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A mathematician is a person whose primary area study is the field of mathematics. Mathematicians are concerned with logic, space, transformations, numbers and more general ideas which encompass these concepts. Some notable mathematicians include Archimedes of Syracuse, Leonhard Paul Euler, Johann Carl Friedrich Gauss, Johann Bernoulli, Jacob Bernoulli, Muhammad ibn Mūsā al-Khwārizmī, Georg Friedrich Bernhard Riemann, Gottfried Leibniz, Euclid of Alexandria, Jules Henri Poincaré, Srinivasa Ramanujan, Alexander Grothendieck, David Hilbert, Joseph-Louis Lagrange, Georg Cantor, Évariste Galois, and Pierre de Fermat.

Some scientists who research other fields are also considered mathematicians if their research provides insights into mathematics—one notable example is Isaac Newton. Conversely, some mathematicians may provide insights into other fields of research—these people are known as applied mathematicians.



Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation. There are notable cases where mathematicians have failed to reflect their ability in their university education, but have nevertheless become remarkable mathematicians. Fermat, for example, is known for having been "Prince of Amateurs", because of his extraordinary achievements with little formal mathematics training.[1]

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