# Arab American Heritage Month

In honor of Arab American Heritage Month, we would like to recognize the accomplishments of a group of Arabic 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.

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, which have since been cited by many other mathematicians. Her skills and intelligence were so admired that she was cited by historians Ibn al-Jawzi, Ibn al-Khatib Baghdadi, and Ibn Kathir.

Zaha Hadid was born in Baghdad, Iraq, Hadid studied mathematics as an undergraduate and then enrolled at the Architectural Association School of Architecture in 1972. She was the first woman to receive the Pritzker Architecture Prize. She also received the Stirling Prize in 2010 and in 2011. Her buildings are described as distinctively neofuturistic, characterized by the “powerful, curving forms of her elongated structures” with “multiple perspective points and fragmented geometry to evoke the chaos of modern life.” Zaha was named an honorary member of the American Academy of Arts and Letters and an honorary fellow of the American Institute of Architects. She has been on the board of trustees of The Architecture Foundation.

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**Abu Kamil Shuja’ ibn Aslam was 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.

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Abdul Jabbar Hassoon Jerri is a contemporary Iraqi American mathematician. One of his most prominent contributions was Shannon Sampling Theory. More than thirty top international experts edited the Generalizations, Error Analysis, and Historical Reviews, and particularly his findings mentioned in The Journal Sampling Theory in Signal and Image Processing. He also contributed to the general understanding of the Gibbs Phenomenon, which was the first book ever on the subject.

Roshidi is a mathematician, philosopher, and historian of science whose work focuses largely on mathematics and physics of the medieval Arab world. 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.

# Women's History Month

Creola Katherine Johnson was an African 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. During her 35-year career at NASA and its predecessor, she earned a reputation for mastering complex manual calculations and helped pioneer the use of computers to perform the tasks. The space agency noted her “historical role as one of the first African-American women to work as a NASA scientist.”

Johnson’s work included calculating trajectories, launch windows, and emergency return paths for Project Mercury spaceflights, including those for astronauts Alan Shepard, the first American in space, and John Glenn, the first American in orbit, and rendezvous paths for the Apollo Lunar Module and command module on flights to the Moon. Her calculations were also essential to the beginning of the Space Shuttle program, and she worked on plans for a mission to Mars.

Dorothy Vaughan was an American mathematician and human computer who worked for the National Advisory Committee for Aeronautics (NACA), and NASA, at Langley Research Center in Hampton, Virginia. In 1949, she became acting supervisor of the West Area Computers, the first African-American woman to supervise a group composed entirely of African-American women mathematicians including Katherine Johnson.

She later was promoted officially to the position. During her 28-year career, Vaughan prepared for the introduction of machine computers in the early 1960s by teaching herself and her staff the programming language of Fortran. She later headed the programming section of the Analysis and Computation Division (ACD) at Langley. Vaughan is one of the women featured in Margot Lee Shetterly‘s history *Hidden Figures: The Story of the African-American Women Who Helped Win the Space Race* (2016). It was adapted as a biographical film of the same name, also released in 2016.

Ada Lovelace was an English mathematician and writer, chiefly known for her work on Charles Babbage‘s proposed mechanical general-purpose computer, the Analytical Engine. She was the first to recognize that the machine had applications beyond pure calculation, and to have published the first algorithm intended to be carried out by such a machine. As a result, she is often regarded as one of the first computer programmers.

Lovelace’s notes are important in the early history of computers, containing what many consider to be the first computer program—that is, an algorithm designed to be carried out by a machine. She also developed a vision of the capability of computers to go beyond mere calculating or number-crunching, while many others, including Babbage himself, focused only on those capabilities. Her mindset of “poetical science” led her to ask questions about the Analytical Engine (as shown in her notes) examining how individuals and society relate to technology as a collaborative tool.

Sofya Kovalevskaya was a Russian mathematician who made noteworthy contributions to analysis, partial differential equations and mechanics. She was a pioneer for women in mathematics around the world – the first woman to obtain a doctorate (in the modern sense) in mathematics, the first woman appointed to a full professorship in northern Europe and one of the first women to work for a scientific journal as an editor. According to historian of science Ann Hibner Koblitz, Kovalevskaia was “the greatest known woman scientist before the twentieth century.”

