-General of the National Economic Development Authority (NEDA) and Executive Director of the National Census and Statistics Office (NCSO) for a number of times.

## Hispanic Heritage Month

Alberto Pedro Calderón, widely considered one of the 20th century’s most important mathematicians, was born in Mendoza, Argentina. He studied at the University of Chicago and the University of Buenos Aires. While in Chicago, he studied under Antoni Zygmund, a Polish mathematician who was an expert analyst. They went on to collaborate for more than 30 years.

Calderón and Zygmund developed the theory of singular integral operators. The theory was the basis for one of the most influential movements in mathematics: the Chicago School of (hard) Analysis. This school of thought emphasizes applying mathematical analysis to the study of partial differential equations (PDEs). PDEs are used in science and engineering to measure and describe a variety of phenomena such as sound, heat, electrostatics, and quantum mechanics.

Calderón’s original work, with and without his mentor, greatly influenced mathematical analysis and ranged over a variety of topics including PDEs, interpolation theory, Cauchy integrals on Lipschitz curves, ergodic theory, and inverse problems in electrical prospection. Some practical applications for Calderón’s work include signal processing, geophysics, and tomography.

## International Peace Month

Anatol Rapoport was a was an American mathematical psychologist. He contributed to general systems theory, to mathematical biology and to the mathematical modeling of social interaction and stochastic models of contagion. He completed his PhD at the University of Chicago in 1941. After the war, he published his first book, *Science and the Goals of Man*, co-authored with semanticist S. I. Hayakawa. From 1955-1970 he was Professor of Mathematical Biology and Senior Research Mathematician at the University of Michigan, as well as founding member, in 1955, of the Mental Health Research Institute at the University. In 1970 he moved and became professor of mathematics and psychology at the University of Toronto. University of Toronto appointed him professor of peace studies in 1984, a position he held until 1996, but continued to teach until 2000. In 1984 he co-founded Science for Peace, was elected president and remained on its executive until 1998.

## Bastille Day

Pierre de Fermat was a French Mathematician and one of the most brilliant and productive mathematicians of his time. He made many contributions to differential and integral calculus, number theory, optics, and analytic geometry, as well as initiating the development of probability theory in correspondence with Pascal. He is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat’s principle for light propagation and his Fermat’s Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus’ *Arithmetica*.

René Descartes was a creative mathematician of the first order, an important scientific thinker, and an original metaphysician. During the course of his life, he was a mathematician first, a natural scientist or “natural philosopher” second, and a metaphysician third. In mathematics, he developed the techniques that made possible algebraic (or “analytic”) geometry. Descartes was known among the learned in his day as a top mathematician, as the developer of a new and comprehensive physics or theory of nature (including living things), and as the proposer of a new metaphysics. In the years following his death, his natural philosophy was widely taught and discussed.

Marie-Sophie Germain was a French mathematician, physicist, and philosopher. When Germain was 13, the Bastille fell, and the revolutionary atmosphere of the city forced her to stay inside. For entertainment, she turned to her father’s library. Here she found J. E. Montucla’s *L’Histoire des Mathématiques*, and his story of the death of Archimedes intrigued her.

She is the first woman known who managed to make great strides in mathematics, especially in number theory, despite her lack of any formal training or instruction. She is best known for one particular theorem that aimed at proving the first case of Fermats Last Theorem. Recent research on some of Germain‘s unpublished manuscripts and letters reveals that this particular theorem was only one minor result in her grand plan to prove Fermat‘s Last Theorem. Her work on Fermats Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her sex, she was unable to make a career out of mathematics, but she worked independently throughout her life.

## Juneteenth

Thomas Fuller was born in Africa and brought as a slave to the USA in 1724 at the age of 14. He was born in 1710 Africa somewhere between present day Liberia and Benin. Late in his life his remarkable powers of calculation made him a tool of abolitionists to demonstrate blacks are not mentally inferior to whites. Fuller, though extraordinarily quick at calculations, appears not so much the equal of idiot savants as someone who had taught himself quick calculations. Many of those who met him advertised his general self-taught intelligence and decried the system which prevented him from formal education.

Our present new understanding of mathematics in Africa at that time allows us to claim that when Thomas Fuller arrived in 1724 Virginia, he had already developed his calculation abilities. His learning of number words, a numeration system, of arithmetical operations, of riddles and mathematical games, etc. As a result, he was known as the “Virginia Calculator.”

Kelly Miller was anAmerican mathematician, sociologist, essayist, newspaper columnist, author, and an important figure in the intellectual life of Black America for close to half a century. He was born in 1863 in South Carolina, and showed an aptitude for mathematics early on in his schooling. He was awarded a scholarship to Howard University, receiving a Bachelor of Science degree in 1886. In 1887, Kelly became the first Black student to be admitted to Johns Hopkins University, where he performed graduate work in mathematics, physics, and astronomy.

