# National Braille Literacy Month

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

# 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. **