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High Quality Content by WIKIPEDIA articles! In mathematics, the notion of infinitely near points was initially part of the intuitive foundations of differential calculus. In the simplest terms, two points which lie at an infinitesimal distance apart are considered infinitely near.In more geometric terms, a notion of infinitely near point is a necessary tool of birational geometry, as soon as algebraic surfaces are considered, and was introduced in the nineteenth century. When blowing up is applied to a point P on a surface S, the new surface S contains a whole curve C where P used to be. The points of C have the geometric interpretation as the tangent directions at P to S. They can be called infinitely near to P as way of visualizing them on S, rather than S .