From 1887 to 1889 Miller performed graduate work in Mathematics, Physics, and Astronomy. When an increase in tuition ($100 to $200) prevented Miller from continuing his studies, Kelly Miller left (and Johns Hopkins closed its doors to Blacks) and taught at the M Street High School in Washington, D.C. (1889-1890), whose principal was Francis L. Cardozo

After teaching mathematics briefly at the M Street High School in Washington, D.C. (1889-1890), he was appointed to the faculty of Howard University in 1890. Five years later, Miller added sociology to Howard’s curriculum because he thought that the new discipline was important for developing objective analyses of the racial system in the United States. As dean of the College of Arts and Sciences, he modernized the classical curriculum, strengthening the natural and social sciences. In February 1924, Miller was elected chairman of the Negro Sanhedrin, a civil rights conference held in Chicago that brought together representatives of 61 African-American organizations to forge closer ties and attempt to craft a common program for social and political reform.

Charles Reason was an American mathematician, linguist, and educator who was born on July 21, 1818 in New York City to West Indies immigrants. Charles attended the African Free School and was an excellent student in mathematics. He was the first black college professor in the United States, teaching at New York Central College, McGrawville.

In addition to teaching, Reason lobbied New York to repeal the state’s “sojourner law,” which allowed slaveholders from other states to bring their slaves to New York, allowing “free and unfettered” movement for them with the accompanying slaves. Reason’s work helped to secure the right of blacks accused of being runaway slaves to a jury trial. In 1847 Reason and Charles B. Ray founded the Society for the Promotion of Education among Colored Children, a black organization authorized by the state legislature to oversee black schools in New York City. Reason served as superintendent of P.S. 2 in 1848, and Frederick Douglass wrote in the *North Star* of 11 May 1849 that, under Reason’s leadership, the school became a rigorous refutation of the calumnies of John C. Calhoun about the potentials of free blacks.

In 1849, Reason became the first African American to hold a professorship at a predominantly white American college when he was hired as professor of belles lettres, Greek, Latin, and French and adjunct professor of mathematics at the integrated New York Central College in McGrawville (Cortland County), New York only to resign in 1852 in order to become the first principal of Philadelphia’s Institute for Colored Youth (1852-56) [now Cheyney University of PA]. In British abolitionist Julia Griffith’s *Autographs for Freedom* (1854), he wrote that a black industrial college would prepare free blacks, who were shut out of the “workshops of the country,” to become “self-providing artisans vindicating their people from the never-ceasing charge of a fitness for servile positions.”

## Asian American And Pacific Islander Heritage Month

Josephine Jue was born in 1946 and is a Chinese-American computer programmer and mathematician who is best known for being the first Asian-American woman working in NASA, where she worked for 37 years. Jue joined NASA in 1963, being one of eight women at the time, and the sole Asian-American woman. She worked for NASA for 34 years, where she held four different positions. During her time, Jue worked as a compiler for the Space Shuttle program, and also worked for Apollo 11. She also was the chief of NASA’s Software Engineering Laboratory (SEL) in 1975. She is best known for development, implementation, and maintenance of the HAL/S system during the Space Shuttle program.

Heisuke Hironaka is a Japanese mathematician who was awarded the Fields Medal in 1970 for his contributions to algebraic geometry. In 1964, Hironaka proved that singularities of algebraic varieties admit resolutions in characteristic zero. This means that any algebraic variety can be replaced by (more precisely is birationally equivalent to) a similar variety which has no singularities. He also introduced Hironaka’s example showing that a deformation of Kähler manifolds need not be Kähler. In 2017, he posted to his personal webpage a manuscript that claims to prove the existence of a resolution of singularities in positive characteristic.

Roy Kerr is a New Zealand mathematician who discovered the Kerr geometry, an exact solution to the Einstein field equation of general relativity. His solution models the gravitational field outside an uncharged rotating massive object, including a rotating black hole. His solution to Einstein’s equations predicted spinning black holes before they were discovered. Roy Kerr is one of the world’s most famous mathematicians.

## 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. Though many think their contribution was developing the existing philosophies of mathematics, it was not the case all the time. Some of the mathematicians also created mathematical concepts and solved problems that were left unsolved by the Greeks and Indians.

Taher Elgamal

Taher Elgamal is an Egyptian cryptographer and entrepreneur. He has served as the Chief Technology Officer (CTO) of Security at Salesforce since 2013. Prior to that, he was the founder and CEO of Security and the director of engineering at RSA Security. From 1995 to 1998, he was the chief scientist at Netscape Communications. He has been described as the “father of SSL” for the work he did in computer security while working at Netscape, which helped in establishing private and secure communications on the Internet.