Kovalevskaya’s mathematical results, such as the Cauchy–Kowalevski theorem, and her pioneering role as a female mathematician in an almost exclusively male-dominated field, have made her the subject of several books, including a biography by Ann Hibner Koblitz, a biography in Russian by Polubarinova-Kochina (translated into English by M. Burov with the title *Love and Mathematics: Sofya Kovalevskaya*, Mir Publishers, 1985), and a book about her mathematics by R. Cooke.

Marjorie Browne was a mathematics educator. She was one of the first African-American women to receive a Ph.D in mathematics. Not only did she chair the Mathematics Department at North Carolina College but also responsible for setting up the first electronic digital computer center at a minority college in 1960. Browne taught undergraduate and graduate level math and published four sets of lecture notes during that time for other teachers to use.

Furthermore, in the 1950s, Browne won a Ford Foundation grant to Cambridge University and other grants to University of California and Columbia University thus allowing her to travel vastly for her field of study as well. Since 1999, the Mathematics Department at the University of Michigan has hosted the Marjorie Lee Browne Colloquium, which annually brings a speaker “to present a talk that highlights their research but also addresses the issue of diversity in the sciences.”

Emmy Noether was a German mathematician who made many important contributions to abstract algebra. She discovered Noether’s theorem, which is fundamental in mathematical physics. She invariably used the name “Emmy Noether” in her life and publications. She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener as the most important woman in the history of mathematics. As one of the leading mathematicians of her time, she developed some theories of rings, fields, and algebras. In physics, Noether’s theorem explains the connection between symmetry and conservation laws.

Noether’s mathematical work has been divided into three “epochs.” In the first (1908–1919), she made contributions to the theories of algebraic invariants and number fields. Her work on differential invariants in the calculus of variations, Noether’s theorem, has been called “one of the most important mathematical theorems ever proved in guiding the development of modern physics.” In the second epoch (1920–1926), she began work that “changed the face of [abstract] algebra.” In her classic 1921 paper *Idealtheorie in Ringbereichen* (*Theory of Ideals in Ring Domains*), Noether developed the theory of ideals in commutative rings into a tool with wide-ranging applications. In the third epoch (1927–1935), she published works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals. In addition to her own publications, Noether was generous with her ideas and is credited with several lines of research published by other mathematicians, even in fields far removed from her main work, such as algebraic topology.

# Black History Month

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.

Dudley Woodard is remembered as the second African-American to achieve a PhD degree in Mathematics from Penn. Woodard had more achievements than any of his predecessors. He managed to publish his masters’ level thesis, ‘Loci Connected with the Problem of Two Bodies’ and taught college-level math for 20 years. He was also the dean at Howard – the most prestigious university for black Americans at the time. At Howard, Woodard established a graduate program in mathematics and furthered it by establishing a mathematics library, sponsored professorships and seminars – in short, Woodard advanced the mathematics faculty steadily in only quarter of a century. He is distinguished as one of the greatest Black Mathematicians of all time.

Although she is remembered as the first black American woman with a Ph.D in mathematics in 1943, this was only a stepping stone in Martha Haynes’ extraordinary and highly influential career. 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.

Perhaps one of the greatest African-American mathematicians, David Blackwell was an American statistician and mathematician who made significant contributions to game theory, probability theory, information theory, and Bayesian statistics. He is part eponymous of the Rao-Blackwell Theorem, first black inductee (and only) into the National Academy of Sciences and first tenured member of faculty at the University of California, Berkeley. Blackwell has also been the President of the American Statistical Society and Vice President of America Mathematics Society.

# National Braille Literacy Month

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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).

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.

Amongst his many discoveries and developments, Euler is credited for introducing the Greek letter pi to denominate the Archimedes constant (the ratio of a circle’s circumference to its diameter), and for developing a new mathematical constant, the “e” (also known as Euler’s Number), which is equivalent to a logarithm’s natural base, and has several applications such as to calculate compound interest.

A statement attributed to Pierre-Simon Laplace expresses Euler’s influence on mathematics: “Read Euler, read Euler, he is the master of us all.”

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.

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Bernard Morin** **was 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.

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Nicholas Saunderson** **was a blind^{ }English scientist and mathematician. According to one historian of statistics, he may have been the earliest discoverer of Bayes theorem.^{ } He worked as Lucasian Professor of Mathematics at Cambridge University, a post also held by Isaac Newton, Charles Babbage and Stephen Hawking.

