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Mathematics

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Katherine Johnson

Katherine Coleman Goble Johnson is 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. manned spaceflights. During her 35-year career at NASA and its predecessor, she earned a reputation for mastering complex manual calculations and helped the space agency pioneer the use of computers to perform the tasks.

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Isaac Newton

Sir Isaac Newton was an English mathematician, astronomer, theologian, author and physicist who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made pathbreaking contributions to optics, and shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

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Alan Turing

Alan Mathison Turing was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. Turing is widely considered to be the father of theoretical computer science and artificial intelligence. Despite these accomplishments, he was never fully recognised in his home country during his lifetime due to his homosexuality, which was then a crime in the UK.

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Srinivasa Ramanujan

Srinivasa Ramanujan FRS was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable. Ramanujan initially developed his own mathematical research in isolation: "He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered". Seeking mathematicians who could better understand his work, in 1913 he began a postal partnership with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognizing the extraordinary work sent to him as samples, Hardy arranged travel for Ramanujan to Cambridge. In his notes, Ramanujan had produced groundbreaking new theorems, including some that Hardy stated had "defeated [him and his colleagues] completely", in addition to rediscovering recently proven but highly advanced results.

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Game theory

Game theory is the study of mathematical models of strategic interaction between rational decision-makers. It has applications in all fields of social science, as well as in logic and computer science. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

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Ada Lovelace

Augusta Ada King, Countess of 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 recognise that the machine had applications beyond pure calculation, and published the first algorithm intended to be carried out by such a machine. As a result, she is sometimes regarded as the first to recognise the full potential of a "computing machine" and the first computer programmer.

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John Forbes Nash Jr.

John Forbes Nash Jr. was an American mathematician who made fundamental contributions to game theory, differential geometry, and the study of partial differential equations. Nash's work has provided insight into the factors that govern chance and decision-making inside complex systems found in everyday life.

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René Descartes

René Descartes was a French philosopher, mathematician, and scientist. Dubbed the father of modern Western philosophy, much of subsequent Western philosophy is a response to his writings, which are studied closely to this day. A native of the Kingdom of France, he spent about 20 years (1629–49) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces. He is generally considered one of the most notable intellectual representatives of the Dutch Golden Age.

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Bertrand Russell

Bertrand Arthur William Russell, 3rd Earl Russell, was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate. At various points in his life, Russell considered himself a liberal, a socialist and a pacifist, but he also admitted that he had "never been any of these things, in any profound sense". Russell was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom.

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Dorothy Vaughan

Dorothy Johnson Vaughan was an African 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 of staff at the center.

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Mary Jackson (engineer)

Mary Winston Jackson was an African American mathematician and aerospace engineer at the National Advisory Committee for Aeronautics (NACA), which in 1958 was succeeded by the National Aeronautics and Space Administration (NASA). She worked at Langley Research Center in Hampton, Virginia, for most of her career. She started as a computer at the segregated West Area Computing division. She took advanced engineering classes and in 1958 became NASA's first black female engineer.

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Archimedes

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. Generally considered the greatest mathematician of antiquity and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals 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, and the area under a parabola.

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Calculus

Calculus, is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

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Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimensions of the matrix below are 2 × 3, because there are two rows and three columns:

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Gamma function

In mathematics, the gamma function is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers. If n is a positive integer,