Elgamal’s 1985 paper entitled “A Public Key Cryptosystem and A Signature Scheme Based on Discrete Logarithms” proposed the design of the ElGamal discrete log cryptosystem and of the ElGamal signature scheme. The latter scheme became the basis for Digital Signature Algorithm (DSA) adopted by National Institute of Standards and Technology (NIST) as the Digital Signature Standard (DSS).

The El Gamal probabilistic public key crypto system is taught in several undergraduate and graduate classes at NC State and is probably used inside of every smartphone.

Manahel Thabet

Manahel Thabet has a PhD in financial engineering and in quantum mechanics. She is known for her brilliance with her IQ of 168, and was even named Genius of the Year in Asia, and chosen to be part of the World Genius Directory. To add to that, she is also a world-class humanitarian and was given a UN award for undertaking humanitarian missions in Africa. From her roots as a member of Young Arab Leaders, Manahel has definitely come far in her life.

Currently, she acts as the head and founder of SmartTips Consultants, President (Middle East and North Africa/MENA) of The Brain Trust Foundation, president of the World IQ Foundation, Vice President of the World Intelligence Network (WIN), Deputy Director of the Institute for Brain Chemistry and Human Nutrition and Vice Chancellor of The Gifted Academy. She has been recognized as one of the most powerful Arabs in the world.

Sutaata al-Mahamili was a mathematician born to an educated family in Baghdad. While she was proficient in fields, such as Arabic literature, hadith, and jurisprudence, she is best known for her many solutions to algebraic equations.

It is said that she was an expert in *hisab* (arithmetics) and *fara’idh* (successoral calculations), both being practical branches of mathematics which were well developed in her time. It is said also that she invented solutions to equations which have been cited by other mathematicians, these include equations which denote aptitude in algebra. Although these equations were few, they demonstrated that her skills in mathematics went beyond a simple aptitude to perform calculations.

## Women’s History Month

**In honor of Women’s History Month, we would like to recognize the accomplishments of a group of Female Mathematicians.**

Annie Easley is a famous NASA computer and rocket scientist and mathematician who contributed to several space programs, inspired others through her participation in numerous outreach programs, and broke down barriers for both women and African Americans in STEM. Most notably, she was a leading member of the team that developed the breakthrough *Centaur *rocket, which opened the door for the launch of many of NASA’s most important missions. Easley was known for being a “human computer” and always fought to do her best in the face of adversity. In a 2001 interview she shared that “I just have my own attitude. I’m out here to get the job done, and I knew I had the ability to do it, and that’s where my focus was.”

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 known as Cartwright’s Theorem.

## Black History Month

**In honor of Black History Month, we would like to recognize the accomplishments of a group of African-American Mathematicians.**

Although best known as an African-American scientist, Benjamin Banneker was a multi-talented person who self-educated himself in astronomy and mathematics. He was also a writer, compiler of almanacs, surveyor and inventor. At the age of 24, Banneker observed a wrist-watch and used it to construct his own clock from wood which struck on the hour. He created puzzles for trigonometry which demonstrated his knowledge of logarithms. Banneker also attempted to find the exact lengths of an equilateral triangle which is inscribed within a circle where the diameter of the circle is known. He brought about a positive contribution in mathematics years before any black mathematician came to rise.

Elbert Frank Cox is a name that will perhaps never be missed out when speaking about black mathematicians. In 1925, Cox became the first African-American to earn a PhD in mathematics. He inspired many future black mathematicians and served a 40 year long teaching career. He taught at Howard University and West Virginia State College. The Cox Talbot Address is annually delivered at the National Association of Mathematicians’ national meetings in his honor and the Elbert F. Cox Scholarship Fund which is used to help black students achieve educational goals is also named in his honor.

Euphemia Haynes became the first black American woman with a PhD in mathematics in 1943. She played an instrumental role in changing the face of the education system from which blacks were often segregated or very few in number. For forty-seven years, Haynes taught at Washington DC’s public schools where she was also the first woman to chair the DC School Board. Haynes also served as chair at Dunbar High School and District of Columbia Teachers College for their respective mathematics departments. At Miner Teachers College, she went as far as establishing the mathematics department altogether. The Catholic University of America established the Euphemia Lofton Haynes Award to recognize outstanding junior mathematics majors who have demonstrated excellence and promise in their study of mathematics.

## Braille Literacy Month

I**n honor of National Braille Literacy Month, we would like to recognize the accomplishments of a group of Blind Mathematicians.**

Abraham Nemeth was an American mathematician and inventor. He was Professor of Mathematics at the University of Detroit Mercy in Detroit, Michigan. Nemeth was blind and was known for developing a system for blind people to read and write mathematics.

