<P> Pure mathematics is mathematics that studies entirely abstract concepts . From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of navigation, astronomy, physics, economics, engineering, and other applications . </P> <P> Another insightful view put forth is that pure mathematics is not necessarily applied mathematics: it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world . Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians . </P> <P> To develop accurate models for describing the real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics . On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research . </P> <P> Many professional mathematicians also engage in the teaching of mathematics . Duties may include: </P>

What is the name of a mathematician who does research today
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