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- Galileo Galilei (1564-1642).
- Johannes Kepler (1571-1630.
- Rene Descartes (1596-1650).
- Pierre de Fermat (1601-1665).
- Isaac Newton (1642-1727).
- Gottfried Wilhelm Leibniz (1646-1716).
- Daniel Bernoulli (1700-1782).
- Euler (1707-1783).
- Adrien-Marie Legendre (1752-1833)
- Carl Friedrich Gauss (1777-1855).
- Bernhard Riemann (1826-1866).
- John von Neumann (1903-1957).
- Andrey Nikolaevich Kolmogorov (1903-1987).
- Alan Turing (1912-1954).
- Kurt Gödel (1906-1978).
- Maryam Mirzakhani.
- See: Mathematics Discipline.
- US, Bureau of Labor Statistics. (2008). Occupational Outlook Handbook, 2008-09 Edition
- Mathematics is one of the oldest and most fundamental sciences. Mathematicians use mathematical theory, computational techniques, algorithms, and the latest computer technology to solve economic, scientific, engineering, physics, and business problems. The work of mathematicians falls into two broad classes — theoretical (pure) mathematics and applied mathematics. These classes, however, are not sharply defined and often overlap.
- Theoretical mathematicians advance mathematical knowledge by developing new principles and recognizing previously unknown relationships between existing principles of mathematics. Although these workers seek to increase basic knowledge without necessarily considering its practical use, such pure and abstract knowledge has been instrumental in producing or furthering many scientific and engineering achievements. Many theoretical mathematicians are employed as university faculty, dividing their time between teaching and conducting research. (See the statement on teachers — postsecondary elsewhere in the Handbook.)
- Applied mathematicians, on the other hand, use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, engineering, and the physical, life, and social sciences. For example, they may analyze the most efficient way to schedule airline routes between cities, the effects and safety of new drugs, the aerodynamic characteristics of an experimental automobile, or the cost-effectiveness of alternative manufacturing processes.