Nemeth taught part-time at various colleges in New York. Though his employers were sometimes reluctant to hire him knowing that he was blind, his reputation grew as it became apparent that he was a capable mathematician and teacher. Nemeth distinguished himself from many other blind people by being able to write visual print letters and mathematical symbols on paper and blackboards just like sighted people, a skill he learned as a child. Nemeth says that this skill allowed him to succeed in mathematics, during an era without much technology, when even Braille was difficult to use in mathematics. During the 1950s he moved to Detroit, Michigan to accept a position at the University of Detroit working with Keith Rosenberg. He remained there for 30 years, retiring in 1985. During the late 1960s he studied computer science and began the university’s program in that subject.

As the coursework became more advanced, he found that he needed a braille code that would more effectively handle the kinds of math and science material he was tackling. Ultimately, he developed the Nemeth Braille Code for Mathematics and Science Notation, which was published in 1952. The Nemeth Code has gone through 4 revisions since its initial development and continues to be widely used today.

Nemeth is also responsible for the rules of MathSpeak, a system for orally communicating mathematical text. In the course of his studies, Nemeth found that he needed to make use of sighted readers to read otherwise inaccessible math texts and other materials. Likewise, he needed a method for dictating his math work and other materials for transcription into print. The conventions Nemeth developed for efficiently reading mathematical text out loud have evolved into MathSpeak.

Nemeth was instrumental in the development of Unified English Braille (UEB) from 1991 to at least 2001, though he eventually parted ways with others developing that code, and instead worked on a parallel effort called the Universal Braille System (sometimes abbreviated as NUBS with his name appended to the front). As of 2012, UEB was officially adopted by BANA as the standard for literary braille, but Nemeth Code was also fully retained as an optional official coding system. Work on NUBS may continue, or it might be merged into a future rules-update to the official Nemeth Code (the most recent official rules-update to Nemeth Code was in 2013).

Bernard Morinwas a French mathematician, specifically a topologist. Morin lost his sight at the age of six due to glaucoma, but his blindness did not prevent him from having a successful career in mathematics. He received his Ph.D. in 1972 from the Centre National de la Recherche Scientifique.

Morin was a member of the group that first exhibited an eversion of the sphere, i.e. a homotopy (topological metamorphosis) which starts with a sphere and ends with the same sphere but turned inside-out. He also discovered the Morin surface, which is a half-way model for the sphere eversion and used it to prove a lower bound on the number of steps needed to turn a sphere inside out.

He discovered the first parametrization of Boy’s surface (earlier used as a half-way model) in 1978. His graduate student François Apéry later discovered (in 1986) another parametrization of Boy’s surface, which conforms to the general method for parametrizing non-orientable surfaces.

Morin worked at the Institute for Advanced Study in Princeton. Most of his career, though, he spent at the University of Strasbourg.

Leonhard Euler was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory.

Euler was one of the most eminent mathematicians of the 18th century and is held to be one of the greatest in history. He is also widely considered to be the most prolific, as his collected works fill 92 volumes,more than anyone else in the field. He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia.

Euler’s eyesight worsened throughout his mathematical career. In 1738, three years after nearly expiring from fever, he became almost blind in his right eye, but Euler rather blamed the painstaking work on cartography he performed for the St. Petersburg Academy for his condition.

## Universal Human Rights Month

In honor of Human Rights Month, we would like to recognize the accomplishments of a group of Mathematicians who were also Human Rights Activists.

Kandalla Balagopal

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.

Katherine Johnson

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.

Lipman “Lipa” Bers is a Latvian American mathematician, born in Riga, who created the theory of pseudo analytic functions and worked on Riemann surfaces and Kleinian groups. He was also known for his work in human rights activism. Bers spent World War II teaching mathematics as a research associate at Brown University, where he was joined by Loewner. After the war, Bers found an assistant professorship at Syracuse University (1945–1951), before moving to New York University (1951–1964) and then Columbia University (1964–1982), where he became the Davies Professor of Mathematics, and where he chaired the mathematics department from 1972 to 1975. His move to NYU coincided with a move of his family to New Rochelle, New York, where he joined a small community of émigré mathematicians. He was a visiting scholar at the Institute for Advanced Study in 1949–51. He was a Vice-President (1963–65) and a President (1975–77) of the American Mathematical Society, chaired the Division of Mathematical Sciences of the United States National Research Council from 1969 to 1971, chaired the U.S. National Committee on Mathematics from 1977 to 1981, and chaired the Mathematics Section of the National Academy of Sciences from 1967 to 1970. He founded the Committee on Human Rights of the National Academy of Sciences and beginning in the 1970s worked to allow the emigration of dissident soviet mathematicians including Yuri Shikhanovich, Leonid Plyushch, Valentin Turchin, and David and Gregory Chudnovsky.

## Native American Heritage Month

In an effort to celebrate Native American Heritage Month, we would like to recognize the accomplishments of a group of Native American Mathematicians.

