Who are some eminent mathematicians?

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Many of the most eminent mathematicians lived in the ancient past.  First among mathematicians is Euclid.  Beyond lending his name to Euclidean geometry, in his greatest work, the Elements, he provides the geometrical axioms that are the foundation of geometrical proofs.  Like Euclid, Archimedes also made a great contribution to the study of mathematics.  Much of his work was done in the application of mathematical principles, rather than studying mathematics on a purely theoretical level.  In the early modern period, particularly the period known as the Scientific Revolution, Galileo and Sir Isaac Newton stand above many of their contemporaries in terms of their mathematical prowess.  Like Archimedes before them, Galileo and Newton applied mathematical principles in their work; both developed their physical theories using mathematical principles.  Sir Isaac Newton, with Leibniz, is credited as the co-inventor of the calculus; Newton developed the calculus as a means of further exploring the implications of his ideas in physics.  In the nineteenth and twentieth centuries, Henri Poincare, Charles Babbage, Alan M. Turing (known for his impressive calculating machine - the Turing machine) and Kurt F. Goedel are among the most skilled mathematicians.  As in the early modern period, many mathematicians of the past two centuries applied their skills in relation to physics and the advancement of computers.

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