International Peace Month
In honor of International Peace Month, we would like to recognize the accomplishments of a group of mathematicians who promoted peace.
Bertrand Russellwas a British polymath. As an academic, he worked in philosophy, mathematics, and logic. His work has had a considerable influence on mathematics, logic, set theory, linguistics, artificial intelligence, cognitive science, computer science, and various areas of analytic philosophy, especially philosophy of mathematics, philosophy of language, epistemology and metaphysics. He was a public intellectual, historian social critic, political activist, and Nobel laureate. He was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom.
Russell was a pacifist who championed anti-imperialism and chaired the India League. He occasionally advocated preventive nuclear war, before the opportunity provided by the atomic monopoly had passed and he decided he would “welcome with enthusiasm” world government. He went to prison for his pacifism during World War I. Later, Russell concluded that the war against Adolf Hitler‘s Nazi Germany was a necessary “lesser of two evils” and also criticized Stalinist totalitarianism, condemned the involvement of the United States in the Vietnam War and was an outspoken proponent of nuclear disarmament. In 1950, Russell was awarded the Nobel Prize in Literature “in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought“. He was also the recipient of the De Morgan Medal (1932), Sylvester Medal (1934), Kalinga Prize (1957), and Jerusalem Prize (1963).
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered to be the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including: the area of a circle; the surface area and volume of a sphere; area of an ellipse; the area under a parabola; the volume of a segment of a paraboloid of revolution; the volume of a segment of a hyperboloid of revolution; and the area of a spiral.
His other mathematical achievements include deriving an accurate approximation of pi; defining and investigating the spiral that now bears his name; and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics. Archimedes’ achievements in this area include an explanation of the principle of the lever, the widespread use of the concept of center of gravity, and the enunciation of the law of buoyancy. He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.
Archimedes died during the siege of Syracuse, where he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, which Archimedes had requested be placed on his tomb to represent his mathematical discoveries.
Benjamin Alvord was an American soldier, mathematician, and botanist. Alvord was born in Rutland, Vermont, where he developed an interest in nature. He attended the United States Military Academy and displayed a talent in mathematics.
Alvord was interested in the classical problem of Apollonius, to find a circle tangent to three given circles, and the special cases of Apollonius’ problem, as well as the generalization to spheres. In 1855 he published in Smithsonian Contributions to Knowledge.
Posted to the remote Fort Vancouver, he continued his investigations and submitted his findings in 1860 but was frustrated by a fire. In 1882, when he found that there are 96 circles which cut four given circles at a fixed angle and there are 640 spheres which cut five given spheres at a fixed angle, he assembled all his results for an article in American Journal of Mathematics.
He was assigned to the 4th U.S. Infantry and participated in the Seminole Wars. He returned to West Point as an assistant professor of mathematics until 1839, when he was again assigned to the 4th Infantry. He spent 21 years of his military career with that regiment.
He was on frontier, garrison, and engineer duty until 1846, when he participated in the military occupation of the new state of Texas. Subsequently, he served during the Mexican–American War, being brevetted successively to captain and major for gallantry in a number of important battles including the Battle of Palo Alto and the Battle of Resaca de la Palma. He served as chief of staff to Major Folliott T. Lally’s column on the march from Vera Cruz to Mexico City in 1847. After the war, he subsequently became paymaster of the District of Omaha and paymaster of the Department of the Platte. He became Paymaster General of the Army in 1872 and served in that capacity until his retirement from active service in 1880. He was promoted to brigadier general in 1876.
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.
In honor of Bastille Day, we would like to recognize the accomplishments of a group of French Mathematicians.
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and philosopher of science who was known as the inventor of topology and theory of functions of analytics. He is often described as a polymath, and in mathematics as “The Last Universalist” since he excelled in all fields of the discipline as it existed during his lifetime.
As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology. The Poincaré group used in physics and mathematics was named after him.
André Weil was a French mathematician known for his foundational work in number theory and algebraic geometry. He was a founding member and the de facto early leader of the mathematical Bourbaki group. He made significant contributions in the field of mathematics. His most important achievement was when he discovered a connection between number theory and algebraic geometry. Moreover, he developed a theory on algebraic curves based on his study of Diophantine equations. In the field of rational numbers, he introduced a topological ring known as the adele ring in algebraic number theory. Weil also laid the groundwork for classical theory of quadratic forms with his development of the Weil representation.
He remained professor at Institute for Advanced Studies at Princeton throughout his lifetime and was also an honorary member of American National Academy of Sciences, London Mathematical Society, the Royal Society of London and the French Academy of Sciences.
Alexander Grothendieck was a mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory and category theory to its foundations, while his so-called “relative” perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the 20th century.
Grothendieck began his productive and public career as a mathematician in 1949. In 1958, he was appointed a research professor at the Institut des hautes études scientifiques (IHÉS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding. He received his Fields Medal in 1966 for advances in algebraic geometry, homological algebra, and K-theory. He later became professor at the University of Montpellier and, while still producing relevant mathematical work, he withdrew from the mathematical community and devoted himself to political and religious pursuits (first Buddhism and later a more Christian vision). In 1991, he moved to the French village of Lasserre in the Pyrenees, where he lived in seclusion, still working tirelessly on mathematics until his death in 2014.
Jacques Salomon Hadamard was a French mathematician who made major contributions in number theory, complex analysis, differential geometry, and partial differential equations.