Mary G. Ross, the first Native American female engineer, graduated from Northeastern State College (now Northeastern University), in 1928, with a degree in mathematics. Her alma mater was founded by her great-great grandfather, Chief John Ross, who led the Cherokee tribes during their forced removal to the west. Ross’ family emphatically supported the Cherokee tradition of emphasizing education, and equally so for both genders.

After teaching high school mathematics and science for several years, Mary served as a statistical clerk for the Bureau of Indian Affairs, and then a girl’s advisor at a Native American boarding school. Earning a master’s degree in mathematics from Colorado State College allowed her to join Lockheed Aircraft Corporation, in 1942. During the first two and a half years at Lockheed, Mary assisted with developing fighter planes. She applied her mathematical expertise to researching compressibility effects on the relatively large P-28 fighter plane, as it reached the sound barrier. Impressed with her performance and motivated by events of the second world war, Lockheed then offered to educate Ross as an engineer. Intense training through Lockheed and the University of California at Los Angeles followed. By 1949, a time when aeronautical engineering distinctions were yet to exist, Ross completed a mechanical engineering classification.

After retiring from Lockheed, in 1973, Ross began another career as a staunch advocate of engineering and mathematics opportunities for women and Native-Americans. As a pioneering member of the Society of Women Engineers (SWE), she traveled to high schools and seminars to mentor college-bound students. Ross co-founded the Los Angeles section of SWE, and then served at their national government levels, for more than a decade. Her involvement with the American Indian Science and Engineering Society (AISES) and the Council of Energy Resource Tribes (CERT) resulted in expanded educational programs within each of those organizations.

Robert Eugene Megginson grew up in a family that enjoyed and valued mathematics, which is certainly one of the reasons for his interest in the field. His maternal Native American grandfather never attended a day of formal school in his life but was very well self-educated and was fascinated by mathematics. He loved to give Megginson small mathematical problems to work out and his interest in these sorts of problems certainly rubbed off. Megginson’s father, whose family is from England, has a bachelor’s degree in physics and mathematics, and that also influenced his decision to go into mathematics.

Megginson was born in 1948 in Washington, Illinois, of Oglala Sioux heritage on his mother’s side, and grew up in Sheldon, Illinois, where his father was mayor. He earned a degree in physics from the University of Illinois at Urbana–Champaign in 1969, and became a software specialist for the Roper Corporation until 1977, when he returned to graduate school. He earned a master’s degree in statistics in 1983 and he completed his Ph.D. in 1984 at the University of Illinois, with a thesis on normed vector spaces supervised by Mahlon M. Day. This accomplishment made him one of only approximately 12 Native Americans to hold a doctorate in mathematics, and he has taken great interest in underrepresented minorities in mathematics.

Because his wife was employed nearby in Decatur, Illinois, Megginson took a teaching position in 1983, joining the faculty of Eastern Illinois University as an assistant professor, rather than doing postdoctoral research. He moved to the University of Michigan in 1992, was on leave as the deputy director of the Mathematical Sciences Research Institute in Berkeley, California from 2002 to 2004, and became the Thurnau Professor at Michigan in 2008.

Megginson won the U.S. Presidential Award for Excellence in Science, Mathematics, and Engineering Mentoring in 1997. The American Indian Science and Engineering Society gave him their Ely S. Parker Award for lifetime service to the Native American community in 1999. The American Association for the Advancement of Science elected him as a fellow in 2009, and in the same year the Mathematical Association of America gave him their Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service, for his work on underrepresented minorities. In 2012, Megginson became one of the inaugural fellows of the American Mathematical Society.

Freda Porter is among the small number of American Indian women who have earned a Ph.D. in mathematics. A member of the Lumbee tribe, she was born in Lumberton, North Carolina. In 1978 she earned her Bachelor of Science degree in applied mathematics from Pembroke State University. After completing an IBM Graduate Internship Program, she entered North Carolina State University where she earned a Masters in Applied Mathematics with a computer science minor in 1981.

While married and raising a family, she commuted to Duke University where she received her Ph.D. in 1991 in applied mathematics and computational sciences with a dissertation on “A numerical study of propagation of singularities for semilinear hyperbolic systems” written under the direction of Michael Reed. After receiving her degree, Porter began teaching mathematics at Pembroke State University. She then taught at the University of North Carolina at Chapel Hill while doing post-doctoral work in applications of mathematical models to the study of groundwater contamination. She was the co-author of a paper in the SIAM Review on “Estimating the rate of natural bio attenuation of ground water contaminants by a mass conservation approach.” In 1998 she also earned a Water Pollution Control System Operators Certification at North Carolina State University.

## Filipino American History Month

In an effort to celebrate Filipino American History Month, we would like to recognize the accomplishments of a group of Filipino Mathematicians.