His importance was as a charismatic and skilled teacher at exactly the time when mathematics started to become important at University of Cambridge. Part of Saunderson’s role as the Lucasian professor was to disseminate the *Principia Mathematica* so that it was accessible to undergraduates and college tutors. Ultimately through his teaching during his term in office, he reformed the decaying, traditional curriculum of Cambridge to emphasize mathematics and Newtonian natural philosophy, defending it from opponents. He provided the first systematic introduction to Differential calculus, detailed in his posthumous work *The Method of Fluxions Applied to a Select Number of Useful Problems*.

Saunderson did not follow the common practice of publishing his work; however, manuscripts of his lectures and treatises were in circulation and were used by a number of notable individuals including the astronomers James Bradley at Oxford University, Samuel Vince at Cambridge University and John Harrison for self-education prior to designing the marine chronometer. After he died, his work *The Elements of Algebra in Ten Books* was published in his name.

The discovery of Bayes’ theorem remains a controversial topic in the history of mathematics. While it is certain to have been discovered before Thomas Bayes‘ time, there are several contenders for priority including Saunderson. At the time, much of mathematics research was performed through the exchange of private letters, and through verbal discussions, rather than publications. Historian of statistics Stephen Stigler concluded that Saunderson was the most probable discoverer after attempting to trace some of these letters and discussions but has been challenged by other statisticians. Somewhat fittingly for a question about probability, it seems likely that the question will never be resolved completely but will remain as a probabilistic belief about Saunderson and others.

# Human Rights Month

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 he developed in 1982 and currently runs in an 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.

Lipman “Lipa” Bers was a Latvian-American mathematician

# Native American Heritage Month

**Freda Porter **

Freda Porter is president and CEO of Porter Scientific Inc., a company that provides environmental consulting, industrial water and wastewater treatment services. She earned her B.S. in Applied Mathematics from University of North Carolina Pembroke, her M.S. from North Carolina State University, and her Ph.D. from Duke University in Applied Mathematics. She is a member of the Lumbee tribe and is now the Tribal Administrator. She was awarded the 2010 Stellar Award by US Women’s Chamber of Commerce, 2009 NC Minority Business Person of the Year, the 2007 UIDA American Indian Business of the Year and UNCP Business Person of the Year. Porter has been honored by the North Carolina Equity Commission with the CARPATHIAN Award for Speaking Out and was featured in a PBS documentary entitled BREAKTHROUGH: The Changing Face of Science in America.

**Mary G. Ross**

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 Megginson**

Robert Megginson is a mathematician of Oglala Lakota (also known as Oglala Sioux) heritage. He obtained a B.S. in Physics from University of Illinois at Urbana-Champaign and went on to work as a programmer for years. While working, he realized that his true passion was mathematics and went back to school to get an M.S. in Statistics and a Ph.D. in Mathematics. Robert has talked about how his cultural background has affected his worldview; his dislike of the Native American sports mascot at Illinois, Chief Illiniwek, and his interactions with professors are examples of this. He is concerned with the problem of underrepresentation of minorities in mathematics and works directly with Native American middle and high school students on the Turtle Mountain Chippewa (Ojibwa) reservation in North Dakota.

**Thomas Storer**

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.

# Hispanic Heritage Month

In an effort to celebrate Hispanic Heritage Month that runs from September 15th – October 15th, we would like to recognize the accomplishments of a group of Hispanic and Latinx Mathematicians.

**Alberto Pedro Calderón – Argentinian mathematician widely considered one of the 20th century’s most important mathematicians.**

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**Ruy Luís Gomes – Brilliant Portuguese mathematician who is known as one of the leading intellectuals of the 20th century.**

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**Pedro Nunes – Portuguese mathematician who is considered to be one of the most skilled and creative mathematicians of his time.**

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**Victor Neumann-Lara – Mexican mathematician who was a pioneer in the field of graph theory.**

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**Júlio César de Mello e Souza – Brazilian writer, educator, and mathematics professor known for his entertaining books explaining mathematics.**

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**Ruth Gonzalez – First US-born Hispanic woman to earn a doctorate in mathematics. **