In Paris, Hadamard concentrated his interests on the problems of mathematical physics, in particular partial differential equations, the calculus of variations, and the foundations of functional analysis. He introduced the idea of well-posed problem and the method of descent in the theory of partial differential equations, culminating in his seminal book on the subject, based on lectures given at Yale University in 1922. Later in his life he wrote on probability theory and mathematical education.
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.
Sophie Germain thought that if the geometry method, which at that time referred to all of pure mathematics, could hold such fascination for Archimedes, it was a subject worthy of study. So she pored over every book on mathematics in her father’s library, even teaching herself Latin and Greek, so she could read works like those of Sir Isaac Newton and Leonhard Euler. She also enjoyed Traité d’Arithmétique by Étienne Bézout and Le Calcul Différentiel by Jacques Antoine-Joseph Cousin. Later, Cousin visited Germain at home, encouraging her in her studies.
Germain’s parents did not at all approve of her sudden fascination with mathematics, which was then thought inappropriate for a woman. When night came, they would deny her warm clothes and a fire for her bedroom to try to keep her from studying, but after they left, she would take out candles, wrap herself in quilts and do mathematics. After some time, her mother even secretly supported her.
Her work on Fermat’s 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. Before her death, Gauss had recommended that she be awarded an honorary degree, but that never occurred. On June 27, 1831, she died from breast cancer. At the centenary of her life, a street and a girls’ school were named after her. The Academy of Sciences established the Sophie Germain Prize in her honor.
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.
In honor of Juneteenth, we will celebrate prominent mathematicians who excelled during the slavery era this month.
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 1889 to 1890, taught mathematics at the M Street High School in Washington, D.C. Appointed professor of mathematics at Howard in 1890, Miller introduced sociology the development structure and functioning of human society into the curriculum in 1895, serving as professor of sociology from 1895 to 1934. Miller graduated from Howard University School of Law in 1903. In 1907, Miller was appointed dean of the College of Arts and Sciences.
He was a participant in the March 5, 1897 meeting to celebrate the memory of Frederick Douglass, which founded the American Negro Academy led by Alexander Crummell. Until the organization was discontinued in 1928, Miller remained one of the most active members of this first major African American learned society, refuting racist scholarship, promoting black claims to individual, social, and political equality, and publishing early histories and sociological studies of African American life.
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. An excellent student in mathematics, Reason became an instructor in 1832 at the school at age fourteen receiving a salary of $25 a year.
Reason aided in drafting a call to the first New York State Convention of Negroes in 1840 and advocated in New York City a manual-labor school to provide training in the industrial arts. He created a normal teaching school as a remedy to the charge that black teachers were inefficient and incompetent. He decided to pursue a career in teaching, believing strongly that education was the best means for black advancement. 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.”
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]. The Institute was a Quaker institution that had earned a reputation for high academic standards since its founding in 1837.
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.
Shiing-Shen Chern was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the “father of modern differential geometry” and is widely regarded as a leader in geometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including the Wolf Prize and the inaugural Shaw Prize. In memory of Shiing-Shen Chern, the International Mathematical Union established the Chern Medal in 2010 to recognize “an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics.”
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.
Kunihiko Kodaira was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds, and was the founder of the Japanese school of algebraic geometers. He was awarded a Fields Medal in 1954, being the first Japanese national to receive this honor.
Shigefumi Mori is a Japanese mathematician, known for his work in algebraic geometry, particularly in relation to the classification of three-folds. He generalized the classical approach to the classification of algebraic surfaces to the classification of algebraic three-folds. The classical approach used the concept of minimal models of algebraic surfaces. He found that the concept of minimal models can be applied to three-folds as well if we allow some singularities on them. The extension of Mori’s results to dimensions higher than three is called the minimal model program and is an active area of research in algebraic geometry. He has been elected president of the International Mathematical Union, becoming the first head of the group from East Asia.
Fan-Rong King Chung Graham known professionally as Fan Chung, is a Taiwanese-born American mathematician who works mainly in the areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős–Rényi model for graphs with general degree distribution (including power-law graphs in the study of large information networks). Under the influence of her father, an engineer, she became interested in mathematics, especially in the area of combinatorics in high school in Kaohsiung. After high school, Chung entered the National Taiwan University (NTU) to start her career in mathematics formally. While Chung was an undergraduate, she was surrounded by many female mathematicians, and this helped encourage her to pursue and study mathematics.
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.
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.
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
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.
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.
Nicholas Saundersonwas a blindEnglish 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
Lee Lorch Lee Lorch was an Americanmathematician, 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.
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, born in Riga, who created the theory of pseudoanalytic 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 founded the Committee on Human Rights of the National Academy of Sciences, and beginning in the 1970’s 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
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 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 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.
Ruy Luís Gomes – Brilliant Portuguese mathematician who is known as one of the leading intellectuals of the 20th century.
Pedro Nunes – Portuguese mathematician who is considered to be one of the most skilled and creative mathematicians of his time.
Victor Neumann-Lara – Mexican mathematician who was a pioneer in the field of graph theory.
Júlio César de Mello e Souza – Brazilian writer, educator, and mathematics professor known for his entertaining books explaining mathematics.
Ruth Gonzalez – First US-born Hispanic woman to earn a doctorate in mathematics.