Mari-Jo P. Ruiz is a Filipina mathematician, currently a professor emeritus of mathematics at Ateneo de Manila University. She graduated from Marymount Manhattan College in New York City in 1963, and soon afterward completed a master’s degree at New York University. She joined the Ateneo de Manila faculty in 1965, eight years before the school began accepting women as students. She chose academia over a competing job offer from industry because at the time it paid slightly better. She acquired the nickname “Mustang Mary” at this time, because of the Ford Mustang that she drove.

Ruiz completed her PhD at Ateneo in 1981. At Ateneo, she has served as chair of mathematics, chair of management engineering, dean of arts and sciences, and trustee. She retired to become a professor emeritus in 2009.

With Jin Akiyama, she is the author of the book *A Day’s Adventure in Math Wonderland*. The College of the Holy Spirit Alumnae Foundation gave Ruiz their Distinguished Alumna in Education Award in 2001. In 2014, Ateneo gave Ruiz their Lux-in-Domino Award.

Raymundo Favila was a Filipino Mathematician who was elected by the National Academy of Science and Technology as an Academician in 1979. He was invaluable in the advancement of mathematics and mathematics education in the Philippines and published information in the field of theoretical physics.

One of the groundbreakers in mathematics in the Philippines, he contributed extensively to the progression of mathematics and the mathematics learning in the country. He has made fundamental studies such as on stratifiable congruences and geometric inequalities and has also co-authored textbooks in algebra and trigonometry.

Bienvenido Nebres is a Filipino scientist, mathematician, and a Jesuit priest who was the longest-serving university president of the Ateneo de Manila University. He contributed much to the development of higher mathematics teaching in the nation being the president of Mathematical Society of the Philippines for years. He has successfully published 15 documents about pure mathematics and mathematics education.

With masters and doctoral degrees in Mathematics from Stanford, Nebres has dedicated much of his career to educational development, especially in math and the sciences. He also helped found the Southeast Asian Mathematical Society and is involved with the Technical Panel on Science and Mathematics of the Commission on Higher Education. He works with the public and private sectors towards nation-building in the Philippines.

## National Hispanic Heritage Month

In an effort to celebrate Hispanic Heritage Month, we would like to recognize the accomplishments of a group of Hispanic and Latinx Mathematicians.

Ruth Gonzalez, born in Houston to Mexican parents, was interested in math throughout elementary school and high school. In 1976, she earned her bachelor’s degree in mathematics at the University of Texas. While doing research at the Applied Research Laboratories at the University of Texas from 1976 to 1980, she earned her master’s degree in mathematics.

In 1980, Gonzalez joined the Exxon Production Research Company as a geophysical mathematician and continued her graduate work at Rice University. In 1986, she received her Ph.D. in applied mathematics from Rice University, making her the first U.S born Hispanic woman to earn a doctorate in mathematics.

She’s had an extensive career developing seismic imaging tools and encourages other minority girls and women to pursue a career in math and science.

Alberto Pedro Calderón, widely considered one of the 20th century’s most important mathematicians, was born in Mendoza, Argentina. He studied at the University of Chicago and the University of Buenos Aires. While in Chicago, he studied under Antoni Zygmund, a Polish mathematician who was an expert analyst. They went on to collaborate for more than 30 years.

Calderón and Zygmund developed the theory of singular integral operators. The theory was the basis for one of the most influential movements in mathematics: the Chicago School of (hard) Analysis. This school of thought emphasizes applying mathematical analysis to the study of partial differential equations (PDEs). PDEs are used in science and engineering to measure and describe a variety of phenomena such as sound, heat, electrostatics, and quantum mechanics.

Calderón’s original work, with and without his mentor, greatly influenced mathematical analysis and ranged over a variety of topics including PDEs, interpolation theory, Cauchy integrals on Lipschitz curves, ergodic theory, and inverse problems in electrical prospection. Some practical applications for Calderón’s work include signal processing, geophysics, and tomography.

Portuguese mathematician Ruy Luís Gomes was one of the leading intellectuals of the 20th century. However, he was persecuted by Portugal’s government for his outspoken ideas and independent thinking. Nonetheless, he was committed to teaching and research, making many significant mathematical contributions and serving as a role model for a generation of intelligent, creative mathematicians.

Gomes passionately believed that teachers should be more than the transmitters of theory. Rather, they should act as active research agents, inspiring students to come up with their own new theories and conclusions. He was an innovator in connecting Portuguese mathematicians with mathematicians and other scientists around the globe. He believed in a global mathematics community, promoted through seminars, conferences, short courses, study and research centers and scientific societies. At the time, this idea of global cooperation was radical. The Portuguese government didn’t approve. Gomes, his associates and his students created two influential magazines dedicated to mathematics: Portugaliae Mathematica, mainly composed of research articles and Gazeta Matemática. Both magazines are still published today by the Portuguese Mathematical Society.

