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Although mathematics may be considered a "pure" science—that is, one that may be studied for its own sake—math has often been applied to produce engineering and other scientific achievements. The non-Euclidean geometry developed by Bernhard Riemann in 1854 seemed quite impractical at the time, yet some years later Albert Einstein used it as part of his work in the development of his theory of relativity. Einstein's theory similarly appeared to have no practical application at the time but later became the basis for work in nuclear energy.

Mathematics is a discipline used in the study of all sciences. In addition to contributing to the development of nuclear energy, mathematicians played important roles in the 20th century in the development of the automobile, the television, and space exploration. They have been instrumental in advancing research and experimental efforts in sociology, psychology, and education, among other fields. The development of spacecraft and computer technology are but two examples that characterize the dynamic nature and increasing importance of mathematicians now in the 21st century. Mathematicians, although working in one of the oldest and most basic of sciences, are always contributing new ideas.

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