## Peace Month

Lewis Fry Richardson was a mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them. He is also noted for his pioneering work concerning fractals and a method for solving a system of linear equations known as modified Richardson iteration.

Richardson worked from 1916 to 1919 for the Friends’ Ambulance Unit attached to the 16th French Infantry Division. After the war, he rejoined the Meteorological Office but was compelled to resign on grounds of conscience when it was amalgamated into the Air Ministry in 1920. He subsequently pursued a career on the fringes of the academic world before retiring in 1940 to research his own ideas. His pacifism had direct consequences on his research interests. According to Thomas Körner the discovery that his meteorological work was of value to chemical weapons designers caused him to abandon all his efforts in this field, and destroy findings that he had yet to publish.

Richardson also applied his mathematical skills in the service of his pacifist principles, in particular in understanding the basis of international conflict. For this reason, he is now considered the initiator, or co-initiator of the scientific analysis of conflict—an interdisciplinary topic of quantitative and mathematical social science dedicated to systematic investigation of the causes of war and conditions of peace. As he had done with weather, he analyzed war using mainly differential equations and probability theory. Considering the armament of two nations, Richardson posited an idealized system of equations whereby the rate of a nation’s armament build-up is directly proportional to the amount of arms its rival has and also to the grievances felt toward the rival, and negatively proportional to the amount of arms it already has itself. Solution of this system of equations allows insightful conclusions to be made regarding the nature, and the stability or instability, of various hypothetical conditions which might be obtained between nations.

Bob Moses was an American educator and civil rights activist known for his work as a leader of the Student Nonviolent Coordinating Committee (SNCC) on voter education and registration in Mississippi during the Civil Rights Movement, and his co-founding of the Mississippi Freedom Democratic Party. As part of his work with the Council of Federated Organizations (COFO), a coalition of the Mississippi branches of the four major civil rights organizations (SNCC, CORE, NAACP, SCLC), he was the main organizer for the Freedom Summer Project.

Born and raised in Harlem, he was a graduate of Hamilton College and later earned a Master’s degree in philosophy at Harvard University. He spent the 1960s working in the civil rights and anti-war movements, until he was drafted in 1966 and left the country, spending much of the following decade in Tanzania, teaching and working with the Ministry of Education.

After returning to the US, in 1982, Moses received a MacArthur Fellowship and began developing the Algebra Project. The math literacy program emphasizes teaching algebra skills to minority students based on broad-based community organizing and collaboration with parents, teachers, and students, to improve college and job readiness.

Helene Stähelin was a Swiss mathematician, teacher, and peace activist. Helene Stähelin was born in the vicarage of Wintersingen Stähelin attended the Basel girls’ school and then studied mathematics at the Universities of Basel and Göttingen. Since there was a surplus of teachers in Basel at the time, in 1922 she accepted a position as a teacher of mathematics and natural sciences at the Daughters’ Institute in Ftan in Graubünden. In 1924 she received her doctorate from Hans Mohrmann and Otto Spiess in Basel. From 1934 to 1956 Stähelin was a secondary school teacher at the Protestant high school in Zug. After her retirement she returned to Basel and worked for several years as a colleague of Otto Spiess on the Bernoulli Edition.

As a pacifist, Stähelin was active in the International Women’s League for Peace and Freedom (IFFF) against scientific warfare. She chaired the Swiss section of the IFFF from 1948 to 1967. During Stähelin’s tenure, the UN, the atomic bomb and the Vietnam War were particularly important issues for the IFFF. Through her commitment, she attracted the attention of the authorities in the mid-1950s and was temporarily under state surveillance. Stähelin represented the League in the Swiss Peace Council. She campaigned for the introduction of women’s suffrage and suffrage.

Stähelin was a member of the Swiss Mathematical Society from 1926 until her death.

## Bastille Day

Bastille Day, which is a national holiday in France, is the anniversary of the Storming of the Bastille on July 14, 1789. It celebrates the actions of a mob of Frenchmen, tired of the rule of their king, who stormed a prison to get weapons and free prisoners. It marked the start of the French Revolution. The Revolution resulted in the Declaration of the Rights of Man and of the Citizen which served as a constitution and proclaimed the rights of French citizens.

Blaise Pascal was a French philosopher, physicist, inventor, writer, and mathematician who is known for his invention of the mechanical calculator.

Pascal also contributed greatly to other research areas such as probability theory, projective geometry, cycloid and the arithmetic triangle known as Pascal’s triangle.

Pascal’s development of probability theory was his most influential contribution to mathematics. Originally applied to gambling, today it is extremely important in economics, especially in actuarial science. John Ross writes, “Probability theory and the discoveries following it changed the way we regard uncertainty, risk, decision-making, and an individual’s and society’s ability to influence the course of future events.” However, Pascal and Fermat, though doing important early work in probability theory, did not develop the field very far. Christiaan Huygens, learning of the subject from the correspondence of Pascal and Fermat, wrote the first book on the subject. Later figures who continued the development of the theory include Abraham de Moivre and Pierre-Simon Laplace.

In 1654, prompted by his friend the Chevalier de Méré, he corresponded with Pierre de Fermat on the subject of gambling problems, and from that collaboration was born the mathematical theory of probabilities. The specific problem was that of two players who want to finish a game early and, given the current circumstances of the game, want to divide the stakes fairly, based on the chance each has of winning the game from that point. From this discussion, the notion of expected value was introduced. Pascal later (in the *Pensées*) used a probabilistic argument, Pascal’s wager, to justify belief in God and a virtuous life. The work done by Fermat and Pascal into the calculus of probabilities laid important groundwork for Leibniz’ formulation of the calculus.

Joseph Fourier was a pioneering French mathematician and physicist, famous for developing the Fourier Series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. Fourier is also famously known for discovering the greenhouse effect explaining how the Earth should ideally be much cooler than it is and the reason for this heat was incoming solar radiation.

Fourier left an unfinished work on determining and locating real roots of polynomials, which was edited by Claude-Louis Navier and published in 1831. This work contains much original matter—in particular, Fourier’s theorem on polynomial real roots, published in 1820. François Budan, in 1807 and 1811, had published independently his theorem (also known by the name of Fourier), which is very close to Fourier’s theorem (each theorem is a corollary of the other). Fourier’s proof^{ }is the one that was usually given, during the 19th century, in textbooks on the theory of equations. A complete solution of the problem was given in 1829 by Jacques Charles François Sturm.

## Juneteenth

**Juneteenth** is a holiday celebrating the emancipation of those who had been enslaved in the United States. Originating in Galveston, Texas, it is now celebrated annually on June 19 throughout the United States, with varying official recognition. It is commemorated on the anniversary date of the June 19, 1865 announcement by Union Army general Gordon Granger, proclaiming freedom from slavery in Texas.

Through much of the 1800s and even into the twentieth century, African-Americans were thought incapable of high intellectual achievement. In the United States, this is partly a result of slavery, which created a negative image of blacks in the public mind, a view that was reinforced by pseudoscientific findings that “proved” the inferiority of African-Americans. While there are many other reasons for these erroneous views, the truth is that African-Americans are as capable as members of any other race, a fact that is amply demonstrated by the success of the African-American mathematicians below.

Although best known as an African-American scientist, Benjamin Banneker was a multi-talented person who self-educated himself in astronomy and mathematics. He was also a writer, compiler of almanacs, surveyor and inventor. At the age of 24, Banneker observed a wrist-watch and used it to construct his own clock from wood which struck on the hour. He created puzzles for trigonometry which demonstrated his knowledge of logarithms. Banneker also attempted to find the exact lengths of an equilateral triangle which is inscribed within a circle where the diameter of the circle is known. He brought about a positive contribution in mathematics years before any black mathematician came to rise.

In August 19, 1791, Banneker wrote a letter to Thomas Jefferson, then Secretary of State, where he complains that although African Americans “have long been considered rather as brutish than human, and scarcely capable of mental endowments, . . . one universal Father hath given being to us all; and that he hath not only made us all of one flesh, but that he hath also, without partiality, afforded us all the same sensations and endowed us all with the same faculties.” In the letter Banneker also quotes from the first lines of the Declaration of Independence: “We hold these truths to be self-evident, that all men are created equal…”

Elbert Frank Cox was the first African-American ever to receive a PhD in Mathematics, which he earned in 1925 from Cornell University. In his 40 year-long teaching career, he taught at Howard University and West Virginia State College.

The National Association of Mathematicians established the Cox-Talbot Address in his honor, which is annually delivered at the NAM’s national meetings. The Elbert F. Cox Scholarship Fund, which is used to help black students pursue studies, is also named in his honor.

Evelyn Boyd Granville was the second African-American woman to receive a PhD in Mathematics from an American university which she earned in 1949 from Yale University. She graduated from Smith College in 1945 and performed pioneering work in the field of computing.

She took a position at California State University, Los Angeles in 1967 as a full professor of mathematics. After retiring from CSULA in 1984, she taught at Texas College for four years, and then in 1990 joined the faculty of the University of Texas at Tyler as the Sam A. Lindsey Professor of mathematics. There she developed elementary school math enrichment programs. Since 1967, Granville has remained a strong advocate for women’s education in tech.

## 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.

**Muhammad ibn Musa al-Khwarizmi**

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**

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**

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 **

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.